Properties

Label 882.2.bc.a.551.39
Level $882$
Weight $2$
Character 882.551
Analytic conductor $7.043$
Analytic rank $0$
Dimension $672$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(47,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([7, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.bc (of order \(42\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(672\)
Relative dimension: \(56\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 551.39
Character \(\chi\) \(=\) 882.551
Dual form 882.2.bc.a.437.39

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.997204 - 0.0747301i) q^{2} +(-0.688101 - 1.58950i) q^{3} +(0.988831 - 0.149042i) q^{4} +(-0.0503270 - 0.220497i) q^{5} +(-0.804961 - 1.53364i) q^{6} +(-2.35502 - 1.20577i) q^{7} +(0.974928 - 0.222521i) q^{8} +(-2.05303 + 2.18748i) q^{9} +O(q^{10})\) \(q+(0.997204 - 0.0747301i) q^{2} +(-0.688101 - 1.58950i) q^{3} +(0.988831 - 0.149042i) q^{4} +(-0.0503270 - 0.220497i) q^{5} +(-0.804961 - 1.53364i) q^{6} +(-2.35502 - 1.20577i) q^{7} +(0.974928 - 0.222521i) q^{8} +(-2.05303 + 2.18748i) q^{9} +(-0.0666640 - 0.216119i) q^{10} +(-1.68290 + 3.49457i) q^{11} +(-0.917319 - 1.46919i) q^{12} +(-6.24929 + 0.468320i) q^{13} +(-2.43854 - 1.02641i) q^{14} +(-0.315850 + 0.231719i) q^{15} +(0.955573 - 0.294755i) q^{16} +(-3.98883 - 0.601220i) q^{17} +(-1.88382 + 2.33478i) q^{18} +(-1.66969 - 0.963996i) q^{19} +(-0.0826282 - 0.210533i) q^{20} +(-0.296085 + 4.57300i) q^{21} +(-1.41704 + 3.61056i) q^{22} +(-0.659725 + 0.526113i) q^{23} +(-1.02455 - 1.39653i) q^{24} +(4.45876 - 2.14722i) q^{25} +(-6.19682 + 0.934020i) q^{26} +(4.88969 + 1.75810i) q^{27} +(-2.50843 - 0.841307i) q^{28} +(5.53116 - 2.17082i) q^{29} +(-0.297651 + 0.254675i) q^{30} +(-1.65442 - 0.955180i) q^{31} +(0.930874 - 0.365341i) q^{32} +(6.71263 + 0.270349i) q^{33} +(-4.02261 - 0.301453i) q^{34} +(-0.147348 + 0.579957i) q^{35} +(-1.70408 + 2.46903i) q^{36} +(1.25255 + 3.19144i) q^{37} +(-1.73706 - 0.836524i) q^{38} +(5.04454 + 9.61101i) q^{39} +(-0.0981304 - 0.203770i) q^{40} +(-3.04136 + 2.82197i) q^{41} +(0.0464838 + 4.58234i) q^{42} +(-7.87560 - 7.30749i) q^{43} +(-1.14326 + 3.70636i) q^{44} +(0.585655 + 0.342599i) q^{45} +(-0.618564 + 0.573944i) q^{46} +(-0.698227 - 9.31719i) q^{47} +(-1.12604 - 1.31606i) q^{48} +(4.09223 + 5.67923i) q^{49} +(4.28583 - 2.47442i) q^{50} +(1.78908 + 6.75396i) q^{51} +(-6.10969 + 1.39450i) q^{52} +(-7.70061 - 3.02227i) q^{53} +(5.00740 + 1.38777i) q^{54} +(0.855238 + 0.195202i) q^{55} +(-2.56428 - 0.651499i) q^{56} +(-0.383358 + 3.31730i) q^{57} +(5.35347 - 2.57809i) q^{58} +(-0.170049 - 0.157782i) q^{59} +(-0.277787 + 0.276206i) q^{60} +(-1.14498 + 7.59647i) q^{61} +(-1.72117 - 0.828874i) q^{62} +(7.47253 - 2.67606i) q^{63} +(0.900969 - 0.433884i) q^{64} +(0.417771 + 1.35438i) q^{65} +(6.71407 - 0.232042i) q^{66} +(-4.98171 + 8.62857i) q^{67} -4.03389 q^{68} +(1.29022 + 0.686616i) q^{69} +(-0.103596 + 0.589347i) q^{70} +(6.51096 - 5.19232i) q^{71} +(-1.51480 + 2.58947i) q^{72} +(-4.49258 + 6.58941i) q^{73} +(1.48754 + 3.08892i) q^{74} +(-6.48109 - 5.60970i) q^{75} +(-1.79472 - 0.704374i) q^{76} +(8.17691 - 6.20060i) q^{77} +(5.74866 + 9.20716i) q^{78} +(-7.01322 - 12.1472i) q^{79} +(-0.113084 - 0.195867i) q^{80} +(-0.570106 - 8.98193i) q^{81} +(-2.82197 + 3.04136i) q^{82} +(0.956792 - 12.7675i) q^{83} +(0.388792 + 4.56605i) q^{84} +(0.0681788 + 0.909783i) q^{85} +(-8.39966 - 6.69851i) q^{86} +(-7.25652 - 7.29805i) q^{87} +(-0.863088 + 3.78144i) q^{88} +(0.0644591 - 0.860147i) q^{89} +(0.609620 + 0.297875i) q^{90} +(15.2819 + 6.43231i) q^{91} +(-0.573944 + 0.618564i) q^{92} +(-0.379852 + 3.28697i) q^{93} +(-1.39255 - 9.23895i) q^{94} +(-0.128528 + 0.416676i) q^{95} +(-1.22125 - 1.22823i) q^{96} +(-9.00570 - 5.19945i) q^{97} +(4.50520 + 5.35754i) q^{98} +(-4.18925 - 10.8558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 672 q - 56 q^{4} + 14 q^{6} - 2 q^{7} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 672 q - 56 q^{4} + 14 q^{6} - 2 q^{7} - 26 q^{9} + 6 q^{13} + 6 q^{14} + 6 q^{15} + 56 q^{16} - 18 q^{17} - 4 q^{18} + 18 q^{21} + 126 q^{23} + 6 q^{24} - 112 q^{25} + 12 q^{26} - 6 q^{27} + 2 q^{28} + 36 q^{29} + 10 q^{30} - 6 q^{31} - 18 q^{33} + 30 q^{35} - 10 q^{36} - 26 q^{37} + 22 q^{39} - 6 q^{41} + 110 q^{42} + 2 q^{43} - 26 q^{45} + 78 q^{46} + 18 q^{47} - 10 q^{49} + 24 q^{50} - 12 q^{51} + 14 q^{52} - 12 q^{53} - 18 q^{54} - 42 q^{55} - 28 q^{57} - 30 q^{58} - 30 q^{59} - 6 q^{60} - 136 q^{61} + 36 q^{62} - 42 q^{63} + 112 q^{64} - 42 q^{65} - 48 q^{66} - 14 q^{67} - 36 q^{68} - 70 q^{69} - 126 q^{71} + 4 q^{72} + 54 q^{75} + 18 q^{77} - 8 q^{78} + 4 q^{79} + 26 q^{81} - 66 q^{84} + 104 q^{87} + 186 q^{89} + 60 q^{90} + 12 q^{91} - 18 q^{92} + 22 q^{93} + 18 q^{95} + 6 q^{96} + 6 q^{97} - 24 q^{98} + 194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.997204 0.0747301i 0.705130 0.0528422i
\(3\) −0.688101 1.58950i −0.397275 0.917699i
\(4\) 0.988831 0.149042i 0.494415 0.0745211i
\(5\) −0.0503270 0.220497i −0.0225069 0.0986092i 0.962427 0.271541i \(-0.0875332\pi\)
−0.984934 + 0.172932i \(0.944676\pi\)
\(6\) −0.804961 1.53364i −0.328624 0.626104i
\(7\) −2.35502 1.20577i −0.890114 0.455739i
\(8\) 0.974928 0.222521i 0.344689 0.0786730i
\(9\) −2.05303 + 2.18748i −0.684345 + 0.729159i
\(10\) −0.0666640 0.216119i −0.0210810 0.0683430i
\(11\) −1.68290 + 3.49457i −0.507413 + 1.05365i 0.477183 + 0.878804i \(0.341658\pi\)
−0.984595 + 0.174849i \(0.944056\pi\)
\(12\) −0.917319 1.46919i −0.264807 0.424119i
\(13\) −6.24929 + 0.468320i −1.73324 + 0.129888i −0.903591 0.428396i \(-0.859079\pi\)
−0.829650 + 0.558284i \(0.811460\pi\)
\(14\) −2.43854 1.02641i −0.651728 0.274319i
\(15\) −0.315850 + 0.231719i −0.0815522 + 0.0598296i
\(16\) 0.955573 0.294755i 0.238893 0.0736888i
\(17\) −3.98883 0.601220i −0.967434 0.145817i −0.353725 0.935349i \(-0.615085\pi\)
−0.613709 + 0.789532i \(0.710323\pi\)
\(18\) −1.88382 + 2.33478i −0.444021 + 0.550314i
\(19\) −1.66969 0.963996i −0.383053 0.221156i 0.296093 0.955159i \(-0.404316\pi\)
−0.679146 + 0.734003i \(0.737650\pi\)
\(20\) −0.0826282 0.210533i −0.0184762 0.0470767i
\(21\) −0.296085 + 4.57300i −0.0646110 + 0.997911i
\(22\) −1.41704 + 3.61056i −0.302114 + 0.769775i
\(23\) −0.659725 + 0.526113i −0.137562 + 0.109702i −0.689853 0.723949i \(-0.742325\pi\)
0.552291 + 0.833651i \(0.313754\pi\)
\(24\) −1.02455 1.39653i −0.209135 0.285066i
\(25\) 4.45876 2.14722i 0.891752 0.429445i
\(26\) −6.19682 + 0.934020i −1.21530 + 0.183176i
\(27\) 4.88969 + 1.75810i 0.941022 + 0.338346i
\(28\) −2.50843 0.841307i −0.474048 0.158992i
\(29\) 5.53116 2.17082i 1.02711 0.403111i 0.208843 0.977949i \(-0.433030\pi\)
0.818267 + 0.574838i \(0.194935\pi\)
\(30\) −0.297651 + 0.254675i −0.0543433 + 0.0464970i
\(31\) −1.65442 0.955180i −0.297143 0.171555i 0.344016 0.938964i \(-0.388213\pi\)
−0.641159 + 0.767408i \(0.721546\pi\)
\(32\) 0.930874 0.365341i 0.164557 0.0645838i
\(33\) 6.71263 + 0.270349i 1.16852 + 0.0470618i
\(34\) −4.02261 0.301453i −0.689872 0.0516987i
\(35\) −0.147348 + 0.579957i −0.0249063 + 0.0980307i
\(36\) −1.70408 + 2.46903i −0.284013 + 0.411505i
\(37\) 1.25255 + 3.19144i 0.205918 + 0.524670i 0.996103 0.0881983i \(-0.0281109\pi\)
−0.790185 + 0.612868i \(0.790016\pi\)
\(38\) −1.73706 0.836524i −0.281788 0.135702i
\(39\) 5.04454 + 9.61101i 0.807773 + 1.53899i
\(40\) −0.0981304 0.203770i −0.0155158 0.0322188i
\(41\) −3.04136 + 2.82197i −0.474980 + 0.440717i −0.880978 0.473157i \(-0.843114\pi\)
0.405998 + 0.913874i \(0.366924\pi\)
\(42\) 0.0464838 + 4.58234i 0.00717260 + 0.707070i
\(43\) −7.87560 7.30749i −1.20102 1.11438i −0.990603 0.136769i \(-0.956328\pi\)
−0.210414 0.977612i \(-0.567481\pi\)
\(44\) −1.14326 + 3.70636i −0.172353 + 0.558755i
\(45\) 0.585655 + 0.342599i 0.0873043 + 0.0510716i
\(46\) −0.618564 + 0.573944i −0.0912023 + 0.0846234i
\(47\) −0.698227 9.31719i −0.101847 1.35905i −0.780759 0.624832i \(-0.785167\pi\)
0.678912 0.734219i \(-0.262452\pi\)
\(48\) −1.12604 1.31606i −0.162531 0.189957i
\(49\) 4.09223 + 5.67923i 0.584604 + 0.811319i
\(50\) 4.28583 2.47442i 0.606108 0.349936i
\(51\) 1.78908 + 6.75396i 0.250521 + 0.945743i
\(52\) −6.10969 + 1.39450i −0.847262 + 0.193382i
\(53\) −7.70061 3.02227i −1.05776 0.415140i −0.228233 0.973607i \(-0.573295\pi\)
−0.829527 + 0.558466i \(0.811390\pi\)
\(54\) 5.00740 + 1.38777i 0.681421 + 0.188852i
\(55\) 0.855238 + 0.195202i 0.115320 + 0.0263211i
\(56\) −2.56428 0.651499i −0.342667 0.0870602i
\(57\) −0.383358 + 3.31730i −0.0507770 + 0.439387i
\(58\) 5.35347 2.57809i 0.702945 0.338520i
\(59\) −0.170049 0.157782i −0.0221385 0.0205415i 0.669026 0.743239i \(-0.266711\pi\)
−0.691164 + 0.722698i \(0.742902\pi\)
\(60\) −0.277787 + 0.276206i −0.0358621 + 0.0356580i
\(61\) −1.14498 + 7.59647i −0.146600 + 0.972628i 0.787679 + 0.616086i \(0.211283\pi\)
−0.934279 + 0.356542i \(0.883956\pi\)
\(62\) −1.72117 0.828874i −0.218589 0.105267i
\(63\) 7.47253 2.67606i 0.941450 0.337152i
\(64\) 0.900969 0.433884i 0.112621 0.0542355i
\(65\) 0.417771 + 1.35438i 0.0518181 + 0.167990i
\(66\) 6.71407 0.232042i 0.826445 0.0285624i
\(67\) −4.98171 + 8.62857i −0.608612 + 1.05415i 0.382857 + 0.923808i \(0.374940\pi\)
−0.991469 + 0.130340i \(0.958393\pi\)
\(68\) −4.03389 −0.489181
\(69\) 1.29022 + 0.686616i 0.155324 + 0.0826588i
\(70\) −0.103596 + 0.589347i −0.0123820 + 0.0704404i
\(71\) 6.51096 5.19232i 0.772709 0.616215i −0.155687 0.987806i \(-0.549759\pi\)
0.928396 + 0.371592i \(0.121188\pi\)
\(72\) −1.51480 + 2.58947i −0.178521 + 0.305173i
\(73\) −4.49258 + 6.58941i −0.525817 + 0.771232i −0.993642 0.112589i \(-0.964086\pi\)
0.467824 + 0.883821i \(0.345038\pi\)
\(74\) 1.48754 + 3.08892i 0.172923 + 0.359079i
\(75\) −6.48109 5.60970i −0.748372 0.647752i
\(76\) −1.79472 0.704374i −0.205868 0.0807973i
\(77\) 8.17691 6.20060i 0.931846 0.706623i
\(78\) 5.74866 + 9.20716i 0.650908 + 1.04251i
\(79\) −7.01322 12.1472i −0.789049 1.36667i −0.926550 0.376171i \(-0.877241\pi\)
0.137502 0.990502i \(-0.456093\pi\)
\(80\) −0.113084 0.195867i −0.0126431 0.0218986i
\(81\) −0.570106 8.98193i −0.0633451 0.997992i
\(82\) −2.82197 + 3.04136i −0.311634 + 0.335862i
\(83\) 0.956792 12.7675i 0.105022 1.40142i −0.657013 0.753879i \(-0.728180\pi\)
0.762034 0.647537i \(-0.224201\pi\)
\(84\) 0.388792 + 4.56605i 0.0424207 + 0.498197i
\(85\) 0.0681788 + 0.909783i 0.00739503 + 0.0986798i
\(86\) −8.39966 6.69851i −0.905759 0.722319i
\(87\) −7.25652 7.29805i −0.777981 0.782433i
\(88\) −0.863088 + 3.78144i −0.0920055 + 0.403102i
\(89\) 0.0644591 0.860147i 0.00683266 0.0911755i −0.992745 0.120240i \(-0.961634\pi\)
0.999578 + 0.0290642i \(0.00925274\pi\)
\(90\) 0.609620 + 0.297875i 0.0642596 + 0.0313987i
\(91\) 15.2819 + 6.43231i 1.60198 + 0.674290i
\(92\) −0.573944 + 0.618564i −0.0598378 + 0.0644898i
\(93\) −0.379852 + 3.28697i −0.0393888 + 0.340842i
\(94\) −1.39255 9.23895i −0.143630 0.952925i
\(95\) −0.128528 + 0.416676i −0.0131867 + 0.0427501i
\(96\) −1.22125 1.22823i −0.124643 0.125356i
\(97\) −9.00570 5.19945i −0.914391 0.527924i −0.0325494 0.999470i \(-0.510363\pi\)
−0.881841 + 0.471546i \(0.843696\pi\)
\(98\) 4.50520 + 5.35754i 0.455094 + 0.541193i
\(99\) −4.18925 10.8558i −0.421035 1.09105i
\(100\) 4.08893 2.78779i 0.408893 0.278779i
\(101\) 0.113902 + 0.499039i 0.0113337 + 0.0496562i 0.980279 0.197621i \(-0.0633214\pi\)
−0.968945 + 0.247277i \(0.920464\pi\)
\(102\) 2.28880 + 6.60137i 0.226625 + 0.653634i
\(103\) 16.3730 3.73703i 1.61328 0.368220i 0.681663 0.731666i \(-0.261257\pi\)
0.931615 + 0.363445i \(0.118400\pi\)
\(104\) −5.98840 + 1.84718i −0.587211 + 0.181130i
\(105\) 1.02323 0.164860i 0.0998574 0.0160886i
\(106\) −7.90493 2.43835i −0.767795 0.236833i
\(107\) 8.83514 + 0.662103i 0.854126 + 0.0640079i 0.494593 0.869125i \(-0.335317\pi\)
0.359533 + 0.933133i \(0.382936\pi\)
\(108\) 5.09711 + 1.00969i 0.490470 + 0.0971573i
\(109\) 0.603935 + 8.05895i 0.0578465 + 0.771907i 0.948410 + 0.317048i \(0.102692\pi\)
−0.890563 + 0.454860i \(0.849689\pi\)
\(110\) 0.867434 + 0.130745i 0.0827066 + 0.0124660i
\(111\) 4.21092 4.18696i 0.399683 0.397409i
\(112\) −2.60580 0.458048i −0.246225 0.0432815i
\(113\) −10.2266 + 14.9997i −0.962040 + 1.41105i −0.0510176 + 0.998698i \(0.516246\pi\)
−0.911023 + 0.412356i \(0.864706\pi\)
\(114\) −0.134384 + 3.33667i −0.0125862 + 0.312508i
\(115\) 0.149208 + 0.118990i 0.0139138 + 0.0110958i
\(116\) 5.14584 2.97095i 0.477779 0.275846i
\(117\) 11.8056 14.6317i 1.09142 1.35270i
\(118\) −0.181365 0.144633i −0.0166960 0.0133146i
\(119\) 8.66884 + 6.22551i 0.794672 + 0.570691i
\(120\) −0.256369 + 0.296193i −0.0234032 + 0.0270386i
\(121\) −2.52150 3.16187i −0.229228 0.287442i
\(122\) −0.574097 + 7.66079i −0.0519763 + 0.693576i
\(123\) 6.57828 + 2.89244i 0.593144 + 0.260803i
\(124\) −1.77830 0.697933i −0.159696 0.0626762i
\(125\) −1.40292 1.75920i −0.125481 0.157348i
\(126\) 7.25165 3.22700i 0.646029 0.287484i
\(127\) −7.24622 + 9.08647i −0.642998 + 0.806294i −0.991374 0.131061i \(-0.958162\pi\)
0.348377 + 0.937355i \(0.386733\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −6.19606 + 17.5466i −0.545532 + 1.54489i
\(130\) 0.517816 + 1.31937i 0.0454154 + 0.115717i
\(131\) 4.26018 18.6651i 0.372214 1.63077i −0.348335 0.937370i \(-0.613253\pi\)
0.720549 0.693404i \(-0.243890\pi\)
\(132\) 6.67795 0.733136i 0.581241 0.0638113i
\(133\) 2.76979 + 4.28349i 0.240171 + 0.371426i
\(134\) −4.32296 + 8.97673i −0.373447 + 0.775471i
\(135\) 0.141571 1.16664i 0.0121845 0.100409i
\(136\) −4.02261 + 0.301453i −0.344936 + 0.0258494i
\(137\) 1.06757 + 0.243667i 0.0912089 + 0.0208178i 0.267882 0.963452i \(-0.413676\pi\)
−0.176673 + 0.984270i \(0.556533\pi\)
\(138\) 1.33792 + 0.588278i 0.113891 + 0.0500775i
\(139\) −3.35248 3.61312i −0.284354 0.306461i 0.574681 0.818377i \(-0.305126\pi\)
−0.859035 + 0.511917i \(0.828936\pi\)
\(140\) −0.0592640 + 0.595441i −0.00500872 + 0.0503239i
\(141\) −14.3292 + 7.52100i −1.20674 + 0.633382i
\(142\) 6.10473 5.66436i 0.512298 0.475343i
\(143\) 8.88034 22.6267i 0.742611 1.89214i
\(144\) −1.31705 + 2.69544i −0.109754 + 0.224620i
\(145\) −0.757026 1.11035i −0.0628676 0.0922098i
\(146\) −3.98760 + 6.90672i −0.330016 + 0.571604i
\(147\) 6.21128 10.4125i 0.512298 0.858808i
\(148\) 1.71422 + 2.96911i 0.140908 + 0.244060i
\(149\) −0.323342 + 0.671428i −0.0264892 + 0.0550055i −0.913794 0.406179i \(-0.866861\pi\)
0.887304 + 0.461184i \(0.152575\pi\)
\(150\) −6.88219 5.10968i −0.561928 0.417204i
\(151\) −5.29310 6.63734i −0.430746 0.540139i 0.518332 0.855180i \(-0.326553\pi\)
−0.949078 + 0.315041i \(0.897982\pi\)
\(152\) −1.84234 0.568285i −0.149433 0.0460940i
\(153\) 9.50436 7.49115i 0.768382 0.605624i
\(154\) 7.69068 6.79432i 0.619732 0.547502i
\(155\) −0.127352 + 0.412866i −0.0102292 + 0.0331622i
\(156\) 6.42064 + 8.75181i 0.514063 + 0.700706i
\(157\) −11.1269 + 11.9919i −0.888022 + 0.957061i −0.999325 0.0367260i \(-0.988307\pi\)
0.111303 + 0.993787i \(0.464498\pi\)
\(158\) −7.90137 11.5892i −0.628599 0.921986i
\(159\) 0.494900 + 14.3198i 0.0392481 + 1.13563i
\(160\) −0.127405 0.186868i −0.0100722 0.0147732i
\(161\) 2.18804 0.443529i 0.172442 0.0349550i
\(162\) −1.23973 8.91421i −0.0974026 0.700366i
\(163\) 0.0414442 + 0.0384546i 0.00324616 + 0.00301199i 0.681794 0.731544i \(-0.261200\pi\)
−0.678548 + 0.734556i \(0.737390\pi\)
\(164\) −2.58680 + 3.24374i −0.201995 + 0.253293i
\(165\) −0.278215 1.49372i −0.0216590 0.116286i
\(166\) 12.8033i 0.993729i
\(167\) 2.21427 + 0.333747i 0.171345 + 0.0258261i 0.234154 0.972199i \(-0.424768\pi\)
−0.0628092 + 0.998026i \(0.520006\pi\)
\(168\) 0.728927 + 4.52423i 0.0562379 + 0.349052i
\(169\) 25.9795 3.91578i 1.99842 0.301214i
\(170\) 0.135976 + 0.902144i 0.0104289 + 0.0691913i
\(171\) 5.53665 1.67329i 0.423398 0.127960i
\(172\) −8.87676 6.05207i −0.676846 0.461466i
\(173\) 7.89117 20.1064i 0.599955 1.52866i −0.231366 0.972867i \(-0.574319\pi\)
0.831321 0.555793i \(-0.187585\pi\)
\(174\) −7.78162 6.73536i −0.589923 0.510606i
\(175\) −13.0895 0.319488i −0.989475 0.0241510i
\(176\) −0.578088 + 3.83536i −0.0435750 + 0.289101i
\(177\) −0.133785 + 0.378863i −0.0100559 + 0.0284771i
\(178\) 0.862559i 0.0646516i
\(179\) −2.51458 + 16.6832i −0.187949 + 1.24696i 0.673528 + 0.739162i \(0.264778\pi\)
−0.861477 + 0.507797i \(0.830460\pi\)
\(180\) 0.630175 + 0.251485i 0.0469705 + 0.0187446i
\(181\) 6.13869 + 12.7471i 0.456285 + 0.947486i 0.994506 + 0.104682i \(0.0333825\pi\)
−0.538221 + 0.842804i \(0.680903\pi\)
\(182\) 15.7198 + 5.27231i 1.16523 + 0.390810i
\(183\) 12.8625 3.40719i 0.950821 0.251866i
\(184\) −0.526113 + 0.659725i −0.0387856 + 0.0486356i
\(185\) 0.640666 0.436799i 0.0471027 0.0321141i
\(186\) −0.133155 + 3.30616i −0.00976338 + 0.242419i
\(187\) 8.81380 12.9275i 0.644529 0.945351i
\(188\) −2.07908 9.10905i −0.151633 0.664346i
\(189\) −9.39546 10.0362i −0.683419 0.730026i
\(190\) −0.0970300 + 0.425116i −0.00703930 + 0.0308412i
\(191\) 8.34031 + 8.98871i 0.603484 + 0.650401i 0.958712 0.284379i \(-0.0917874\pi\)
−0.355228 + 0.934780i \(0.615597\pi\)
\(192\) −1.30962 1.13354i −0.0945135 0.0818059i
\(193\) −17.7053 5.46136i −1.27446 0.393117i −0.417579 0.908640i \(-0.637121\pi\)
−0.856876 + 0.515523i \(0.827598\pi\)
\(194\) −9.36908 4.51191i −0.672661 0.323936i
\(195\) 1.86532 1.59600i 0.133578 0.114292i
\(196\) 4.89297 + 5.00588i 0.349498 + 0.357563i
\(197\) 26.7227i 1.90392i −0.306230 0.951958i \(-0.599068\pi\)
0.306230 0.951958i \(-0.400932\pi\)
\(198\) −4.98879 10.5124i −0.354538 0.747081i
\(199\) −12.4253 13.3912i −0.880803 0.949280i 0.118241 0.992985i \(-0.462274\pi\)
−0.999044 + 0.0437047i \(0.986084\pi\)
\(200\) 3.86917 3.08556i 0.273591 0.218182i
\(201\) 17.1431 + 1.98111i 1.20918 + 0.139736i
\(202\) 0.150877 + 0.489132i 0.0106157 + 0.0344152i
\(203\) −15.6435 1.55699i −1.09796 0.109279i
\(204\) 2.77572 + 6.41187i 0.194339 + 0.448921i
\(205\) 0.775297 + 0.528589i 0.0541491 + 0.0369182i
\(206\) 16.0479 4.95013i 1.11811 0.344892i
\(207\) 0.203578 2.52326i 0.0141496 0.175379i
\(208\) −5.83361 + 2.28952i −0.404488 + 0.158750i
\(209\) 6.17867 4.21254i 0.427387 0.291388i
\(210\) 1.00805 0.240865i 0.0695622 0.0166213i
\(211\) 13.9329 + 9.49931i 0.959183 + 0.653960i 0.938300 0.345822i \(-0.112400\pi\)
0.0208826 + 0.999782i \(0.493352\pi\)
\(212\) −8.06505 1.84079i −0.553910 0.126426i
\(213\) −12.7334 6.77635i −0.872478 0.464308i
\(214\) 8.85992 0.605652
\(215\) −1.21492 + 2.10431i −0.0828571 + 0.143513i
\(216\) 5.15831 + 0.625958i 0.350979 + 0.0425910i
\(217\) 2.74446 + 4.24432i 0.186306 + 0.288123i
\(218\) 1.20449 + 7.99128i 0.0815785 + 0.541238i
\(219\) 13.5652 + 2.60679i 0.916654 + 0.176151i
\(220\) 0.874779 + 0.0655556i 0.0589776 + 0.00441976i
\(221\) 25.2089 + 1.88915i 1.69574 + 0.127078i
\(222\) 3.88626 4.48994i 0.260828 0.301345i
\(223\) −0.669259 4.44024i −0.0448169 0.297341i −0.999999 0.00132218i \(-0.999579\pi\)
0.955182 0.296018i \(-0.0956590\pi\)
\(224\) −2.63274 0.262036i −0.175908 0.0175080i
\(225\) −4.45698 + 14.1618i −0.297132 + 0.944117i
\(226\) −9.07710 + 15.7220i −0.603800 + 1.04581i
\(227\) −5.87378 −0.389857 −0.194928 0.980817i \(-0.562447\pi\)
−0.194928 + 0.980817i \(0.562447\pi\)
\(228\) 0.115342 + 3.33739i 0.00763872 + 0.221024i
\(229\) 7.75040 + 1.76898i 0.512161 + 0.116897i 0.470788 0.882246i \(-0.343970\pi\)
0.0413728 + 0.999144i \(0.486827\pi\)
\(230\) 0.157683 + 0.107507i 0.0103973 + 0.00708878i
\(231\) −15.4824 8.73058i −1.01867 0.574430i
\(232\) 4.90943 3.34719i 0.322320 0.219754i
\(233\) 11.1018 4.35713i 0.727302 0.285445i 0.0273412 0.999626i \(-0.491296\pi\)
0.699961 + 0.714181i \(0.253201\pi\)
\(234\) 10.6791 15.4730i 0.698117 1.01150i
\(235\) −2.01927 + 0.622863i −0.131723 + 0.0406311i
\(236\) −0.191666 0.130676i −0.0124764 0.00850626i
\(237\) −14.4823 + 19.5061i −0.940725 + 1.26705i
\(238\) 9.10984 + 5.56027i 0.590503 + 0.360419i
\(239\) −6.33205 20.5280i −0.409586 1.32785i −0.892053 0.451932i \(-0.850735\pi\)
0.482466 0.875915i \(-0.339741\pi\)
\(240\) −0.233518 + 0.314523i −0.0150735 + 0.0203024i
\(241\) 0.682279 0.544099i 0.0439495 0.0350485i −0.601269 0.799047i \(-0.705338\pi\)
0.645218 + 0.763998i \(0.276766\pi\)
\(242\) −2.75074 2.96459i −0.176824 0.190571i
\(243\) −13.8845 + 7.08666i −0.890691 + 0.454609i
\(244\) 7.68228i 0.491807i
\(245\) 1.04630 1.18814i 0.0668459 0.0759077i
\(246\) 6.77604 + 2.39276i 0.432025 + 0.152557i
\(247\) 10.8858 + 5.24234i 0.692649 + 0.333562i
\(248\) −1.82549 0.563089i −0.115919 0.0357562i
\(249\) −20.9523 + 7.26451i −1.32780 + 0.460370i
\(250\) −1.53046 1.64944i −0.0967948 0.104320i
\(251\) −5.66953 + 24.8398i −0.357857 + 1.56788i 0.400663 + 0.916226i \(0.368780\pi\)
−0.758520 + 0.651650i \(0.774077\pi\)
\(252\) 6.99022 3.75989i 0.440343 0.236851i
\(253\) −0.728291 3.19085i −0.0457873 0.200607i
\(254\) −6.54692 + 9.60257i −0.410790 + 0.602519i
\(255\) 1.39919 0.734393i 0.0876206 0.0459895i
\(256\) 0.826239 0.563320i 0.0516399 0.0352075i
\(257\) 2.34945 2.94612i 0.146555 0.183774i −0.703136 0.711056i \(-0.748217\pi\)
0.849690 + 0.527282i \(0.176789\pi\)
\(258\) −4.86747 + 17.9605i −0.303036 + 1.11817i
\(259\) 0.898374 9.02619i 0.0558222 0.560860i
\(260\) 0.614965 + 1.27699i 0.0381385 + 0.0791954i
\(261\) −6.60704 + 16.5561i −0.408966 + 1.02479i
\(262\) 2.85343 18.9312i 0.176285 1.16958i
\(263\) 7.93798i 0.489477i −0.969589 0.244739i \(-0.921298\pi\)
0.969589 0.244739i \(-0.0787021\pi\)
\(264\) 6.60449 1.23013i 0.406478 0.0757093i
\(265\) −0.278852 + 1.85006i −0.0171297 + 0.113648i
\(266\) 3.08215 + 4.06453i 0.188979 + 0.249212i
\(267\) −1.41156 + 0.489411i −0.0863861 + 0.0299514i
\(268\) −3.64004 + 9.27468i −0.222351 + 0.566541i
\(269\) −2.85019 1.94323i −0.173779 0.118481i 0.473307 0.880898i \(-0.343060\pi\)
−0.647086 + 0.762417i \(0.724013\pi\)
\(270\) 0.0539921 1.17396i 0.00328586 0.0714449i
\(271\) 1.97734 + 13.1188i 0.120115 + 0.796910i 0.965055 + 0.262049i \(0.0843982\pi\)
−0.844940 + 0.534862i \(0.820364\pi\)
\(272\) −3.98883 + 0.601220i −0.241859 + 0.0364543i
\(273\) −0.291305 28.7167i −0.0176306 1.73801i
\(274\) 1.08280 + 0.163205i 0.0654142 + 0.00985960i
\(275\) 19.1950i 1.15750i
\(276\) 1.37814 + 0.486650i 0.0829543 + 0.0292929i
\(277\) −18.0211 + 22.5978i −1.08278 + 1.35777i −0.153607 + 0.988132i \(0.549089\pi\)
−0.929177 + 0.369636i \(0.879482\pi\)
\(278\) −3.61312 3.35248i −0.216700 0.201069i
\(279\) 5.48601 1.65799i 0.328439 0.0992612i
\(280\) −0.0146009 + 0.598205i −0.000872573 + 0.0357496i
\(281\) −1.62538 2.38400i −0.0969621 0.142217i 0.774692 0.632339i \(-0.217905\pi\)
−0.871654 + 0.490121i \(0.836952\pi\)
\(282\) −13.7271 + 8.57079i −0.817438 + 0.510383i
\(283\) 2.21935 + 3.25519i 0.131927 + 0.193501i 0.886518 0.462694i \(-0.153117\pi\)
−0.754591 + 0.656195i \(0.772165\pi\)
\(284\) 5.66436 6.10473i 0.336118 0.362249i
\(285\) 0.750748 0.0824206i 0.0444705 0.00488217i
\(286\) 7.16461 23.2271i 0.423652 1.37345i
\(287\) 10.5651 2.97860i 0.623638 0.175821i
\(288\) −1.11194 + 2.78632i −0.0655217 + 0.164186i
\(289\) −0.695414 0.214507i −0.0409067 0.0126180i
\(290\) −0.837886 1.05068i −0.0492024 0.0616978i
\(291\) −2.06769 + 17.8923i −0.121210 + 1.04887i
\(292\) −3.46031 + 7.18540i −0.202499 + 0.420494i
\(293\) 7.23412 + 12.5299i 0.422622 + 0.732003i 0.996195 0.0871516i \(-0.0277765\pi\)
−0.573573 + 0.819154i \(0.694443\pi\)
\(294\) 5.41578 10.8475i 0.315855 0.632642i
\(295\) −0.0262325 + 0.0454360i −0.00152731 + 0.00264539i
\(296\) 1.93131 + 2.83271i 0.112255 + 0.164648i
\(297\) −14.3726 + 14.1287i −0.833985 + 0.819830i
\(298\) −0.272262 + 0.693714i −0.0157717 + 0.0401857i
\(299\) 3.87643 3.59680i 0.224180 0.208008i
\(300\) −7.24479 4.58108i −0.418278 0.264489i
\(301\) 9.73602 + 26.7054i 0.561175 + 1.53928i
\(302\) −5.77431 6.22322i −0.332274 0.358106i
\(303\) 0.714847 0.524437i 0.0410669 0.0301281i
\(304\) −1.87965 0.429018i −0.107805 0.0246059i
\(305\) 1.73262 0.129842i 0.0992097 0.00743474i
\(306\) 8.91797 8.18047i 0.509807 0.467646i
\(307\) −12.6333 + 26.2333i −0.721019 + 1.49721i 0.140824 + 0.990035i \(0.455025\pi\)
−0.861842 + 0.507176i \(0.830689\pi\)
\(308\) 7.16143 7.35005i 0.408060 0.418808i
\(309\) −17.2063 23.4535i −0.978832 1.33422i
\(310\) −0.0961427 + 0.421229i −0.00546054 + 0.0239242i
\(311\) 6.42467 + 16.3698i 0.364310 + 0.928246i 0.989072 + 0.147431i \(0.0471006\pi\)
−0.624762 + 0.780815i \(0.714804\pi\)
\(312\) 7.05671 + 8.24752i 0.399508 + 0.466924i
\(313\) 2.47915 1.43134i 0.140130 0.0809039i −0.428296 0.903638i \(-0.640886\pi\)
0.568426 + 0.822735i \(0.307553\pi\)
\(314\) −10.1996 + 12.7899i −0.575598 + 0.721777i
\(315\) −0.966133 1.51299i −0.0544354 0.0852474i
\(316\) −8.74534 10.9663i −0.491964 0.616903i
\(317\) 10.9581 + 4.30072i 0.615466 + 0.241553i 0.652533 0.757760i \(-0.273706\pi\)
−0.0370670 + 0.999313i \(0.511801\pi\)
\(318\) 1.56363 + 14.2427i 0.0876842 + 0.798693i
\(319\) −1.72229 + 22.9823i −0.0964295 + 1.28676i
\(320\) −0.141013 0.176825i −0.00788287 0.00988481i
\(321\) −5.02706 14.4991i −0.280583 0.809259i
\(322\) 2.14878 0.605801i 0.119747 0.0337600i
\(323\) 6.08054 + 4.84907i 0.338330 + 0.269809i
\(324\) −1.90243 8.79663i −0.105690 0.488702i
\(325\) −26.8585 + 15.5068i −1.48984 + 0.860160i
\(326\) 0.0442020 + 0.0352499i 0.00244812 + 0.00195231i
\(327\) 12.3941 6.50533i 0.685398 0.359745i
\(328\) −2.33716 + 3.42798i −0.129048 + 0.189279i
\(329\) −9.59006 + 22.7841i −0.528717 + 1.25613i
\(330\) −0.389063 1.46875i −0.0214172 0.0808522i
\(331\) −4.59033 0.691880i −0.252307 0.0380292i 0.0216708 0.999765i \(-0.493101\pi\)
−0.273978 + 0.961736i \(0.588340\pi\)
\(332\) −0.956792 12.7675i −0.0525108 0.700708i
\(333\) −9.55273 3.81222i −0.523486 0.208908i
\(334\) 2.23302 + 0.167342i 0.122185 + 0.00915652i
\(335\) 2.15329 + 0.664201i 0.117647 + 0.0362892i
\(336\) 1.06498 + 4.45711i 0.0580997 + 0.243155i
\(337\) −0.901177 + 0.277976i −0.0490903 + 0.0151423i −0.319203 0.947686i \(-0.603415\pi\)
0.270113 + 0.962829i \(0.412939\pi\)
\(338\) 25.6142 5.84628i 1.39323 0.317996i
\(339\) 30.8790 + 5.93393i 1.67712 + 0.322287i
\(340\) 0.203013 + 0.889460i 0.0110100 + 0.0482377i
\(341\) 6.12217 4.17402i 0.331534 0.226036i
\(342\) 5.39612 2.08237i 0.291789 0.112601i
\(343\) −2.78943 18.3090i −0.150615 0.988593i
\(344\) −9.30421 5.37179i −0.501649 0.289627i
\(345\) 0.0864639 0.319044i 0.00465506 0.0171768i
\(346\) 6.36656 20.6399i 0.342268 1.10961i
\(347\) −2.93454 19.4694i −0.157534 1.04517i −0.918226 0.396057i \(-0.870378\pi\)
0.760692 0.649113i \(-0.224860\pi\)
\(348\) −8.26319 6.13501i −0.442954 0.328871i
\(349\) 0.153164 0.165072i 0.00819870 0.00883610i −0.728939 0.684578i \(-0.759986\pi\)
0.737138 + 0.675742i \(0.236177\pi\)
\(350\) −13.0768 + 0.659586i −0.698984 + 0.0352564i
\(351\) −31.3805 8.69691i −1.67497 0.464207i
\(352\) −0.289854 + 3.86784i −0.0154493 + 0.206156i
\(353\) 6.41855 28.1215i 0.341625 1.49676i −0.454018 0.890992i \(-0.650010\pi\)
0.795643 0.605765i \(-0.207133\pi\)
\(354\) −0.105098 + 0.387802i −0.00558589 + 0.0206114i
\(355\) −1.47257 1.17433i −0.0781558 0.0623271i
\(356\) −0.0644591 0.860147i −0.00341633 0.0455877i
\(357\) 3.93041 18.0629i 0.208019 0.955991i
\(358\) −1.26082 + 16.8244i −0.0666363 + 0.889199i
\(359\) −1.89536 + 2.04271i −0.100033 + 0.107810i −0.781084 0.624426i \(-0.785333\pi\)
0.681051 + 0.732236i \(0.261523\pi\)
\(360\) 0.647207 + 0.203688i 0.0341108 + 0.0107353i
\(361\) −7.64142 13.2353i −0.402180 0.696597i
\(362\) 7.07412 + 12.2527i 0.371807 + 0.643989i
\(363\) −3.29074 + 6.18362i −0.172719 + 0.324556i
\(364\) 16.0699 + 4.08282i 0.842291 + 0.213998i
\(365\) 1.67904 + 0.658976i 0.0878852 + 0.0344924i
\(366\) 12.5719 4.35887i 0.657143 0.227842i
\(367\) 2.85765 + 5.93397i 0.149168 + 0.309751i 0.962142 0.272550i \(-0.0878669\pi\)
−0.812974 + 0.582301i \(0.802153\pi\)
\(368\) −0.475341 + 0.697197i −0.0247789 + 0.0363439i
\(369\) 0.0710219 12.4465i 0.00369725 0.647938i
\(370\) 0.606233 0.483455i 0.0315165 0.0251336i
\(371\) 14.4909 + 16.4027i 0.752331 + 0.851584i
\(372\) 0.114287 + 3.30687i 0.00592552 + 0.171453i
\(373\) 23.8048 1.23257 0.616283 0.787525i \(-0.288638\pi\)
0.616283 + 0.787525i \(0.288638\pi\)
\(374\) 7.82309 13.5500i 0.404522 0.700653i
\(375\) −1.83091 + 3.44045i −0.0945477 + 0.177664i
\(376\) −2.75399 8.92821i −0.142026 0.460437i
\(377\) −33.5492 + 16.1564i −1.72787 + 0.832099i
\(378\) −10.1192 9.30602i −0.520475 0.478650i
\(379\) −24.1025 11.6071i −1.23806 0.596219i −0.303776 0.952744i \(-0.598247\pi\)
−0.934286 + 0.356524i \(0.883962\pi\)
\(380\) −0.0649897 + 0.431179i −0.00333390 + 0.0221190i
\(381\) 19.4291 + 5.26547i 0.995382 + 0.269758i
\(382\) 8.98871 + 8.34031i 0.459903 + 0.426727i
\(383\) −24.9555 + 12.0179i −1.27517 + 0.614088i −0.944143 0.329535i \(-0.893108\pi\)
−0.331023 + 0.943623i \(0.607394\pi\)
\(384\) −1.39066 1.03250i −0.0709670 0.0526895i
\(385\) −1.77873 1.49093i −0.0906526 0.0759847i
\(386\) −18.0639 4.12297i −0.919429 0.209854i
\(387\) 32.1538 2.22517i 1.63447 0.113112i
\(388\) −9.68005 3.79914i −0.491430 0.192872i
\(389\) 13.3219 3.04063i 0.675445 0.154166i 0.128979 0.991647i \(-0.458830\pi\)
0.546466 + 0.837481i \(0.315973\pi\)
\(390\) 1.74084 1.73093i 0.0881507 0.0876491i
\(391\) 2.94784 1.70194i 0.149079 0.0860707i
\(392\) 5.25338 + 4.62623i 0.265336 + 0.233660i
\(393\) −32.5996 + 6.07189i −1.64443 + 0.306286i
\(394\) −1.99699 26.6480i −0.100607 1.34251i
\(395\) −2.32548 + 2.15773i −0.117007 + 0.108567i
\(396\) −5.76043 10.1101i −0.289472 0.508054i
\(397\) −10.7976 + 35.0050i −0.541917 + 1.75685i 0.105190 + 0.994452i \(0.466455\pi\)
−0.647107 + 0.762399i \(0.724021\pi\)
\(398\) −13.3912 12.4253i −0.671242 0.622822i
\(399\) 4.90272 7.35007i 0.245443 0.367964i
\(400\) 3.62776 3.36607i 0.181388 0.168304i
\(401\) 5.03195 + 10.4489i 0.251283 + 0.521795i 0.988009 0.154396i \(-0.0493433\pi\)
−0.736726 + 0.676192i \(0.763629\pi\)
\(402\) 17.2432 + 0.694464i 0.860011 + 0.0346367i
\(403\) 10.7863 + 5.19440i 0.537303 + 0.258751i
\(404\) 0.187008 + 0.476489i 0.00930400 + 0.0237062i
\(405\) −1.95180 + 0.577740i −0.0969855 + 0.0287081i
\(406\) −15.7161 0.383598i −0.779978 0.0190376i
\(407\) −13.2606 0.993747i −0.657305 0.0492582i
\(408\) 3.24712 + 6.18651i 0.160756 + 0.306278i
\(409\) −8.36550 + 3.28322i −0.413648 + 0.162345i −0.563033 0.826434i \(-0.690366\pi\)
0.149386 + 0.988779i \(0.452270\pi\)
\(410\) 0.812631 + 0.469173i 0.0401330 + 0.0231708i
\(411\) −0.347290 1.86458i −0.0171305 0.0919728i
\(412\) 15.6331 6.13556i 0.770190 0.302277i
\(413\) 0.210219 + 0.576621i 0.0103442 + 0.0283736i
\(414\) 0.0144447 2.53142i 0.000709920 0.124413i
\(415\) −2.86335 + 0.431580i −0.140556 + 0.0211854i
\(416\) −5.64620 + 2.71907i −0.276828 + 0.133313i
\(417\) −3.43621 + 7.81497i −0.168272 + 0.382701i
\(418\) 5.84659 4.66250i 0.285966 0.228050i
\(419\) −1.30865 + 3.33439i −0.0639318 + 0.162896i −0.959270 0.282492i \(-0.908839\pi\)
0.895338 + 0.445388i \(0.146934\pi\)
\(420\) 0.987234 0.315523i 0.0481721 0.0153960i
\(421\) −0.413971 1.05478i −0.0201757 0.0514069i 0.920431 0.390905i \(-0.127838\pi\)
−0.940607 + 0.339498i \(0.889743\pi\)
\(422\) 14.6039 + 8.43154i 0.710905 + 0.410441i
\(423\) 21.8146 + 17.6011i 1.06066 + 0.855797i
\(424\) −8.18006 1.23295i −0.397259 0.0598771i
\(425\) −19.0762 + 5.88423i −0.925331 + 0.285427i
\(426\) −13.2042 5.80583i −0.639745 0.281293i
\(427\) 11.8561 16.5092i 0.573755 0.798938i
\(428\) 8.83514 0.662103i 0.427063 0.0320039i
\(429\) −42.0758 + 1.45417i −2.03144 + 0.0702078i
\(430\) −1.05427 + 2.18922i −0.0508415 + 0.105573i
\(431\) −12.0127 38.9443i −0.578632 1.87588i −0.472039 0.881577i \(-0.656482\pi\)
−0.106593 0.994303i \(-0.533994\pi\)
\(432\) 5.19067 + 0.238726i 0.249736 + 0.0114857i
\(433\) −10.8927 + 2.48620i −0.523472 + 0.119479i −0.476088 0.879398i \(-0.657946\pi\)
−0.0473840 + 0.998877i \(0.515088\pi\)
\(434\) 3.05397 + 4.02736i 0.146595 + 0.193319i
\(435\) −1.24400 + 1.96733i −0.0596452 + 0.0943262i
\(436\) 1.79831 + 7.87893i 0.0861236 + 0.377332i
\(437\) 1.60871 0.242474i 0.0769549 0.0115991i
\(438\) 13.7221 + 1.58577i 0.655668 + 0.0757710i
\(439\) 21.5197 1.61268i 1.02708 0.0769689i 0.449480 0.893290i \(-0.351609\pi\)
0.577598 + 0.816321i \(0.303990\pi\)
\(440\) 0.877232 0.0418204
\(441\) −20.8247 2.70799i −0.991651 0.128952i
\(442\) 25.2796 1.20243
\(443\) −15.2524 + 1.14301i −0.724662 + 0.0543059i −0.431953 0.901896i \(-0.642175\pi\)
−0.292708 + 0.956202i \(0.594556\pi\)
\(444\) 3.53986 4.76780i 0.167994 0.226270i
\(445\) −0.192904 + 0.0290756i −0.00914452 + 0.00137832i
\(446\) −0.999207 4.37781i −0.0473138 0.207295i
\(447\) 1.28973 + 0.0519434i 0.0610020 + 0.00245684i
\(448\) −2.64496 0.0645581i −0.124963 0.00305008i
\(449\) 16.2682 3.71311i 0.767744 0.175232i 0.179326 0.983790i \(-0.442608\pi\)
0.588418 + 0.808557i \(0.299751\pi\)
\(450\) −3.38620 + 14.4552i −0.159627 + 0.681426i
\(451\) −4.74328 15.3773i −0.223352 0.724090i
\(452\) −7.87682 + 16.3564i −0.370494 + 0.769339i
\(453\) −6.90787 + 12.9806i −0.324560 + 0.609880i
\(454\) −5.85736 + 0.438948i −0.274900 + 0.0206009i
\(455\) 0.649214 3.69333i 0.0304356 0.173146i
\(456\) 0.364423 + 3.31943i 0.0170657 + 0.155447i
\(457\) −25.6002 + 7.89662i −1.19753 + 0.369388i −0.828478 0.560021i \(-0.810793\pi\)
−0.369050 + 0.929410i \(0.620317\pi\)
\(458\) 7.86092 + 1.18484i 0.367317 + 0.0553641i
\(459\) −18.4472 9.95253i −0.861040 0.464544i
\(460\) 0.165276 + 0.0954224i 0.00770605 + 0.00444909i
\(461\) 9.14777 + 23.3081i 0.426054 + 1.08557i 0.969275 + 0.245979i \(0.0791093\pi\)
−0.543221 + 0.839590i \(0.682795\pi\)
\(462\) −16.0915 7.54917i −0.748646 0.351219i
\(463\) 10.6554 27.1496i 0.495199 1.26175i −0.436889 0.899516i \(-0.643920\pi\)
0.932088 0.362232i \(-0.117985\pi\)
\(464\) 4.64557 3.70472i 0.215665 0.171987i
\(465\) 0.743883 0.0816668i 0.0344967 0.00378721i
\(466\) 10.7451 5.17458i 0.497759 0.239708i
\(467\) 9.05611 1.36499i 0.419067 0.0631642i 0.0638757 0.997958i \(-0.479654\pi\)
0.355191 + 0.934794i \(0.384416\pi\)
\(468\) 9.49297 16.2278i 0.438813 0.750128i
\(469\) 22.1361 14.3136i 1.02215 0.660943i
\(470\) −1.96708 + 0.772021i −0.0907346 + 0.0356107i
\(471\) 26.7176 + 9.43455i 1.23108 + 0.434721i
\(472\) −0.200895 0.115987i −0.00924696 0.00533873i
\(473\) 38.7904 15.2241i 1.78358 0.700005i
\(474\) −12.9841 + 20.5338i −0.596379 + 0.943148i
\(475\) −9.51466 0.713025i −0.436562 0.0327158i
\(476\) 9.49988 + 4.86395i 0.435426 + 0.222939i
\(477\) 22.4208 10.6401i 1.02658 0.487176i
\(478\) −7.84840 19.9974i −0.358978 0.914660i
\(479\) −1.10444 0.531871i −0.0504632 0.0243018i 0.408482 0.912766i \(-0.366058\pi\)
−0.458945 + 0.888465i \(0.651773\pi\)
\(480\) −0.209360 + 0.331094i −0.00955595 + 0.0151123i
\(481\) −9.32215 19.3577i −0.425054 0.882633i
\(482\) 0.639711 0.593565i 0.0291380 0.0270361i
\(483\) −2.21058 3.17270i −0.100585 0.144363i
\(484\) −2.96459 2.75074i −0.134754 0.125034i
\(485\) −0.693232 + 2.24740i −0.0314780 + 0.102049i
\(486\) −13.3161 + 8.10443i −0.604030 + 0.367625i
\(487\) −5.19577 + 4.82097i −0.235443 + 0.218459i −0.789066 0.614308i \(-0.789435\pi\)
0.553623 + 0.832767i \(0.313245\pi\)
\(488\) 0.574097 + 7.66079i 0.0259882 + 0.346788i
\(489\) 0.0326058 0.0923362i 0.00147449 0.00417559i
\(490\) 0.954588 1.26301i 0.0431239 0.0570570i
\(491\) −28.8017 + 16.6287i −1.29980 + 0.750442i −0.980370 0.197167i \(-0.936826\pi\)
−0.319433 + 0.947609i \(0.603493\pi\)
\(492\) 6.93591 + 1.87970i 0.312695 + 0.0847432i
\(493\) −23.3680 + 5.33360i −1.05244 + 0.240213i
\(494\) 11.2472 + 4.41418i 0.506033 + 0.198603i
\(495\) −2.18283 + 1.47006i −0.0981110 + 0.0660741i
\(496\) −1.86246 0.425095i −0.0836271 0.0190873i
\(497\) −21.5942 + 4.37728i −0.968632 + 0.196348i
\(498\) −20.3509 + 8.80997i −0.911945 + 0.394784i
\(499\) 2.90578 1.39935i 0.130081 0.0626435i −0.367711 0.929940i \(-0.619859\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(500\) −1.64944 1.53046i −0.0737654 0.0684443i
\(501\) −0.993149 3.74924i −0.0443706 0.167504i
\(502\) −3.79739 + 25.1940i −0.169486 + 1.12447i
\(503\) 9.81594 + 4.72711i 0.437671 + 0.210771i 0.639726 0.768603i \(-0.279048\pi\)
−0.202055 + 0.979374i \(0.564762\pi\)
\(504\) 6.68970 4.27176i 0.297983 0.190279i
\(505\) 0.104304 0.0502303i 0.00464148 0.00223522i
\(506\) −0.964708 3.12751i −0.0428865 0.139035i
\(507\) −24.1007 38.6000i −1.07035 1.71429i
\(508\) −5.81101 + 10.0650i −0.257822 + 0.446561i
\(509\) −17.7365 −0.786159 −0.393079 0.919505i \(-0.628590\pi\)
−0.393079 + 0.919505i \(0.628590\pi\)
\(510\) 1.34039 0.836901i 0.0593537 0.0370586i
\(511\) 18.5254 10.1012i 0.819518 0.446849i
\(512\) 0.781831 0.623490i 0.0345524 0.0275546i
\(513\) −6.46947 7.64912i −0.285634 0.337717i
\(514\) 2.12272 3.11346i 0.0936291 0.137329i
\(515\) −1.64801 3.42212i −0.0726199 0.150797i
\(516\) −3.51167 + 18.2741i −0.154593 + 0.804471i
\(517\) 33.7346 + 13.2399i 1.48365 + 0.582289i
\(518\) 0.221333 9.06809i 0.00972483 0.398429i
\(519\) −37.3891 + 1.29219i −1.64120 + 0.0567208i
\(520\) 0.708675 + 1.22746i 0.0310774 + 0.0538277i
\(521\) 2.12397 + 3.67882i 0.0930527 + 0.161172i 0.908794 0.417245i \(-0.137004\pi\)
−0.815742 + 0.578417i \(0.803671\pi\)
\(522\) −5.35133 + 17.0035i −0.234221 + 0.744223i
\(523\) 15.9269 17.1651i 0.696436 0.750579i −0.281482 0.959566i \(-0.590826\pi\)
0.977918 + 0.208987i \(0.0670166\pi\)
\(524\) 1.43071 19.0915i 0.0625010 0.834018i
\(525\) 8.49909 + 21.0257i 0.370931 + 0.917635i
\(526\) −0.593206 7.91579i −0.0258650 0.345145i
\(527\) 6.02493 + 4.80472i 0.262450 + 0.209297i
\(528\) 6.49410 1.72024i 0.282619 0.0748640i
\(529\) −4.95954 + 21.7292i −0.215632 + 0.944746i
\(530\) −0.139817 + 1.86573i −0.00607326 + 0.0810421i
\(531\) 0.694261 0.0480456i 0.0301284 0.00208500i
\(532\) 3.37728 + 3.82283i 0.146424 + 0.165741i
\(533\) 17.6847 19.0596i 0.766011 0.825564i
\(534\) −1.37104 + 0.593528i −0.0593307 + 0.0256845i
\(535\) −0.298655 1.98144i −0.0129120 0.0856653i
\(536\) −2.93677 + 9.52077i −0.126849 + 0.411235i
\(537\) 28.2482 7.48277i 1.21900 0.322906i
\(538\) −2.98744 1.72480i −0.128798 0.0743613i
\(539\) −26.7333 + 4.74303i −1.15148 + 0.204297i
\(540\) −0.0338889 1.17471i −0.00145835 0.0505515i
\(541\) 28.5582 19.4706i 1.22781 0.837108i 0.236889 0.971537i \(-0.423872\pi\)
0.990923 + 0.134429i \(0.0429200\pi\)
\(542\) 2.95218 + 12.9344i 0.126807 + 0.555578i
\(543\) 16.0375 18.5288i 0.688237 0.795146i
\(544\) −3.93275 + 0.897625i −0.168615 + 0.0384853i
\(545\) 1.74658 0.538748i 0.0748152 0.0230774i
\(546\) −2.43649 28.6146i −0.104272 1.22459i
\(547\) −11.3520 3.50163i −0.485377 0.149719i 0.0424024 0.999101i \(-0.486499\pi\)
−0.527779 + 0.849382i \(0.676975\pi\)
\(548\) 1.09197 + 0.0818315i 0.0466465 + 0.00349567i
\(549\) −14.2664 18.1004i −0.608876 0.772508i
\(550\) 1.43445 + 19.1413i 0.0611649 + 0.816189i
\(551\) −11.3280 1.70742i −0.482588 0.0727385i
\(552\) 1.41065 + 0.382301i 0.0600414 + 0.0162718i
\(553\) 1.86945 + 37.0633i 0.0794973 + 1.57609i
\(554\) −16.2820 + 23.8813i −0.691755 + 1.01462i
\(555\) −1.13514 0.717779i −0.0481838 0.0304680i
\(556\) −3.85355 3.07310i −0.163427 0.130329i
\(557\) −29.8293 + 17.2219i −1.26391 + 0.729717i −0.973828 0.227286i \(-0.927015\pi\)
−0.290078 + 0.957003i \(0.593681\pi\)
\(558\) 5.34677 2.06332i 0.226347 0.0873474i
\(559\) 52.6391 + 41.9783i 2.22640 + 1.77549i
\(560\) 0.0301438 + 0.597623i 0.00127381 + 0.0252542i
\(561\) −26.6130 5.11415i −1.12360 0.215919i
\(562\) −1.79899 2.25586i −0.0758859 0.0951579i
\(563\) −1.52199 + 20.3095i −0.0641441 + 0.855944i 0.868625 + 0.495470i \(0.165004\pi\)
−0.932769 + 0.360474i \(0.882615\pi\)
\(564\) −13.0482 + 9.57266i −0.549430 + 0.403082i
\(565\) 3.82207 + 1.50005i 0.160796 + 0.0631076i
\(566\) 2.45640 + 3.08023i 0.103250 + 0.129472i
\(567\) −9.48754 + 21.8400i −0.398439 + 0.917195i
\(568\) 5.19232 6.51096i 0.217865 0.273194i
\(569\) −15.1763 + 8.76203i −0.636223 + 0.367324i −0.783158 0.621823i \(-0.786393\pi\)
0.146935 + 0.989146i \(0.453059\pi\)
\(570\) 0.742489 0.138294i 0.0310995 0.00579248i
\(571\) −7.38798 18.8243i −0.309177 0.787771i −0.998022 0.0628623i \(-0.979977\pi\)
0.688845 0.724909i \(-0.258118\pi\)
\(572\) 5.40881 23.6976i 0.226154 0.990845i
\(573\) 8.54860 19.4421i 0.357123 0.812205i
\(574\) 10.3130 3.75981i 0.430455 0.156931i
\(575\) −1.81187 + 3.76239i −0.0755603 + 0.156903i
\(576\) −0.900609 + 2.86163i −0.0375254 + 0.119234i
\(577\) 8.73281 0.654433i 0.363551 0.0272444i 0.108298 0.994119i \(-0.465460\pi\)
0.255254 + 0.966874i \(0.417841\pi\)
\(578\) −0.709500 0.161939i −0.0295113 0.00673576i
\(579\) 3.50219 + 31.9006i 0.145546 + 1.32574i
\(580\) −0.914060 0.985123i −0.0379543 0.0409050i
\(581\) −17.6480 + 28.9141i −0.732161 + 1.19956i
\(582\) −0.724817 + 17.9968i −0.0300446 + 0.745992i
\(583\) 23.5209 21.8242i 0.974135 0.903865i
\(584\) −2.91366 + 7.42390i −0.120568 + 0.307203i
\(585\) −3.82037 1.86672i −0.157953 0.0771795i
\(586\) 8.15025 + 11.9542i 0.336684 + 0.493825i
\(587\) −12.5492 + 21.7358i −0.517959 + 0.897132i 0.481823 + 0.876268i \(0.339975\pi\)
−0.999782 + 0.0208631i \(0.993359\pi\)
\(588\) 4.59000 11.2219i 0.189289 0.462785i
\(589\) 1.84158 + 3.18971i 0.0758809 + 0.131430i
\(590\) −0.0227637 + 0.0472693i −0.000937166 + 0.00194605i
\(591\) −42.4758 + 18.3879i −1.74722 + 0.756379i
\(592\) 2.13760 + 2.68046i 0.0878546 + 0.110166i
\(593\) −31.7479 9.79294i −1.30373 0.402148i −0.436343 0.899780i \(-0.643727\pi\)
−0.867388 + 0.497632i \(0.834203\pi\)
\(594\) −13.2766 + 15.1633i −0.544746 + 0.622156i
\(595\) 0.936428 2.22476i 0.0383898 0.0912065i
\(596\) −0.219660 + 0.712120i −0.00899762 + 0.0291696i
\(597\) −12.7356 + 28.9645i −0.521232 + 1.18544i
\(598\) 3.59680 3.87643i 0.147084 0.158519i
\(599\) 15.1066 + 22.1573i 0.617239 + 0.905323i 0.999827 0.0185959i \(-0.00591959\pi\)
−0.382588 + 0.923919i \(0.624967\pi\)
\(600\) −7.56688 4.02687i −0.308916 0.164396i
\(601\) −18.7702 27.5308i −0.765651 1.12300i −0.988949 0.148254i \(-0.952635\pi\)
0.223298 0.974750i \(-0.428318\pi\)
\(602\) 11.7045 + 25.9032i 0.477040 + 1.05574i
\(603\) −8.64718 28.6121i −0.352140 1.16518i
\(604\) −6.22322 5.77431i −0.253219 0.234953i
\(605\) −0.570282 + 0.715111i −0.0231853 + 0.0290734i
\(606\) 0.673657 0.576392i 0.0273654 0.0234143i
\(607\) 25.1643i 1.02139i −0.859763 0.510693i \(-0.829389\pi\)
0.859763 0.510693i \(-0.170611\pi\)
\(608\) −1.90646 0.287352i −0.0773170 0.0116537i
\(609\) 8.28947 + 25.9367i 0.335906 + 1.05101i
\(610\) 1.71807 0.258958i 0.0695628 0.0104849i
\(611\) 8.72684 + 57.8988i 0.353050 + 2.34233i
\(612\) 8.28171 8.82404i 0.334768 0.356690i
\(613\) −14.2051 9.68490i −0.573740 0.391170i 0.241406 0.970424i \(-0.422391\pi\)
−0.815147 + 0.579255i \(0.803344\pi\)
\(614\) −10.6375 + 27.1040i −0.429296 + 1.09383i
\(615\) 0.306710 1.59606i 0.0123677 0.0643593i
\(616\) 6.59214 7.86467i 0.265605 0.316876i
\(617\) −2.20719 + 14.6437i −0.0888580 + 0.589534i 0.899445 + 0.437033i \(0.143971\pi\)
−0.988303 + 0.152501i \(0.951267\pi\)
\(618\) −18.9109 22.1020i −0.760706 0.889075i
\(619\) 36.2862i 1.45846i −0.684267 0.729232i \(-0.739878\pi\)
0.684267 0.729232i \(-0.260122\pi\)
\(620\) −0.0643954 + 0.427235i −0.00258618 + 0.0171582i
\(621\) −4.15081 + 1.41267i −0.166566 + 0.0566886i
\(622\) 7.63003 + 15.8439i 0.305936 + 0.635283i
\(623\) −1.18894 + 1.94794i −0.0476340 + 0.0780426i
\(624\) 7.65332 + 7.69711i 0.306378 + 0.308131i
\(625\) 15.1105 18.9480i 0.604420 0.757918i
\(626\) 2.36525 1.61260i 0.0945345 0.0644525i
\(627\) −10.9474 6.92235i −0.437197 0.276452i
\(628\) −9.21531 + 13.5164i −0.367731 + 0.539362i
\(629\) −3.07745 13.4832i −0.122706 0.537610i
\(630\) −1.07650 1.43656i −0.0428887 0.0572340i
\(631\) 5.91159 25.9004i 0.235337 1.03108i −0.709801 0.704403i \(-0.751215\pi\)
0.945137 0.326674i \(-0.105928\pi\)
\(632\) −9.54040 10.2821i −0.379497 0.409000i
\(633\) 5.51191 28.6829i 0.219079 1.14004i
\(634\) 11.2488 + 3.46980i 0.446748 + 0.137803i
\(635\) 2.36822 + 1.14047i 0.0939799 + 0.0452583i
\(636\) 2.62362 + 14.0861i 0.104033 + 0.558549i
\(637\) −28.2332 33.5747i −1.11864 1.33028i
\(638\) 23.0468i 0.912430i
\(639\) −2.00915 + 24.9026i −0.0794807 + 0.985131i
\(640\) −0.153833 0.165792i −0.00608078 0.00655352i
\(641\) −18.4685 + 14.7282i −0.729463 + 0.581727i −0.916218 0.400679i \(-0.868774\pi\)
0.186756 + 0.982406i \(0.440203\pi\)
\(642\) −6.09652 14.0829i −0.240610 0.555806i
\(643\) 7.41142 + 24.0272i 0.292278 + 0.947542i 0.975995 + 0.217794i \(0.0698862\pi\)
−0.683717 + 0.729747i \(0.739638\pi\)
\(644\) 2.09750 0.764685i 0.0826529 0.0301328i
\(645\) 4.18079 + 0.483146i 0.164619 + 0.0190238i
\(646\) 6.42591 + 4.38111i 0.252824 + 0.172372i
\(647\) 30.6681 9.45984i 1.20569 0.371905i 0.374146 0.927370i \(-0.377936\pi\)
0.831540 + 0.555465i \(0.187460\pi\)
\(648\) −2.55448 8.62987i −0.100349 0.339013i
\(649\) 0.837557 0.328717i 0.0328770 0.0129033i
\(650\) −25.6246 + 17.4705i −1.00508 + 0.685251i
\(651\) 4.85789 7.28285i 0.190396 0.285437i
\(652\) 0.0467126 + 0.0318481i 0.00182941 + 0.00124727i
\(653\) 1.02773 + 0.234572i 0.0402180 + 0.00917950i 0.242583 0.970131i \(-0.422005\pi\)
−0.202365 + 0.979310i \(0.564863\pi\)
\(654\) 11.8733 7.41335i 0.464285 0.289885i
\(655\) −4.32999 −0.169187
\(656\) −2.07445 + 3.59305i −0.0809936 + 0.140285i
\(657\) −5.19076 23.3557i −0.202511 0.911193i
\(658\) −7.86059 + 23.4370i −0.306438 + 0.913670i
\(659\) 2.93217 + 19.4537i 0.114221 + 0.757807i 0.970466 + 0.241237i \(0.0775531\pi\)
−0.856245 + 0.516570i \(0.827209\pi\)
\(660\) −0.497736 1.43557i −0.0193743 0.0558796i
\(661\) 29.4601 + 2.20773i 1.14586 + 0.0858706i 0.634097 0.773254i \(-0.281372\pi\)
0.511767 + 0.859124i \(0.328991\pi\)
\(662\) −4.62919 0.346910i −0.179919 0.0134830i
\(663\) −14.3435 41.3696i −0.557055 1.60666i
\(664\) −1.90823 12.6603i −0.0740538 0.491315i
\(665\) 0.805102 0.826306i 0.0312205 0.0320428i
\(666\) −9.81090 3.08768i −0.380165 0.119645i
\(667\) −2.50695 + 4.34216i −0.0970695 + 0.168129i
\(668\) 2.23928 0.0866403
\(669\) −6.59725 + 4.11912i −0.255065 + 0.159254i
\(670\) 2.19690 + 0.501429i 0.0848738 + 0.0193719i
\(671\) −24.6195 16.7853i −0.950426 0.647990i
\(672\) 1.39509 + 4.36506i 0.0538167 + 0.168386i
\(673\) 18.0576 12.3115i 0.696069 0.474572i −0.162872 0.986647i \(-0.552076\pi\)
0.858940 + 0.512076i \(0.171123\pi\)
\(674\) −0.877884 + 0.344544i −0.0338148 + 0.0132713i
\(675\) 25.5770 2.66035i 0.984459 0.102397i
\(676\) 25.1057 7.74409i 0.965604 0.297850i
\(677\) 34.3354 + 23.4095i 1.31962 + 0.899699i 0.998873 0.0474669i \(-0.0151149\pi\)
0.320744 + 0.947166i \(0.396067\pi\)
\(678\) 31.2361 + 3.60975i 1.19962 + 0.138631i
\(679\) 14.9393 + 23.1036i 0.573316 + 0.886635i
\(680\) 0.268915 + 0.871802i 0.0103124 + 0.0334321i
\(681\) 4.04176 + 9.33639i 0.154880 + 0.357771i
\(682\) 5.79312 4.61986i 0.221830 0.176904i
\(683\) −19.5685 21.0898i −0.748766 0.806978i 0.237631 0.971355i \(-0.423629\pi\)
−0.986398 + 0.164377i \(0.947439\pi\)
\(684\) 5.22542 2.47980i 0.199799 0.0948174i
\(685\) 0.247660i 0.00946259i
\(686\) −4.14986 18.0493i −0.158442 0.689127i
\(687\) −2.52126 13.5365i −0.0961922 0.516450i
\(688\) −9.67962 4.66146i −0.369032 0.177717i
\(689\) 49.5387 + 15.2807i 1.88728 + 0.582147i
\(690\) 0.0623800 0.324613i 0.00237477 0.0123578i
\(691\) 16.9227 + 18.2383i 0.643770 + 0.693819i 0.967655 0.252277i \(-0.0811795\pi\)
−0.323885 + 0.946097i \(0.604989\pi\)
\(692\) 4.80633 21.0579i 0.182709 0.800502i
\(693\) −3.22382 + 30.6168i −0.122463 + 1.16304i
\(694\) −4.38128 19.1956i −0.166311 0.728656i
\(695\) −0.627961 + 0.921050i −0.0238199 + 0.0349374i
\(696\) −8.69855 5.50034i −0.329718 0.208490i
\(697\) 13.8281 9.42783i 0.523776 0.357105i
\(698\) 0.140400 0.176056i 0.00531423 0.00666383i
\(699\) −14.5648 14.6482i −0.550892 0.554044i
\(700\) −12.9909 + 1.63497i −0.491011 + 0.0617962i
\(701\) 8.85284 + 18.3831i 0.334367 + 0.694320i 0.998583 0.0532205i \(-0.0169486\pi\)
−0.664216 + 0.747541i \(0.731234\pi\)
\(702\) −31.9426 6.32753i −1.20560 0.238817i
\(703\) 0.985169 6.53617i 0.0371563 0.246516i
\(704\) 3.87868i 0.146183i
\(705\) 2.37950 + 2.78104i 0.0896173 + 0.104740i
\(706\) 4.29908 28.5226i 0.161798 1.07346i
\(707\) 0.333485 1.31259i 0.0125420 0.0493649i
\(708\) −0.0758236 + 0.394571i −0.00284963 + 0.0148289i
\(709\) −2.70848 + 6.90110i −0.101719 + 0.259176i −0.972669 0.232195i \(-0.925409\pi\)
0.870950 + 0.491372i \(0.163504\pi\)
\(710\) −1.55621 1.06100i −0.0584034 0.0398188i
\(711\) 40.9702 + 9.59746i 1.53650 + 0.359933i
\(712\) −0.128558 0.852925i −0.00481791 0.0319647i
\(713\) 1.59400 0.240256i 0.0596956 0.00899767i
\(714\) 2.56958 18.3061i 0.0961640 0.685090i
\(715\) −5.43605 0.819352i −0.203297 0.0306420i
\(716\) 16.8716i 0.630522i
\(717\) −28.2722 + 24.1902i −1.05585 + 0.903398i
\(718\) −1.73741 + 2.17864i −0.0648394 + 0.0813061i
\(719\) −24.6535 22.8751i −0.919420 0.853097i 0.0700933 0.997540i \(-0.477670\pi\)
−0.989513 + 0.144444i \(0.953861\pi\)
\(720\) 0.660619 + 0.154753i 0.0246198 + 0.00576731i
\(721\) −43.0647 10.9413i −1.60381 0.407476i
\(722\) −8.60914 12.6273i −0.320399 0.469939i
\(723\) −1.33432 0.710089i −0.0496241 0.0264085i
\(724\) 7.96999 + 11.6898i 0.296202 + 0.434449i
\(725\) 20.0009 21.5558i 0.742814 0.800563i
\(726\) −2.81944 + 6.41225i −0.104639 + 0.237981i
\(727\) −12.0527 + 39.0740i −0.447011 + 1.44917i 0.399465 + 0.916748i \(0.369196\pi\)
−0.846476 + 0.532426i \(0.821280\pi\)
\(728\) 16.3301 + 2.87050i 0.605232 + 0.106388i
\(729\) 20.8182 + 17.1931i 0.771044 + 0.636781i
\(730\) 1.72359 + 0.531658i 0.0637931 + 0.0196776i
\(731\) 27.0210 + 33.8833i 0.999409 + 1.25322i
\(732\) 12.2110 5.28618i 0.451331 0.195383i
\(733\) 5.31697 11.0408i 0.196387 0.407801i −0.779400 0.626527i \(-0.784476\pi\)
0.975786 + 0.218726i \(0.0701901\pi\)
\(734\) 3.29311 + 5.70383i 0.121551 + 0.210532i
\(735\) −2.60852 0.845539i −0.0962166 0.0311882i
\(736\) −0.421910 + 0.730770i −0.0155518 + 0.0269365i
\(737\) −21.7695 31.9299i −0.801888 1.17615i
\(738\) −0.859304 12.4170i −0.0316314 0.457076i
\(739\) −8.27647 + 21.0881i −0.304455 + 0.775738i 0.693990 + 0.719985i \(0.255851\pi\)
−0.998445 + 0.0557533i \(0.982244\pi\)
\(740\) 0.568409 0.527407i 0.0208951 0.0193878i
\(741\) 0.842157 20.9103i 0.0309374 0.768159i
\(742\) 15.6762 + 15.2739i 0.575491 + 0.560723i
\(743\) 26.0439 + 28.0687i 0.955458 + 1.02974i 0.999528 + 0.0307107i \(0.00977707\pi\)
−0.0440700 + 0.999028i \(0.514032\pi\)
\(744\) 0.361090 + 3.28908i 0.0132382 + 0.120583i
\(745\) 0.164321 + 0.0375051i 0.00602024 + 0.00137408i
\(746\) 23.7382 1.77894i 0.869119 0.0651314i
\(747\) 25.9643 + 28.3051i 0.949984 + 1.03563i
\(748\) 6.78862 14.0967i 0.248217 0.515427i
\(749\) −20.0086 12.2124i −0.731098 0.446232i
\(750\) −1.56868 + 3.56765i −0.0572802 + 0.130272i
\(751\) 6.94093 30.4102i 0.253278 1.10968i −0.675006 0.737812i \(-0.735859\pi\)
0.928284 0.371872i \(-0.121284\pi\)
\(752\) −3.41349 8.69744i −0.124477 0.317163i
\(753\) 43.3842 8.08058i 1.58101 0.294473i
\(754\) −32.2480 + 18.6184i −1.17440 + 0.678042i
\(755\) −1.19713 + 1.50115i −0.0435679 + 0.0546324i
\(756\) −10.7863 8.52379i −0.392295 0.310007i
\(757\) 5.77366 + 7.23994i 0.209847 + 0.263140i 0.875605 0.483028i \(-0.160463\pi\)
−0.665758 + 0.746168i \(0.731892\pi\)
\(758\) −24.9025 9.77351i −0.904500 0.354990i
\(759\) −4.57073 + 3.35325i −0.165907 + 0.121715i
\(760\) −0.0325860 + 0.434830i −0.00118202 + 0.0157729i
\(761\) −19.2997 24.2011i −0.699615 0.877289i 0.297380 0.954759i \(-0.403887\pi\)
−0.996995 + 0.0774703i \(0.975316\pi\)
\(762\) 19.7682 + 3.79881i 0.716128 + 0.137616i
\(763\) 8.29497 19.7072i 0.300298 0.713448i
\(764\) 9.58685 + 7.64526i 0.346840 + 0.276596i
\(765\) −2.13010 1.71868i −0.0770140 0.0621389i
\(766\) −23.9876 + 13.8493i −0.866708 + 0.500394i
\(767\) 1.13658 + 0.906391i 0.0410394 + 0.0327279i
\(768\) −1.46393 0.925687i −0.0528252 0.0334029i
\(769\) −12.7786 + 18.7428i −0.460809 + 0.675883i −0.984371 0.176104i \(-0.943650\pi\)
0.523562 + 0.851987i \(0.324603\pi\)
\(770\) −1.88518 1.35383i −0.0679370 0.0487888i
\(771\) −6.29952 1.70723i −0.226872 0.0614844i
\(772\) −18.3215 2.76152i −0.659406 0.0993894i
\(773\) −1.27686 17.0385i −0.0459254 0.612832i −0.971922 0.235302i \(-0.924392\pi\)
0.925997 0.377531i \(-0.123227\pi\)
\(774\) 31.8976 4.62180i 1.14654 0.166127i
\(775\) −9.42765 0.706504i −0.338651 0.0253784i
\(776\) −9.93690 3.06513i −0.356714 0.110032i
\(777\) −14.9653 + 4.78297i −0.536878 + 0.171588i
\(778\) 13.0574 4.02767i 0.468130 0.144399i
\(779\) 7.79849 1.77995i 0.279410 0.0637734i
\(780\) 1.60662 1.85618i 0.0575261 0.0664621i
\(781\) 7.18765 + 31.4912i 0.257194 + 1.12684i
\(782\) 2.81242 1.91747i 0.100572 0.0685687i
\(783\) 30.8622 0.890335i 1.10292 0.0318180i
\(784\) 5.58441 + 4.22071i 0.199443 + 0.150740i
\(785\) 3.20417 + 1.84993i 0.114362 + 0.0660267i
\(786\) −32.0547 + 8.49108i −1.14335 + 0.302867i
\(787\) 6.56209 21.2738i 0.233913 0.758328i −0.760172 0.649722i \(-0.774885\pi\)
0.994085 0.108606i \(-0.0346386\pi\)
\(788\) −3.98282 26.4243i −0.141882 0.941325i
\(789\) −12.6174 + 5.46214i −0.449193 + 0.194457i
\(790\) −2.15773 + 2.32548i −0.0767685 + 0.0827368i
\(791\) 42.1701 22.9936i 1.49940 0.817559i
\(792\) −6.49985 9.65140i −0.230962 0.342948i
\(793\) 3.59776 48.0088i 0.127760 1.70484i
\(794\) −8.15150 + 35.7140i −0.289286 + 1.26744i
\(795\) 3.13256 0.829794i 0.111100 0.0294298i
\(796\) −14.2823 11.3898i −0.506224 0.403700i
\(797\) 0.993820 + 13.2616i 0.0352029 + 0.469750i 0.986750 + 0.162248i \(0.0518743\pi\)
−0.951547 + 0.307503i \(0.900507\pi\)
\(798\) 4.33974 7.69589i 0.153625 0.272432i
\(799\) −2.81657 + 37.5845i −0.0996430 + 1.32964i
\(800\) 3.36607 3.62776i 0.119009 0.128261i
\(801\) 1.74922 + 1.90691i 0.0618055 + 0.0673775i
\(802\) 5.79873 + 10.0437i 0.204760 + 0.354655i
\(803\) −15.4666 26.7890i −0.545805 0.945362i
\(804\) 17.2468 0.596061i 0.608249 0.0210215i
\(805\) −0.207914 0.460134i −0.00732801 0.0162176i
\(806\) 11.1443 + 4.37382i 0.392541 + 0.154061i
\(807\) −1.12754 + 5.86752i −0.0396914 + 0.206546i
\(808\) 0.222093 + 0.461181i 0.00781321 + 0.0162243i
\(809\) 19.8224 29.0742i 0.696919 1.02219i −0.300733 0.953708i \(-0.597231\pi\)
0.997652 0.0684845i \(-0.0218164\pi\)
\(810\) −1.90316 + 0.721982i −0.0668703 + 0.0253679i
\(811\) −23.3608 + 18.6296i −0.820309 + 0.654175i −0.940959 0.338521i \(-0.890074\pi\)
0.120650 + 0.992695i \(0.461502\pi\)
\(812\) −15.7008 + 0.791942i −0.550991 + 0.0277917i
\(813\) 19.4918 12.1701i 0.683606 0.426822i
\(814\) −13.2978 −0.466088
\(815\) 0.00639335 0.0110736i 0.000223949 0.000387892i
\(816\) 3.70036 + 5.92656i 0.129539 + 0.207471i
\(817\) 6.10542 + 19.7933i 0.213601 + 0.692479i
\(818\) −8.09676 + 3.89919i −0.283096 + 0.136332i
\(819\) −45.4448 + 20.2230i −1.58797 + 0.706649i
\(820\) 0.845420 + 0.407133i 0.0295234 + 0.0142177i
\(821\) 3.27841 21.7508i 0.114417 0.759109i −0.855877 0.517180i \(-0.826982\pi\)
0.970294 0.241929i \(-0.0777802\pi\)
\(822\) −0.485659 1.83341i −0.0169393 0.0639475i
\(823\) −16.9229 15.7022i −0.589896 0.547343i 0.327739 0.944768i \(-0.393713\pi\)
−0.917635 + 0.397425i \(0.869904\pi\)
\(824\) 15.1309 7.28667i 0.527111 0.253843i
\(825\) 30.5105 13.2081i 1.06224 0.459847i
\(826\) 0.252722 + 0.559299i 0.00879333 + 0.0194605i
\(827\) −22.8161 5.20762i −0.793392 0.181087i −0.193429 0.981114i \(-0.561961\pi\)
−0.599963 + 0.800028i \(0.704818\pi\)
\(828\) −0.174769 2.52542i −0.00607364 0.0877645i
\(829\) −29.0104 11.3857i −1.00757 0.395443i −0.196572 0.980489i \(-0.562981\pi\)
−0.811000 + 0.585047i \(0.801076\pi\)
\(830\) −2.82309 + 0.644352i −0.0979909 + 0.0223658i
\(831\) 48.3195 + 13.0950i 1.67619 + 0.454262i
\(832\) −5.42722 + 3.13341i −0.188155 + 0.108631i
\(833\) −12.9088 25.1138i −0.447262 0.870143i
\(834\) −2.84259 + 8.04991i −0.0984308 + 0.278746i
\(835\) −0.0378472 0.505036i −0.00130976 0.0174775i
\(836\) 5.48181 5.08638i 0.189592 0.175916i
\(837\) −6.41031 7.57917i −0.221573 0.261974i
\(838\) −1.05581 + 3.42286i −0.0364724 + 0.118241i
\(839\) −24.4225 22.6608i −0.843159 0.782337i 0.134858 0.990865i \(-0.456942\pi\)
−0.978016 + 0.208528i \(0.933133\pi\)
\(840\) 0.960894 0.388417i 0.0331540 0.0134017i
\(841\) 4.62278 4.28931i 0.159406 0.147907i
\(842\) −0.491637 1.02090i −0.0169429 0.0351824i
\(843\) −2.67094 + 4.22398i −0.0919920 + 0.145481i
\(844\) 15.1931 + 7.31662i 0.522968 + 0.251848i
\(845\) −2.17089 5.53133i −0.0746808 0.190284i
\(846\) 23.0689 + 15.9217i 0.793127 + 0.547400i
\(847\) 2.12570 + 10.4866i 0.0730400 + 0.360324i
\(848\) −8.24932 0.618201i −0.283283 0.0212291i
\(849\) 3.64699 5.76756i 0.125164 0.197942i
\(850\) −18.5831 + 7.29334i −0.637396 + 0.250159i
\(851\) −2.50540 1.44649i −0.0858840 0.0495851i
\(852\) −13.6011 4.80285i −0.465967 0.164543i
\(853\) 45.9761 18.0443i 1.57419 0.617825i 0.592039 0.805910i \(-0.298323\pi\)
0.982153 + 0.188085i \(0.0602281\pi\)
\(854\) 10.5892 17.3491i 0.362354 0.593674i
\(855\) −0.647598 1.13660i −0.0221474 0.0388710i
\(856\) 8.76096 1.32050i 0.299443 0.0451338i
\(857\) 6.85974 3.30348i 0.234324 0.112845i −0.313037 0.949741i \(-0.601347\pi\)
0.547362 + 0.836896i \(0.315632\pi\)
\(858\) −41.8495 + 4.59443i −1.42872 + 0.156851i
\(859\) −33.3472 + 26.5935i −1.13779 + 0.907359i −0.996581 0.0826206i \(-0.973671\pi\)
−0.141211 + 0.989980i \(0.545100\pi\)
\(860\) −0.887723 + 2.26188i −0.0302711 + 0.0771295i
\(861\) −12.0044 14.7437i −0.409107 0.502463i
\(862\) −14.8894 37.9377i −0.507136 1.29216i
\(863\) 40.5312 + 23.4007i 1.37970 + 0.796569i 0.992123 0.125269i \(-0.0399793\pi\)
0.387576 + 0.921838i \(0.373313\pi\)
\(864\) 5.19399 0.149840i 0.176703 0.00509766i
\(865\) −4.83053 0.728086i −0.164243 0.0247557i
\(866\) −10.6765 + 3.29326i −0.362802 + 0.111910i
\(867\) 0.137556 + 1.25296i 0.00467165 + 0.0425529i
\(868\) 3.34639 + 3.78787i 0.113584 + 0.128569i
\(869\) 54.2520 4.06562i 1.84037 0.137917i
\(870\) −1.09350 + 2.05479i −0.0370732 + 0.0696640i
\(871\) 27.0912 56.2555i 0.917951 1.90614i
\(872\) 2.38208 + 7.72251i 0.0806673 + 0.261517i
\(873\) 29.8627 9.02513i 1.01070 0.305454i
\(874\) 1.58609 0.362014i 0.0536503 0.0122453i
\(875\) 1.18270 + 5.83456i 0.0399826 + 0.197244i
\(876\) 13.8022 + 0.555882i 0.466335 + 0.0187815i
\(877\) −4.13792 18.1294i −0.139728 0.612187i −0.995494 0.0948245i \(-0.969771\pi\)
0.855766 0.517363i \(-0.173086\pi\)
\(878\) 21.3390 3.21634i 0.720156 0.108546i
\(879\) 14.9384 20.1205i 0.503861 0.678647i
\(880\) 0.874779 0.0655556i 0.0294888 0.00220988i
\(881\) −18.5371 −0.624532 −0.312266 0.949995i \(-0.601088\pi\)
−0.312266 + 0.949995i \(0.601088\pi\)
\(882\) −20.9688 1.14419i −0.706056 0.0385269i
\(883\) 50.8498 1.71123 0.855617 0.517610i \(-0.173178\pi\)
0.855617 + 0.517610i \(0.173178\pi\)
\(884\) 25.2089 1.88915i 0.847868 0.0635389i
\(885\) 0.0902712 + 0.0104320i 0.00303443 + 0.000350669i
\(886\) −15.1243 + 2.27962i −0.508111 + 0.0765854i
\(887\) 4.01372 + 17.5852i 0.134767 + 0.590455i 0.996537 + 0.0831544i \(0.0264995\pi\)
−0.861769 + 0.507301i \(0.830643\pi\)
\(888\) 3.17366 5.01901i 0.106501 0.168427i
\(889\) 28.0212 12.6615i 0.939800 0.424654i
\(890\) −0.190192 + 0.0434100i −0.00637524 + 0.00145511i
\(891\) 32.3474 + 13.1234i 1.08368 + 0.439650i
\(892\) −1.32357 4.29090i −0.0443163 0.143670i
\(893\) −7.81590 + 16.2299i −0.261549 + 0.543113i
\(894\) 1.29000 0.0445833i 0.0431442 0.00149109i
\(895\) 3.80514 0.285156i 0.127192 0.00953171i
\(896\) −2.64239 + 0.133281i −0.0882761 + 0.00445260i
\(897\) −8.38449 3.68663i −0.279950 0.123093i
\(898\) 15.9452 4.91845i 0.532099 0.164131i
\(899\) −11.2244 1.69180i −0.374354 0.0564248i
\(900\) −2.29650 + 14.6679i −0.0765499 + 0.488929i
\(901\) 28.8994 + 16.6851i 0.962779 + 0.555861i
\(902\) −5.87916 14.9799i −0.195755 0.498775i
\(903\) 35.7490 33.8515i 1.18965 1.12651i
\(904\) −6.63248 + 16.8993i −0.220593 + 0.562062i
\(905\) 2.50176 1.99509i 0.0831613 0.0663189i
\(906\) −5.91852 + 13.4605i −0.196630 + 0.447195i
\(907\) 3.11507 1.50014i 0.103434 0.0498113i −0.381451 0.924389i \(-0.624576\pi\)
0.484885 + 0.874578i \(0.338861\pi\)
\(908\) −5.80818 + 0.875442i −0.192751 + 0.0290526i
\(909\) −1.32548 0.775385i −0.0439634 0.0257179i
\(910\) 0.371396 3.73152i 0.0123117 0.123699i
\(911\) 47.8844 18.7932i 1.58648 0.622648i 0.602055 0.798454i \(-0.294349\pi\)
0.984425 + 0.175807i \(0.0562533\pi\)
\(912\) 0.611465 + 3.28292i 0.0202476 + 0.108708i
\(913\) 43.0068 + 24.8300i 1.42332 + 0.821753i
\(914\) −24.9385 + 9.78765i −0.824893 + 0.323747i
\(915\) −1.39860 2.66466i −0.0462364 0.0880910i
\(916\) 7.92748 + 0.594083i 0.261931 + 0.0196290i
\(917\) −32.5386 + 38.8198i −1.07452 + 1.28194i
\(918\) −19.1393 8.54614i −0.631692 0.282065i
\(919\) −17.7149 45.1368i −0.584360 1.48892i −0.851020 0.525134i \(-0.824015\pi\)
0.266660 0.963791i \(-0.414080\pi\)
\(920\) 0.171945 + 0.0828044i 0.00566886 + 0.00272998i
\(921\) 50.3908 + 2.02947i 1.66043 + 0.0668735i
\(922\) 10.8640 + 22.5594i 0.357787 + 0.742953i
\(923\) −38.2572 + 35.4975i −1.25925 + 1.16842i
\(924\) −16.6107 6.32554i −0.546452 0.208095i
\(925\) 12.4376 + 11.5404i 0.408944 + 0.379445i
\(926\) 8.59674 27.8699i 0.282506 0.915863i
\(927\) −25.4396 + 43.4878i −0.835547 + 1.42833i
\(928\) 4.35572 4.04152i 0.142984 0.132669i
\(929\) −1.06339 14.1900i −0.0348888 0.465559i −0.987099 0.160114i \(-0.948814\pi\)
0.952210 0.305445i \(-0.0988052\pi\)
\(930\) 0.735700 0.137029i 0.0241245 0.00449335i
\(931\) −1.35800 13.4274i −0.0445067 0.440067i
\(932\) 10.3284 5.96310i 0.338318 0.195328i
\(933\) 21.5990 21.4761i 0.707120 0.703096i
\(934\) 8.92878 2.03794i 0.292159 0.0666833i
\(935\) −3.29404 1.29282i −0.107727 0.0422796i
\(936\) 8.25373 16.8918i 0.269781 0.552125i
\(937\) −37.9735 8.66720i −1.24054 0.283145i −0.448593 0.893736i \(-0.648075\pi\)
−0.791946 + 0.610591i \(0.790932\pi\)
\(938\) 21.0045 15.9279i 0.685823 0.520063i
\(939\) −3.98102 2.95571i −0.129916 0.0964558i
\(940\) −1.90388 + 0.916863i −0.0620979 + 0.0299048i
\(941\) −10.1258 9.39537i −0.330092 0.306280i 0.497663 0.867370i \(-0.334192\pi\)
−0.827755 + 0.561090i \(0.810382\pi\)
\(942\) 27.3480 + 7.41156i 0.891045 + 0.241482i
\(943\) 0.521786 3.46182i 0.0169917 0.112732i
\(944\) −0.209001 0.100650i −0.00680241 0.00327587i
\(945\) −1.74011 + 2.57676i −0.0566057 + 0.0838221i
\(946\) 37.5442 18.0803i 1.22067 0.587842i
\(947\) −12.1837 39.4985i −0.395916 1.28353i −0.905954 0.423376i \(-0.860845\pi\)
0.510038 0.860152i \(-0.329631\pi\)
\(948\) −11.4133 + 21.4467i −0.370686 + 0.696555i
\(949\) 24.9895 43.2831i 0.811194 1.40503i
\(950\) −9.54134 −0.309562
\(951\) −0.704248 20.3772i −0.0228368 0.660776i
\(952\) 9.83680 + 4.14042i 0.318813 + 0.134192i
\(953\) 10.1984 8.13294i 0.330358 0.263452i −0.444237 0.895909i \(-0.646525\pi\)
0.774595 + 0.632458i \(0.217954\pi\)
\(954\) 21.5629 12.2858i 0.698125 0.397769i
\(955\) 1.56224 2.29139i 0.0505530 0.0741476i
\(956\) −9.32087 19.3550i −0.301458 0.625985i
\(957\) 37.7155 13.0766i 1.21917 0.422706i
\(958\) −1.14110 0.447849i −0.0368673 0.0144693i
\(959\) −2.22035 1.86109i −0.0716988 0.0600977i
\(960\) −0.184032 + 0.345814i −0.00593961 + 0.0111611i
\(961\) −13.6753 23.6862i −0.441137 0.764073i
\(962\) −10.7427 18.6069i −0.346358 0.599910i
\(963\) −19.5872 + 17.9674i −0.631188 + 0.578990i
\(964\) 0.593565 0.639711i 0.0191174 0.0206037i
\(965\) −0.313159 + 4.17882i −0.0100809 + 0.134521i
\(966\) −2.44150 2.99863i −0.0785539 0.0964793i
\(967\) −1.09831 14.6560i −0.0353193 0.471304i −0.986620 0.163038i \(-0.947871\pi\)
0.951300 0.308265i \(-0.0997485\pi\)
\(968\) −3.16187 2.52150i −0.101626 0.0810442i
\(969\) 3.52358 13.0017i 0.113194 0.417674i
\(970\) −0.523345 + 2.29292i −0.0168036 + 0.0736213i
\(971\) 1.76060 23.4936i 0.0565003 0.753944i −0.894955 0.446157i \(-0.852792\pi\)
0.951455 0.307787i \(-0.0995886\pi\)
\(972\) −12.6732 + 9.07688i −0.406493 + 0.291141i
\(973\) 3.53857 + 12.5513i 0.113441 + 0.402376i
\(974\) −4.82097 + 5.19577i −0.154474 + 0.166483i
\(975\) 43.1294 + 32.0214i 1.38125 + 1.02551i
\(976\) 1.14498 + 7.59647i 0.0366500 + 0.243157i
\(977\) 8.46856 27.4544i 0.270933 0.878344i −0.713207 0.700953i \(-0.752758\pi\)
0.984140 0.177391i \(-0.0567657\pi\)
\(978\) 0.0256144 0.0945146i 0.000819057 0.00302225i
\(979\) 2.89737 + 1.67280i 0.0926003 + 0.0534628i
\(980\) 0.857533 1.33082i 0.0273929 0.0425113i
\(981\) −18.8687 15.2242i −0.602430 0.486071i
\(982\) −27.4785 + 18.7345i −0.876875 + 0.597843i
\(983\) −6.27833 27.5071i −0.200247 0.877342i −0.970786 0.239948i \(-0.922870\pi\)
0.770538 0.637394i \(-0.219987\pi\)
\(984\) 7.05698 + 1.35612i 0.224968 + 0.0432315i
\(985\) −5.89228 + 1.34487i −0.187744 + 0.0428513i
\(986\) −22.9041 + 7.06498i −0.729415 + 0.224995i
\(987\) 42.8142 0.434312i 1.36279 0.0138243i
\(988\) 11.5456 + 3.56134i 0.367314 + 0.113301i
\(989\) 9.04030 + 0.677477i 0.287465 + 0.0215425i
\(990\) −2.06687 + 1.62907i −0.0656895 + 0.0517752i
\(991\) −0.756305 10.0922i −0.0240248 0.320589i −0.996249 0.0865362i \(-0.972420\pi\)
0.972224 0.234053i \(-0.0751989\pi\)
\(992\) −1.88902 0.284724i −0.0599765 0.00904001i
\(993\) 2.05886 + 7.77242i 0.0653361 + 0.246650i
\(994\) −21.2067 + 5.97877i −0.672635 + 0.189635i
\(995\) −2.32740 + 3.41367i −0.0737836 + 0.108221i
\(996\) −19.6356 + 10.3062i −0.622178 + 0.326563i
\(997\) 28.3628 + 22.6185i 0.898258 + 0.716337i 0.959477 0.281788i \(-0.0909274\pi\)
−0.0612190 + 0.998124i \(0.519499\pi\)
\(998\) 2.79308 1.61259i 0.0884135 0.0510456i
\(999\) 0.513717 + 17.8073i 0.0162533 + 0.563397i
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 882.2.bc.a.551.39 yes 672
9.5 odd 6 882.2.bk.a.257.32 yes 672
49.45 odd 42 882.2.bk.a.731.32 yes 672
441.437 even 42 inner 882.2.bc.a.437.39 672
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.bc.a.437.39 672 441.437 even 42 inner
882.2.bc.a.551.39 yes 672 1.1 even 1 trivial
882.2.bk.a.257.32 yes 672 9.5 odd 6
882.2.bk.a.731.32 yes 672 49.45 odd 42