Properties

Label 570.2.u.i.511.2
Level $570$
Weight $2$
Character 570.511
Analytic conductor $4.551$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(61,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.u (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 511.2
Root \(2.01431i\) of defining polynomial
Character \(\chi\) \(=\) 570.511
Dual form 570.2.u.i.541.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 - 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(0.766044 - 0.642788i) q^{6} +(1.48371 + 2.56987i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\) \(q+(0.173648 - 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(0.766044 - 0.642788i) q^{6} +(1.48371 + 2.56987i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.173648 + 0.984808i) q^{10} +(-1.71767 + 2.97509i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.25638 + 1.05423i) q^{13} +(2.78847 - 1.01492i) q^{14} +(-0.939693 - 0.342020i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.0455330 + 0.258230i) q^{17} +1.00000 q^{18} +(-0.0583546 + 4.35851i) q^{19} +1.00000 q^{20} +(-0.515288 + 2.92234i) q^{21} +(2.63162 + 2.20819i) q^{22} +(-0.142073 - 0.0517103i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.820043 + 1.42036i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.515288 - 2.92234i) q^{28} +(-0.841640 - 4.77318i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(1.71287 + 2.96678i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-3.22816 + 1.17495i) q^{33} +(0.246401 + 0.0896825i) q^{34} +(-2.27318 - 1.90742i) q^{35} +(0.173648 - 0.984808i) q^{36} +12.0459 q^{37} +(4.28216 + 0.814315i) q^{38} -1.64009 q^{39} +(0.173648 - 0.984808i) q^{40} +(4.43490 + 3.72132i) q^{41} +(2.78847 + 1.01492i) q^{42} +(0.567130 - 0.206418i) q^{43} +(2.63162 - 2.20819i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.0755955 + 0.130935i) q^{46} +(0.582418 + 3.30305i) q^{47} +(0.173648 + 0.984808i) q^{48} +(-0.902808 + 1.56371i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.200868 + 0.168548i) q^{51} +(1.54118 - 0.560943i) q^{52} +(-11.1393 - 4.05436i) q^{53} +(0.766044 + 0.642788i) q^{54} +(0.596540 - 3.38315i) q^{55} -2.96743 q^{56} +(-2.84630 + 3.30130i) q^{57} -4.84681 q^{58} +(0.473734 - 2.68668i) q^{59} +(0.766044 + 0.642788i) q^{60} +(-2.41562 - 0.879213i) q^{61} +(3.21915 - 1.17167i) q^{62} +(-2.27318 + 1.90742i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.820043 - 1.42036i) q^{65} +(0.596540 + 3.38315i) q^{66} +(0.0888612 + 0.503957i) q^{67} +(0.131107 - 0.227084i) q^{68} +(-0.0755955 - 0.130935i) q^{69} +(-2.27318 + 1.90742i) q^{70} +(4.34247 - 1.58053i) q^{71} +(-0.939693 - 0.342020i) q^{72} +(-4.88951 - 4.10279i) q^{73} +(2.09174 - 11.8629i) q^{74} +1.00000 q^{75} +(1.54553 - 4.07570i) q^{76} -10.1941 q^{77} +(-0.284798 + 1.61517i) q^{78} +(4.61178 + 3.86975i) q^{79} +(-0.939693 - 0.342020i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(4.43490 - 3.72132i) q^{82} +(-3.78497 - 6.55577i) q^{83} +(1.48371 - 2.56987i) q^{84} +(-0.0455330 - 0.258230i) q^{85} +(-0.104801 - 0.594358i) q^{86} +(2.42341 - 4.19746i) q^{87} +(-1.71767 - 2.97509i) q^{88} +(6.99321 - 5.86800i) q^{89} +(-0.939693 + 0.342020i) q^{90} +(-4.57333 - 1.66456i) q^{91} +(0.115819 + 0.0971837i) q^{92} +(-0.594874 + 3.37370i) q^{93} +3.35401 q^{94} +(-1.43586 - 4.11562i) q^{95} +1.00000 q^{96} +(-1.28262 + 7.27409i) q^{97} +(1.38318 + 1.16063i) q^{98} +(-3.22816 - 1.17495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{7} - 6 q^{8} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{9}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 0.984808i 0.122788 0.696364i
\(3\) 0.766044 + 0.642788i 0.442276 + 0.371114i
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) −0.939693 + 0.342020i −0.420243 + 0.152956i
\(6\) 0.766044 0.642788i 0.312736 0.262417i
\(7\) 1.48371 + 2.56987i 0.560791 + 0.971318i 0.997428 + 0.0716803i \(0.0228361\pi\)
−0.436637 + 0.899638i \(0.643831\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 0.173648 + 0.984808i 0.0578827 + 0.328269i
\(10\) 0.173648 + 0.984808i 0.0549124 + 0.311424i
\(11\) −1.71767 + 2.97509i −0.517897 + 0.897023i 0.481887 + 0.876233i \(0.339951\pi\)
−0.999784 + 0.0207899i \(0.993382\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) −1.25638 + 1.05423i −0.348457 + 0.292390i −0.800170 0.599773i \(-0.795257\pi\)
0.451713 + 0.892163i \(0.350813\pi\)
\(14\) 2.78847 1.01492i 0.745249 0.271249i
\(15\) −0.939693 0.342020i −0.242628 0.0883092i
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) −0.0455330 + 0.258230i −0.0110434 + 0.0626301i −0.989831 0.142245i \(-0.954568\pi\)
0.978788 + 0.204875i \(0.0656789\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.0583546 + 4.35851i −0.0133875 + 0.999910i
\(20\) 1.00000 0.223607
\(21\) −0.515288 + 2.92234i −0.112445 + 0.637708i
\(22\) 2.63162 + 2.20819i 0.561063 + 0.470788i
\(23\) −0.142073 0.0517103i −0.0296243 0.0107824i 0.327166 0.944967i \(-0.393907\pi\)
−0.356790 + 0.934185i \(0.616129\pi\)
\(24\) −0.939693 + 0.342020i −0.191814 + 0.0698146i
\(25\) 0.766044 0.642788i 0.153209 0.128558i
\(26\) 0.820043 + 1.42036i 0.160824 + 0.278555i
\(27\) −0.500000 + 0.866025i −0.0962250 + 0.166667i
\(28\) −0.515288 2.92234i −0.0973803 0.552271i
\(29\) −0.841640 4.77318i −0.156289 0.886357i −0.957598 0.288107i \(-0.906974\pi\)
0.801310 0.598250i \(-0.204137\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 1.71287 + 2.96678i 0.307641 + 0.532850i 0.977846 0.209326i \(-0.0671271\pi\)
−0.670205 + 0.742176i \(0.733794\pi\)
\(32\) 0.766044 0.642788i 0.135419 0.113630i
\(33\) −3.22816 + 1.17495i −0.561951 + 0.204533i
\(34\) 0.246401 + 0.0896825i 0.0422574 + 0.0153804i
\(35\) −2.27318 1.90742i −0.384238 0.322414i
\(36\) 0.173648 0.984808i 0.0289414 0.164135i
\(37\) 12.0459 1.98033 0.990165 0.139906i \(-0.0446800\pi\)
0.990165 + 0.139906i \(0.0446800\pi\)
\(38\) 4.28216 + 0.814315i 0.694658 + 0.132099i
\(39\) −1.64009 −0.262624
\(40\) 0.173648 0.984808i 0.0274562 0.155712i
\(41\) 4.43490 + 3.72132i 0.692615 + 0.581173i 0.919662 0.392711i \(-0.128463\pi\)
−0.227047 + 0.973884i \(0.572907\pi\)
\(42\) 2.78847 + 1.01492i 0.430270 + 0.156605i
\(43\) 0.567130 0.206418i 0.0864865 0.0314785i −0.298415 0.954436i \(-0.596458\pi\)
0.384901 + 0.922958i \(0.374236\pi\)
\(44\) 2.63162 2.20819i 0.396732 0.332897i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) −0.0755955 + 0.130935i −0.0111459 + 0.0193053i
\(47\) 0.582418 + 3.30305i 0.0849543 + 0.481800i 0.997366 + 0.0725273i \(0.0231064\pi\)
−0.912412 + 0.409273i \(0.865782\pi\)
\(48\) 0.173648 + 0.984808i 0.0250640 + 0.142145i
\(49\) −0.902808 + 1.56371i −0.128973 + 0.223387i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) −0.200868 + 0.168548i −0.0281271 + 0.0236014i
\(52\) 1.54118 0.560943i 0.213723 0.0777888i
\(53\) −11.1393 4.05436i −1.53009 0.556909i −0.566450 0.824096i \(-0.691684\pi\)
−0.963645 + 0.267187i \(0.913906\pi\)
\(54\) 0.766044 + 0.642788i 0.104245 + 0.0874723i
\(55\) 0.596540 3.38315i 0.0804374 0.456183i
\(56\) −2.96743 −0.396539
\(57\) −2.84630 + 3.30130i −0.377001 + 0.437268i
\(58\) −4.84681 −0.636417
\(59\) 0.473734 2.68668i 0.0616750 0.349776i −0.938317 0.345776i \(-0.887616\pi\)
0.999992 0.00399993i \(-0.00127322\pi\)
\(60\) 0.766044 + 0.642788i 0.0988959 + 0.0829835i
\(61\) −2.41562 0.879213i −0.309288 0.112572i 0.182713 0.983166i \(-0.441512\pi\)
−0.492001 + 0.870595i \(0.663734\pi\)
\(62\) 3.21915 1.17167i 0.408832 0.148803i
\(63\) −2.27318 + 1.90742i −0.286394 + 0.240313i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0.820043 1.42036i 0.101714 0.176174i
\(66\) 0.596540 + 3.38315i 0.0734290 + 0.416437i
\(67\) 0.0888612 + 0.503957i 0.0108561 + 0.0615681i 0.989755 0.142779i \(-0.0456039\pi\)
−0.978898 + 0.204347i \(0.934493\pi\)
\(68\) 0.131107 0.227084i 0.0158991 0.0275380i
\(69\) −0.0755955 0.130935i −0.00910062 0.0157627i
\(70\) −2.27318 + 1.90742i −0.271697 + 0.227981i
\(71\) 4.34247 1.58053i 0.515356 0.187574i −0.0712319 0.997460i \(-0.522693\pi\)
0.586588 + 0.809886i \(0.300471\pi\)
\(72\) −0.939693 0.342020i −0.110744 0.0403075i
\(73\) −4.88951 4.10279i −0.572274 0.480195i 0.310126 0.950696i \(-0.399629\pi\)
−0.882400 + 0.470501i \(0.844073\pi\)
\(74\) 2.09174 11.8629i 0.243160 1.37903i
\(75\) 1.00000 0.115470
\(76\) 1.54553 4.07570i 0.177285 0.467515i
\(77\) −10.1941 −1.16173
\(78\) −0.284798 + 1.61517i −0.0322470 + 0.182882i
\(79\) 4.61178 + 3.86975i 0.518866 + 0.435380i 0.864236 0.503086i \(-0.167802\pi\)
−0.345370 + 0.938467i \(0.612247\pi\)
\(80\) −0.939693 0.342020i −0.105061 0.0382390i
\(81\) −0.939693 + 0.342020i −0.104410 + 0.0380022i
\(82\) 4.43490 3.72132i 0.489752 0.410951i
\(83\) −3.78497 6.55577i −0.415455 0.719589i 0.580021 0.814601i \(-0.303044\pi\)
−0.995476 + 0.0950125i \(0.969711\pi\)
\(84\) 1.48371 2.56987i 0.161886 0.280395i
\(85\) −0.0455330 0.258230i −0.00493875 0.0280090i
\(86\) −0.104801 0.594358i −0.0113010 0.0640912i
\(87\) 2.42341 4.19746i 0.259816 0.450015i
\(88\) −1.71767 2.97509i −0.183104 0.317146i
\(89\) 6.99321 5.86800i 0.741278 0.622006i −0.191902 0.981414i \(-0.561466\pi\)
0.933181 + 0.359408i \(0.117021\pi\)
\(90\) −0.939693 + 0.342020i −0.0990523 + 0.0360521i
\(91\) −4.57333 1.66456i −0.479415 0.174493i
\(92\) 0.115819 + 0.0971837i 0.0120750 + 0.0101321i
\(93\) −0.594874 + 3.37370i −0.0616856 + 0.349836i
\(94\) 3.35401 0.345940
\(95\) −1.43586 4.11562i −0.147316 0.422253i
\(96\) 1.00000 0.102062
\(97\) −1.28262 + 7.27409i −0.130230 + 0.738572i 0.847833 + 0.530263i \(0.177907\pi\)
−0.978063 + 0.208309i \(0.933204\pi\)
\(98\) 1.38318 + 1.16063i 0.139722 + 0.117241i
\(99\) −3.22816 1.17495i −0.324442 0.118087i
\(100\) −0.939693 + 0.342020i −0.0939693 + 0.0342020i
\(101\) 7.40227 6.21124i 0.736554 0.618042i −0.195356 0.980732i \(-0.562586\pi\)
0.931910 + 0.362691i \(0.118142\pi\)
\(102\) 0.131107 + 0.227084i 0.0129815 + 0.0224847i
\(103\) −5.17272 + 8.95942i −0.509684 + 0.882798i 0.490254 + 0.871580i \(0.336904\pi\)
−0.999937 + 0.0112179i \(0.996429\pi\)
\(104\) −0.284798 1.61517i −0.0279267 0.158380i
\(105\) −0.515288 2.92234i −0.0502870 0.285192i
\(106\) −5.92708 + 10.2660i −0.575688 + 0.997122i
\(107\) −3.88303 6.72560i −0.375387 0.650189i 0.614998 0.788528i \(-0.289157\pi\)
−0.990385 + 0.138340i \(0.955823\pi\)
\(108\) 0.766044 0.642788i 0.0737127 0.0618523i
\(109\) 6.37643 2.32083i 0.610752 0.222295i −0.0180805 0.999837i \(-0.505756\pi\)
0.628832 + 0.777541i \(0.283533\pi\)
\(110\) −3.22816 1.17495i −0.307793 0.112028i
\(111\) 9.22768 + 7.74294i 0.875852 + 0.734927i
\(112\) −0.515288 + 2.92234i −0.0486901 + 0.276136i
\(113\) −6.17814 −0.581190 −0.290595 0.956846i \(-0.593853\pi\)
−0.290595 + 0.956846i \(0.593853\pi\)
\(114\) 2.75689 + 3.37632i 0.258207 + 0.316221i
\(115\) 0.151191 0.0140986
\(116\) −0.841640 + 4.77318i −0.0781443 + 0.443178i
\(117\) −1.25638 1.05423i −0.116152 0.0974634i
\(118\) −2.56360 0.933074i −0.235999 0.0858965i
\(119\) −0.731176 + 0.266126i −0.0670268 + 0.0243957i
\(120\) 0.766044 0.642788i 0.0699300 0.0586782i
\(121\) −0.400770 0.694154i −0.0364336 0.0631049i
\(122\) −1.28532 + 2.22625i −0.116368 + 0.201555i
\(123\) 1.00531 + 5.70139i 0.0906457 + 0.514077i
\(124\) −0.594874 3.37370i −0.0534213 0.302967i
\(125\) −0.500000 + 0.866025i −0.0447214 + 0.0774597i
\(126\) 1.48371 + 2.56987i 0.132180 + 0.228942i
\(127\) 9.85708 8.27107i 0.874674 0.733939i −0.0904029 0.995905i \(-0.528815\pi\)
0.965077 + 0.261967i \(0.0843710\pi\)
\(128\) −0.939693 + 0.342020i −0.0830579 + 0.0302306i
\(129\) 0.567130 + 0.206418i 0.0499330 + 0.0181741i
\(130\) −1.25638 1.05423i −0.110192 0.0924619i
\(131\) 2.45412 13.9180i 0.214418 1.21602i −0.667496 0.744613i \(-0.732634\pi\)
0.881914 0.471411i \(-0.156255\pi\)
\(132\) 3.43534 0.299008
\(133\) −11.2874 + 6.31681i −0.978739 + 0.547737i
\(134\) 0.511731 0.0442068
\(135\) 0.173648 0.984808i 0.0149453 0.0847588i
\(136\) −0.200868 0.168548i −0.0172243 0.0144529i
\(137\) −10.8478 3.94827i −0.926788 0.337323i −0.165853 0.986151i \(-0.553038\pi\)
−0.760936 + 0.648827i \(0.775260\pi\)
\(138\) −0.142073 + 0.0517103i −0.0120941 + 0.00440188i
\(139\) −4.89713 + 4.10918i −0.415369 + 0.348536i −0.826398 0.563086i \(-0.809614\pi\)
0.411029 + 0.911622i \(0.365169\pi\)
\(140\) 1.48371 + 2.56987i 0.125397 + 0.217193i
\(141\) −1.67700 + 2.90466i −0.141229 + 0.244616i
\(142\) −0.802455 4.55095i −0.0673406 0.381907i
\(143\) −0.978377 5.54865i −0.0818160 0.464002i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 2.42341 + 4.19746i 0.201253 + 0.348580i
\(146\) −4.88951 + 4.10279i −0.404659 + 0.339549i
\(147\) −1.69672 + 0.617557i −0.139943 + 0.0509352i
\(148\) −11.3194 4.11993i −0.930451 0.338656i
\(149\) −0.923697 0.775074i −0.0756722 0.0634965i 0.604167 0.796858i \(-0.293506\pi\)
−0.679839 + 0.733361i \(0.737950\pi\)
\(150\) 0.173648 0.984808i 0.0141783 0.0804092i
\(151\) 24.1672 1.96670 0.983351 0.181716i \(-0.0581651\pi\)
0.983351 + 0.181716i \(0.0581651\pi\)
\(152\) −3.74540 2.22979i −0.303792 0.180860i
\(153\) −0.262214 −0.0211988
\(154\) −1.77019 + 10.0392i −0.142646 + 0.808985i
\(155\) −2.62427 2.20203i −0.210787 0.176871i
\(156\) 1.54118 + 0.560943i 0.123393 + 0.0449114i
\(157\) −19.4420 + 7.07630i −1.55164 + 0.564751i −0.968802 0.247838i \(-0.920280\pi\)
−0.582838 + 0.812588i \(0.698058\pi\)
\(158\) 4.61178 3.86975i 0.366894 0.307860i
\(159\) −5.92708 10.2660i −0.470048 0.814146i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −0.0779069 0.441832i −0.00613992 0.0348212i
\(162\) 0.173648 + 0.984808i 0.0136431 + 0.0773738i
\(163\) 4.65944 8.07039i 0.364956 0.632122i −0.623813 0.781573i \(-0.714418\pi\)
0.988769 + 0.149452i \(0.0477508\pi\)
\(164\) −2.89467 5.01372i −0.226036 0.391506i
\(165\) 2.63162 2.20819i 0.204871 0.171908i
\(166\) −7.11342 + 2.58907i −0.552109 + 0.200951i
\(167\) −2.06049 0.749955i −0.159445 0.0580333i 0.261064 0.965321i \(-0.415926\pi\)
−0.420510 + 0.907288i \(0.638149\pi\)
\(168\) −2.27318 1.90742i −0.175380 0.147161i
\(169\) −1.79033 + 10.1535i −0.137718 + 0.781037i
\(170\) −0.262214 −0.0201109
\(171\) −4.30243 + 0.699379i −0.329015 + 0.0534828i
\(172\) −0.603527 −0.0460185
\(173\) −1.95424 + 11.0830i −0.148578 + 0.842629i 0.815846 + 0.578269i \(0.196272\pi\)
−0.964424 + 0.264359i \(0.914839\pi\)
\(174\) −3.71287 3.11547i −0.281472 0.236183i
\(175\) 2.78847 + 1.01492i 0.210788 + 0.0767207i
\(176\) −3.22816 + 1.17495i −0.243332 + 0.0885655i
\(177\) 2.08987 1.75361i 0.157084 0.131809i
\(178\) −4.56449 7.90593i −0.342123 0.592575i
\(179\) −6.11059 + 10.5839i −0.456727 + 0.791074i −0.998786 0.0492664i \(-0.984312\pi\)
0.542059 + 0.840341i \(0.317645\pi\)
\(180\) 0.173648 + 0.984808i 0.0129430 + 0.0734032i
\(181\) −4.06250 23.0396i −0.301963 1.71252i −0.637465 0.770479i \(-0.720017\pi\)
0.335502 0.942040i \(-0.391094\pi\)
\(182\) −2.43342 + 4.21480i −0.180377 + 0.312422i
\(183\) −1.28532 2.22625i −0.0950138 0.164569i
\(184\) 0.115819 0.0971837i 0.00853829 0.00716447i
\(185\) −11.3194 + 4.11993i −0.832220 + 0.302903i
\(186\) 3.21915 + 1.17167i 0.236039 + 0.0859113i
\(187\) −0.690048 0.579019i −0.0504613 0.0423421i
\(188\) 0.582418 3.30305i 0.0424772 0.240900i
\(189\) −2.96743 −0.215848
\(190\) −4.30243 + 0.699379i −0.312131 + 0.0507383i
\(191\) 21.6181 1.56423 0.782115 0.623134i \(-0.214141\pi\)
0.782115 + 0.623134i \(0.214141\pi\)
\(192\) 0.173648 0.984808i 0.0125320 0.0710724i
\(193\) −18.7544 15.7368i −1.34997 1.13276i −0.978942 0.204138i \(-0.934561\pi\)
−0.371028 0.928622i \(-0.620995\pi\)
\(194\) 6.94086 + 2.52627i 0.498325 + 0.181375i
\(195\) 1.54118 0.560943i 0.110366 0.0401699i
\(196\) 1.38318 1.16063i 0.0987987 0.0829020i
\(197\) 12.4715 + 21.6012i 0.888556 + 1.53902i 0.841583 + 0.540128i \(0.181624\pi\)
0.0469726 + 0.998896i \(0.485043\pi\)
\(198\) −1.71767 + 2.97509i −0.122069 + 0.211430i
\(199\) 1.37086 + 7.77454i 0.0971778 + 0.551123i 0.994058 + 0.108850i \(0.0347167\pi\)
−0.896880 + 0.442273i \(0.854172\pi\)
\(200\) 0.173648 + 0.984808i 0.0122788 + 0.0696364i
\(201\) −0.255866 + 0.443172i −0.0180474 + 0.0312590i
\(202\) −4.83149 8.36839i −0.339942 0.588798i
\(203\) 11.0177 9.24493i 0.773289 0.648867i
\(204\) 0.246401 0.0896825i 0.0172515 0.00627903i
\(205\) −5.44021 1.98007i −0.379960 0.138294i
\(206\) 7.92507 + 6.64992i 0.552166 + 0.463322i
\(207\) 0.0262540 0.148894i 0.00182478 0.0103488i
\(208\) −1.64009 −0.113720
\(209\) −12.8667 7.66008i −0.890009 0.529859i
\(210\) −2.96743 −0.204772
\(211\) −2.37683 + 13.4797i −0.163628 + 0.927980i 0.786840 + 0.617157i \(0.211716\pi\)
−0.950468 + 0.310823i \(0.899395\pi\)
\(212\) 9.08081 + 7.61970i 0.623672 + 0.523323i
\(213\) 4.34247 + 1.58053i 0.297541 + 0.108296i
\(214\) −7.29771 + 2.65615i −0.498861 + 0.181571i
\(215\) −0.462328 + 0.387939i −0.0315305 + 0.0264573i
\(216\) −0.500000 0.866025i −0.0340207 0.0589256i
\(217\) −5.08282 + 8.80371i −0.345044 + 0.597635i
\(218\) −1.17832 6.68257i −0.0798057 0.452601i
\(219\) −1.10836 6.28584i −0.0748962 0.424757i
\(220\) −1.71767 + 2.97509i −0.115805 + 0.200580i
\(221\) −0.215027 0.372438i −0.0144643 0.0250529i
\(222\) 9.22768 7.74294i 0.619321 0.519672i
\(223\) 24.7865 9.02155i 1.65983 0.604128i 0.669492 0.742819i \(-0.266512\pi\)
0.990336 + 0.138692i \(0.0442897\pi\)
\(224\) 2.78847 + 1.01492i 0.186312 + 0.0678122i
\(225\) 0.766044 + 0.642788i 0.0510696 + 0.0428525i
\(226\) −1.07282 + 6.08428i −0.0713631 + 0.404720i
\(227\) 0.229904 0.0152592 0.00762962 0.999971i \(-0.497571\pi\)
0.00762962 + 0.999971i \(0.497571\pi\)
\(228\) 3.80376 2.12872i 0.251910 0.140978i
\(229\) −5.67396 −0.374946 −0.187473 0.982270i \(-0.560030\pi\)
−0.187473 + 0.982270i \(0.560030\pi\)
\(230\) 0.0262540 0.148894i 0.00173114 0.00981778i
\(231\) −7.80914 6.55265i −0.513804 0.431132i
\(232\) 4.55451 + 1.65771i 0.299018 + 0.108834i
\(233\) 14.6842 5.34460i 0.961991 0.350136i 0.187178 0.982326i \(-0.440066\pi\)
0.774813 + 0.632190i \(0.217844\pi\)
\(234\) −1.25638 + 1.05423i −0.0821321 + 0.0689170i
\(235\) −1.67700 2.90466i −0.109396 0.189479i
\(236\) −1.36406 + 2.36263i −0.0887930 + 0.153794i
\(237\) 1.04541 + 5.92879i 0.0679064 + 0.385117i
\(238\) 0.135116 + 0.766280i 0.00875826 + 0.0496705i
\(239\) −1.50448 + 2.60583i −0.0973167 + 0.168557i −0.910573 0.413348i \(-0.864359\pi\)
0.813256 + 0.581905i \(0.197693\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) 11.3550 9.52797i 0.731439 0.613750i −0.199084 0.979982i \(-0.563797\pi\)
0.930524 + 0.366232i \(0.119352\pi\)
\(242\) −0.753201 + 0.274143i −0.0484176 + 0.0176226i
\(243\) −0.939693 0.342020i −0.0602813 0.0219406i
\(244\) 1.96923 + 1.65238i 0.126067 + 0.105783i
\(245\) 0.313542 1.77818i 0.0200315 0.113604i
\(246\) 5.78935 0.369115
\(247\) −4.52154 5.53746i −0.287699 0.352340i
\(248\) −3.42575 −0.217535
\(249\) 1.31451 7.45494i 0.0833035 0.472438i
\(250\) 0.766044 + 0.642788i 0.0484489 + 0.0406535i
\(251\) 26.9396 + 9.80520i 1.70041 + 0.618899i 0.995872 0.0907681i \(-0.0289322\pi\)
0.704538 + 0.709667i \(0.251154\pi\)
\(252\) 2.78847 1.01492i 0.175657 0.0639339i
\(253\) 0.397877 0.333859i 0.0250143 0.0209895i
\(254\) −6.43375 11.1436i −0.403689 0.699210i
\(255\) 0.131107 0.227084i 0.00821024 0.0142206i
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) 1.69638 + 9.62066i 0.105817 + 0.600120i 0.990891 + 0.134669i \(0.0429970\pi\)
−0.885073 + 0.465452i \(0.845892\pi\)
\(258\) 0.301763 0.522669i 0.0187870 0.0325400i
\(259\) 17.8726 + 30.9563i 1.11055 + 1.92353i
\(260\) −1.25638 + 1.05423i −0.0779173 + 0.0653804i
\(261\) 4.55451 1.65771i 0.281917 0.102609i
\(262\) −13.2804 4.83368i −0.820468 0.298626i
\(263\) −4.42346 3.71172i −0.272762 0.228875i 0.496138 0.868244i \(-0.334751\pi\)
−0.768900 + 0.639369i \(0.779196\pi\)
\(264\) 0.596540 3.38315i 0.0367145 0.208218i
\(265\) 11.8542 0.728195
\(266\) 4.26081 + 12.2128i 0.261247 + 0.748814i
\(267\) 9.12898 0.558685
\(268\) 0.0888612 0.503957i 0.00542806 0.0307841i
\(269\) 21.7515 + 18.2517i 1.32621 + 1.11282i 0.984947 + 0.172857i \(0.0552999\pi\)
0.341265 + 0.939967i \(0.389145\pi\)
\(270\) −0.939693 0.342020i −0.0571879 0.0208147i
\(271\) 13.0857 4.76279i 0.794897 0.289319i 0.0875268 0.996162i \(-0.472104\pi\)
0.707370 + 0.706843i \(0.249881\pi\)
\(272\) −0.200868 + 0.168548i −0.0121794 + 0.0102197i
\(273\) −2.43342 4.21480i −0.147277 0.255091i
\(274\) −5.77198 + 9.99737i −0.348698 + 0.603963i
\(275\) 0.596540 + 3.38315i 0.0359727 + 0.204011i
\(276\) 0.0262540 + 0.148894i 0.00158031 + 0.00896237i
\(277\) 5.46936 9.47320i 0.328622 0.569190i −0.653617 0.756826i \(-0.726749\pi\)
0.982239 + 0.187636i \(0.0600825\pi\)
\(278\) 3.19637 + 5.53628i 0.191706 + 0.332044i
\(279\) −2.62427 + 2.20203i −0.157111 + 0.131832i
\(280\) 2.78847 1.01492i 0.166643 0.0606530i
\(281\) 3.95708 + 1.44026i 0.236060 + 0.0859187i 0.457341 0.889291i \(-0.348802\pi\)
−0.221282 + 0.975210i \(0.571024\pi\)
\(282\) 2.56932 + 2.15592i 0.153001 + 0.128383i
\(283\) 4.57509 25.9466i 0.271961 1.54237i −0.476491 0.879179i \(-0.658092\pi\)
0.748452 0.663189i \(-0.230797\pi\)
\(284\) −4.62116 −0.274215
\(285\) 1.54553 4.07570i 0.0915495 0.241424i
\(286\) −5.63425 −0.333160
\(287\) −2.98318 + 16.9185i −0.176092 + 0.998665i
\(288\) 0.766044 + 0.642788i 0.0451396 + 0.0378766i
\(289\) 15.9102 + 5.79083i 0.935892 + 0.340637i
\(290\) 4.55451 1.65771i 0.267450 0.0973439i
\(291\) −5.65824 + 4.74783i −0.331692 + 0.278323i
\(292\) 3.19140 + 5.52767i 0.186763 + 0.323483i
\(293\) −16.3882 + 28.3852i −0.957408 + 1.65828i −0.228648 + 0.973509i \(0.573430\pi\)
−0.728760 + 0.684770i \(0.759903\pi\)
\(294\) 0.313542 + 1.77818i 0.0182861 + 0.103706i
\(295\) 0.473734 + 2.68668i 0.0275819 + 0.156425i
\(296\) −6.02294 + 10.4320i −0.350076 + 0.606350i
\(297\) −1.71767 2.97509i −0.0996692 0.172632i
\(298\) −0.923697 + 0.775074i −0.0535083 + 0.0448988i
\(299\) 0.233012 0.0848094i 0.0134754 0.00490466i
\(300\) −0.939693 0.342020i −0.0542532 0.0197465i
\(301\) 1.37192 + 1.15118i 0.0790764 + 0.0663530i
\(302\) 4.19660 23.8001i 0.241487 1.36954i
\(303\) 9.66298 0.555124
\(304\) −2.84630 + 3.30130i −0.163246 + 0.189343i
\(305\) 2.57065 0.147195
\(306\) −0.0455330 + 0.258230i −0.00260295 + 0.0147621i
\(307\) 8.62432 + 7.23667i 0.492216 + 0.413018i 0.854820 0.518925i \(-0.173668\pi\)
−0.362604 + 0.931943i \(0.618112\pi\)
\(308\) 9.57933 + 3.48659i 0.545833 + 0.198667i
\(309\) −9.72154 + 3.53835i −0.553039 + 0.201290i
\(310\) −2.62427 + 2.20203i −0.149049 + 0.125067i
\(311\) 2.97603 + 5.15463i 0.168755 + 0.292292i 0.937982 0.346683i \(-0.112692\pi\)
−0.769227 + 0.638975i \(0.779359\pi\)
\(312\) 0.820043 1.42036i 0.0464258 0.0804119i
\(313\) −3.44598 19.5431i −0.194778 1.10464i −0.912734 0.408553i \(-0.866033\pi\)
0.717956 0.696088i \(-0.245078\pi\)
\(314\) 3.59273 + 20.3754i 0.202750 + 1.14985i
\(315\) 1.48371 2.56987i 0.0835978 0.144796i
\(316\) −3.01013 5.21369i −0.169333 0.293293i
\(317\) 26.3415 22.1031i 1.47948 1.24143i 0.572751 0.819729i \(-0.305876\pi\)
0.906733 0.421705i \(-0.138568\pi\)
\(318\) −11.1393 + 4.05436i −0.624659 + 0.227357i
\(319\) 15.6463 + 5.69478i 0.876024 + 0.318847i
\(320\) 0.766044 + 0.642788i 0.0428232 + 0.0359329i
\(321\) 1.34856 7.64807i 0.0752694 0.426874i
\(322\) −0.448648 −0.0250022
\(323\) −1.12284 0.213525i −0.0624766 0.0118808i
\(324\) 1.00000 0.0555556
\(325\) −0.284798 + 1.61517i −0.0157978 + 0.0895935i
\(326\) −7.13868 5.99006i −0.395375 0.331759i
\(327\) 6.37643 + 2.32083i 0.352618 + 0.128342i
\(328\) −5.44021 + 1.98007i −0.300385 + 0.109331i
\(329\) −7.62427 + 6.39752i −0.420340 + 0.352707i
\(330\) −1.71767 2.97509i −0.0945545 0.163773i
\(331\) 7.59512 13.1551i 0.417466 0.723072i −0.578218 0.815882i \(-0.696252\pi\)
0.995684 + 0.0928103i \(0.0295850\pi\)
\(332\) 1.31451 + 7.45494i 0.0721430 + 0.409143i
\(333\) 2.09174 + 11.8629i 0.114627 + 0.650081i
\(334\) −1.09636 + 1.89895i −0.0599902 + 0.103906i
\(335\) −0.255866 0.443172i −0.0139794 0.0242131i
\(336\) −2.27318 + 1.90742i −0.124012 + 0.104059i
\(337\) −13.6267 + 4.95972i −0.742295 + 0.270173i −0.685360 0.728205i \(-0.740355\pi\)
−0.0569349 + 0.998378i \(0.518133\pi\)
\(338\) 9.68834 + 3.52627i 0.526976 + 0.191804i
\(339\) −4.73273 3.97123i −0.257046 0.215688i
\(340\) −0.0455330 + 0.258230i −0.00246937 + 0.0140045i
\(341\) −11.7686 −0.637305
\(342\) −0.0583546 + 4.35851i −0.00315545 + 0.235681i
\(343\) 15.4139 0.832275
\(344\) −0.104801 + 0.594358i −0.00565051 + 0.0320456i
\(345\) 0.115819 + 0.0971837i 0.00623548 + 0.00523219i
\(346\) 10.5753 + 3.84910i 0.568533 + 0.206929i
\(347\) −13.1873 + 4.79979i −0.707932 + 0.257666i −0.670794 0.741644i \(-0.734046\pi\)
−0.0371380 + 0.999310i \(0.511824\pi\)
\(348\) −3.71287 + 3.11547i −0.199031 + 0.167007i
\(349\) −6.18174 10.7071i −0.330901 0.573138i 0.651788 0.758402i \(-0.274019\pi\)
−0.982689 + 0.185264i \(0.940686\pi\)
\(350\) 1.48371 2.56987i 0.0793078 0.137365i
\(351\) −0.284798 1.61517i −0.0152014 0.0862114i
\(352\) 0.596540 + 3.38315i 0.0317957 + 0.180322i
\(353\) −17.6282 + 30.5330i −0.938255 + 1.62511i −0.169532 + 0.985525i \(0.554226\pi\)
−0.768723 + 0.639582i \(0.779108\pi\)
\(354\) −1.36406 2.36263i −0.0724992 0.125572i
\(355\) −3.54001 + 2.97042i −0.187884 + 0.157654i
\(356\) −8.57844 + 3.12230i −0.454656 + 0.165481i
\(357\) −0.731176 0.266126i −0.0386979 0.0140849i
\(358\) 9.36197 + 7.85562i 0.494795 + 0.415183i
\(359\) 4.09602 23.2297i 0.216180 1.22602i −0.662668 0.748913i \(-0.730576\pi\)
0.878848 0.477102i \(-0.158313\pi\)
\(360\) 1.00000 0.0527046
\(361\) −18.9932 0.508678i −0.999642 0.0267725i
\(362\) −23.3950 −1.22961
\(363\) 0.139186 0.789363i 0.00730537 0.0414308i
\(364\) 3.72821 + 3.12834i 0.195411 + 0.163970i
\(365\) 5.99788 + 2.18305i 0.313943 + 0.114266i
\(366\) −2.41562 + 0.879213i −0.126266 + 0.0459572i
\(367\) 22.7420 19.0828i 1.18712 0.996113i 0.187216 0.982319i \(-0.440053\pi\)
0.999905 0.0137944i \(-0.00439102\pi\)
\(368\) −0.0755955 0.130935i −0.00394069 0.00682547i
\(369\) −2.89467 + 5.01372i −0.150691 + 0.261004i
\(370\) 2.09174 + 11.8629i 0.108745 + 0.616721i
\(371\) −6.10830 34.6419i −0.317127 1.79852i
\(372\) 1.71287 2.96678i 0.0888083 0.153821i
\(373\) −7.21161 12.4909i −0.373403 0.646753i 0.616684 0.787211i \(-0.288476\pi\)
−0.990087 + 0.140458i \(0.955142\pi\)
\(374\) −0.690048 + 0.579019i −0.0356815 + 0.0299404i
\(375\) −0.939693 + 0.342020i −0.0485255 + 0.0176618i
\(376\) −3.15174 1.14714i −0.162538 0.0591592i
\(377\) 6.08943 + 5.10964i 0.313622 + 0.263160i
\(378\) −0.515288 + 2.92234i −0.0265036 + 0.150309i
\(379\) −12.8755 −0.661368 −0.330684 0.943742i \(-0.607279\pi\)
−0.330684 + 0.943742i \(0.607279\pi\)
\(380\) −0.0583546 + 4.35851i −0.00299353 + 0.223587i
\(381\) 12.8675 0.659222
\(382\) 3.75394 21.2897i 0.192068 1.08927i
\(383\) 12.8350 + 10.7698i 0.655836 + 0.550312i 0.908836 0.417154i \(-0.136973\pi\)
−0.252999 + 0.967466i \(0.581417\pi\)
\(384\) −0.939693 0.342020i −0.0479535 0.0174536i
\(385\) 9.57933 3.48659i 0.488208 0.177693i
\(386\) −18.7544 + 15.7368i −0.954573 + 0.800982i
\(387\) 0.301763 + 0.522669i 0.0153395 + 0.0265688i
\(388\) 3.69315 6.39673i 0.187491 0.324745i
\(389\) −4.56767 25.9045i −0.231590 1.31341i −0.849678 0.527302i \(-0.823204\pi\)
0.618088 0.786109i \(-0.287908\pi\)
\(390\) −0.284798 1.61517i −0.0144213 0.0817873i
\(391\) 0.0198222 0.0343331i 0.00100245 0.00173630i
\(392\) −0.902808 1.56371i −0.0455987 0.0789792i
\(393\) 10.8263 9.08435i 0.546115 0.458245i
\(394\) 23.4387 8.53099i 1.18082 0.429785i
\(395\) −5.65719 2.05905i −0.284644 0.103602i
\(396\) 2.63162 + 2.20819i 0.132244 + 0.110966i
\(397\) −1.79926 + 10.2041i −0.0903024 + 0.512130i 0.905784 + 0.423741i \(0.139283\pi\)
−0.996086 + 0.0883897i \(0.971828\pi\)
\(398\) 7.89448 0.395714
\(399\) −12.7070 2.41642i −0.636145 0.120972i
\(400\) 1.00000 0.0500000
\(401\) −1.64851 + 9.34918i −0.0823228 + 0.466876i 0.915579 + 0.402137i \(0.131733\pi\)
−0.997902 + 0.0647387i \(0.979379\pi\)
\(402\) 0.392009 + 0.328934i 0.0195516 + 0.0164058i
\(403\) −5.27968 1.92165i −0.263000 0.0957240i
\(404\) −9.08023 + 3.30493i −0.451758 + 0.164427i
\(405\) 0.766044 0.642788i 0.0380651 0.0319404i
\(406\) −7.19128 12.4557i −0.356897 0.618164i
\(407\) −20.6908 + 35.8376i −1.02561 + 1.77640i
\(408\) −0.0455330 0.258230i −0.00225422 0.0127843i
\(409\) 2.59587 + 14.7219i 0.128358 + 0.727953i 0.979257 + 0.202623i \(0.0649468\pi\)
−0.850899 + 0.525329i \(0.823942\pi\)
\(410\) −2.89467 + 5.01372i −0.142958 + 0.247610i
\(411\) −5.77198 9.99737i −0.284711 0.493134i
\(412\) 7.92507 6.64992i 0.390440 0.327618i
\(413\) 7.60730 2.76883i 0.374331 0.136245i
\(414\) −0.142073 0.0517103i −0.00698251 0.00254142i
\(415\) 5.79892 + 4.86587i 0.284658 + 0.238856i
\(416\) −0.284798 + 1.61517i −0.0139634 + 0.0791902i
\(417\) −6.39275 −0.313054
\(418\) −9.77799 + 11.3411i −0.478257 + 0.554710i
\(419\) −6.17464 −0.301651 −0.150825 0.988560i \(-0.548193\pi\)
−0.150825 + 0.988560i \(0.548193\pi\)
\(420\) −0.515288 + 2.92234i −0.0251435 + 0.142596i
\(421\) −0.883431 0.741286i −0.0430558 0.0361281i 0.621006 0.783806i \(-0.286724\pi\)
−0.664062 + 0.747678i \(0.731169\pi\)
\(422\) 12.8622 + 4.68145i 0.626121 + 0.227889i
\(423\) −3.15174 + 1.14714i −0.153243 + 0.0557758i
\(424\) 9.08081 7.61970i 0.441003 0.370045i
\(425\) 0.131107 + 0.227084i 0.00635963 + 0.0110152i
\(426\) 2.31058 4.00204i 0.111948 0.193899i
\(427\) −1.32462 7.51231i −0.0641030 0.363546i
\(428\) 1.34856 + 7.64807i 0.0651852 + 0.369684i
\(429\) 2.81713 4.87940i 0.136012 0.235580i
\(430\) 0.301763 + 0.522669i 0.0145523 + 0.0252054i
\(431\) −17.9289 + 15.0441i −0.863605 + 0.724651i −0.962742 0.270423i \(-0.912836\pi\)
0.0991363 + 0.995074i \(0.468392\pi\)
\(432\) −0.939693 + 0.342020i −0.0452110 + 0.0164555i
\(433\) 12.2683 + 4.46528i 0.589575 + 0.214588i 0.619542 0.784963i \(-0.287318\pi\)
−0.0299676 + 0.999551i \(0.509540\pi\)
\(434\) 7.78734 + 6.53435i 0.373804 + 0.313659i
\(435\) −0.841640 + 4.77318i −0.0403535 + 0.228856i
\(436\) −6.78566 −0.324974
\(437\) 0.233671 0.616209i 0.0111780 0.0294773i
\(438\) −6.38281 −0.304982
\(439\) −3.87376 + 21.9692i −0.184885 + 1.04853i 0.741219 + 0.671263i \(0.234248\pi\)
−0.926103 + 0.377270i \(0.876863\pi\)
\(440\) 2.63162 + 2.20819i 0.125458 + 0.105271i
\(441\) −1.69672 0.617557i −0.0807964 0.0294075i
\(442\) −0.404118 + 0.147087i −0.0192220 + 0.00699622i
\(443\) −23.1711 + 19.4428i −1.10089 + 0.923756i −0.997485 0.0708829i \(-0.977418\pi\)
−0.103405 + 0.994639i \(0.532974\pi\)
\(444\) −6.02294 10.4320i −0.285836 0.495082i
\(445\) −4.56449 + 7.90593i −0.216378 + 0.374777i
\(446\) −4.58036 25.9765i −0.216886 1.23002i
\(447\) −0.209385 1.18748i −0.00990357 0.0561660i
\(448\) 1.48371 2.56987i 0.0700988 0.121415i
\(449\) −15.5761 26.9787i −0.735083 1.27320i −0.954687 0.297612i \(-0.903810\pi\)
0.219604 0.975589i \(-0.429524\pi\)
\(450\) 0.766044 0.642788i 0.0361117 0.0303013i
\(451\) −18.6889 + 6.80222i −0.880028 + 0.320304i
\(452\) 5.80555 + 2.11305i 0.273070 + 0.0993894i
\(453\) 18.5132 + 15.5344i 0.869825 + 0.729870i
\(454\) 0.0399224 0.226411i 0.00187365 0.0106260i
\(455\) 4.86684 0.228161
\(456\) −1.43586 4.11562i −0.0672404 0.192731i
\(457\) −29.9630 −1.40161 −0.700806 0.713352i \(-0.747176\pi\)
−0.700806 + 0.713352i \(0.747176\pi\)
\(458\) −0.985273 + 5.58776i −0.0460388 + 0.261099i
\(459\) −0.200868 0.168548i −0.00937570 0.00786715i
\(460\) −0.142073 0.0517103i −0.00662419 0.00241101i
\(461\) −0.909077 + 0.330877i −0.0423399 + 0.0154105i −0.363103 0.931749i \(-0.618283\pi\)
0.320763 + 0.947159i \(0.396061\pi\)
\(462\) −7.80914 + 6.55265i −0.363314 + 0.304857i
\(463\) −5.49734 9.52166i −0.255483 0.442509i 0.709544 0.704661i \(-0.248901\pi\)
−0.965027 + 0.262152i \(0.915568\pi\)
\(464\) 2.42341 4.19746i 0.112504 0.194862i
\(465\) −0.594874 3.37370i −0.0275866 0.156452i
\(466\) −2.71352 15.3892i −0.125702 0.712889i
\(467\) −2.18849 + 3.79057i −0.101271 + 0.175407i −0.912209 0.409726i \(-0.865624\pi\)
0.810937 + 0.585133i \(0.198958\pi\)
\(468\) 0.820043 + 1.42036i 0.0379065 + 0.0656560i
\(469\) −1.16326 + 0.976088i −0.0537142 + 0.0450716i
\(470\) −3.15174 + 1.14714i −0.145379 + 0.0529136i
\(471\) −19.4420 7.07630i −0.895839 0.326059i
\(472\) 2.08987 + 1.75361i 0.0961939 + 0.0807163i
\(473\) −0.360028 + 2.04182i −0.0165541 + 0.0938829i
\(474\) 6.02025 0.276519
\(475\) 2.75689 + 3.37632i 0.126495 + 0.154916i
\(476\) 0.778101 0.0356642
\(477\) 2.05845 11.6741i 0.0942500 0.534518i
\(478\) 2.30500 + 1.93412i 0.105428 + 0.0884646i
\(479\) 13.5919 + 4.94704i 0.621029 + 0.226036i 0.633322 0.773888i \(-0.281691\pi\)
−0.0122930 + 0.999924i \(0.503913\pi\)
\(480\) −0.939693 + 0.342020i −0.0428909 + 0.0156110i
\(481\) −15.1342 + 12.6991i −0.690060 + 0.579029i
\(482\) −7.41144 12.8370i −0.337582 0.584709i
\(483\) 0.224324 0.388540i 0.0102071 0.0176792i
\(484\) 0.139186 + 0.789363i 0.00632663 + 0.0358801i
\(485\) −1.28262 7.27409i −0.0582407 0.330300i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 8.53544 + 14.7838i 0.386778 + 0.669919i 0.992014 0.126127i \(-0.0402547\pi\)
−0.605236 + 0.796046i \(0.706921\pi\)
\(488\) 1.96923 1.65238i 0.0891428 0.0747997i
\(489\) 8.75688 3.18725i 0.396000 0.144132i
\(490\) −1.69672 0.617557i −0.0766502 0.0278984i
\(491\) −9.51109 7.98075i −0.429230 0.360166i 0.402431 0.915450i \(-0.368165\pi\)
−0.831661 + 0.555284i \(0.812610\pi\)
\(492\) 1.00531 5.70139i 0.0453229 0.257039i
\(493\) 1.27090 0.0572386
\(494\) −6.23849 + 3.49128i −0.280683 + 0.157080i
\(495\) 3.43534 0.154407
\(496\) −0.594874 + 3.37370i −0.0267107 + 0.151484i
\(497\) 10.5047 + 8.81451i 0.471201 + 0.395385i
\(498\) −7.11342 2.58907i −0.318760 0.116019i
\(499\) −22.6616 + 8.24816i −1.01447 + 0.369239i −0.795150 0.606413i \(-0.792608\pi\)
−0.219325 + 0.975652i \(0.570385\pi\)
\(500\) 0.766044 0.642788i 0.0342585 0.0287463i
\(501\) −1.09636 1.89895i −0.0489818 0.0848390i
\(502\) 14.3342 24.8276i 0.639768 1.10811i
\(503\) −4.08773 23.1827i −0.182263 1.03366i −0.929422 0.369019i \(-0.879694\pi\)
0.747159 0.664645i \(-0.231417\pi\)
\(504\) −0.515288 2.92234i −0.0229528 0.130172i
\(505\) −4.83149 + 8.36839i −0.214998 + 0.372388i
\(506\) −0.259696 0.449806i −0.0115449 0.0199963i
\(507\) −7.89801 + 6.62721i −0.350763 + 0.294325i
\(508\) −12.0915 + 4.40094i −0.536473 + 0.195260i
\(509\) 16.2932 + 5.93024i 0.722183 + 0.262853i 0.676852 0.736119i \(-0.263344\pi\)
0.0453308 + 0.998972i \(0.485566\pi\)
\(510\) −0.200868 0.168548i −0.00889457 0.00746343i
\(511\) 3.28898 18.6528i 0.145496 0.825149i
\(512\) 1.00000 0.0441942
\(513\) −3.74540 2.22979i −0.165364 0.0984477i
\(514\) 9.76907 0.430895
\(515\) 1.79647 10.1883i 0.0791618 0.448949i
\(516\) −0.462328 0.387939i −0.0203529 0.0170781i
\(517\) −10.8273 3.94081i −0.476183 0.173317i
\(518\) 33.5895 12.2256i 1.47584 0.537162i
\(519\) −8.62108 + 7.23395i −0.378423 + 0.317535i
\(520\) 0.820043 + 1.42036i 0.0359613 + 0.0622868i
\(521\) −20.6188 + 35.7129i −0.903328 + 1.56461i −0.0801812 + 0.996780i \(0.525550\pi\)
−0.823146 + 0.567829i \(0.807783\pi\)
\(522\) −0.841640 4.77318i −0.0368376 0.208916i
\(523\) −0.623075 3.53363i −0.0272452 0.154515i 0.968150 0.250371i \(-0.0805524\pi\)
−0.995395 + 0.0958555i \(0.969441\pi\)
\(524\) −7.06637 + 12.2393i −0.308696 + 0.534677i
\(525\) 1.48371 + 2.56987i 0.0647545 + 0.112158i
\(526\) −4.42346 + 3.71172i −0.192872 + 0.161839i
\(527\) −0.844106 + 0.307229i −0.0367698 + 0.0133831i
\(528\) −3.22816 1.17495i −0.140488 0.0511333i
\(529\) −17.6015 14.7694i −0.765283 0.642149i
\(530\) 2.05845 11.6741i 0.0894134 0.507089i
\(531\) 2.72813 0.118391
\(532\) 12.7671 2.07536i 0.553525 0.0899781i
\(533\) −9.49503 −0.411275
\(534\) 1.58523 8.99029i 0.0685997 0.389048i
\(535\) 5.94915 + 4.99193i 0.257204 + 0.215820i
\(536\) −0.480870 0.175022i −0.0207704 0.00755981i
\(537\) −11.4842 + 4.17989i −0.495578 + 0.180376i
\(538\) 21.7515 18.2517i 0.937774 0.786885i
\(539\) −3.10145 5.37187i −0.133589 0.231383i
\(540\) −0.500000 + 0.866025i −0.0215166 + 0.0372678i
\(541\) −6.81147 38.6298i −0.292848 1.66082i −0.675822 0.737065i \(-0.736211\pi\)
0.382974 0.923759i \(-0.374900\pi\)
\(542\) −2.41813 13.7139i −0.103868 0.589063i
\(543\) 11.6975 20.2607i 0.501988 0.869469i
\(544\) 0.131107 + 0.227084i 0.00562117 + 0.00973615i
\(545\) −5.19812 + 4.36174i −0.222663 + 0.186836i
\(546\) −4.57333 + 1.66456i −0.195720 + 0.0712364i
\(547\) −14.4045 5.24282i −0.615893 0.224167i 0.0151869 0.999885i \(-0.495166\pi\)
−0.631080 + 0.775718i \(0.717388\pi\)
\(548\) 8.84319 + 7.42032i 0.377762 + 0.316980i
\(549\) 0.446388 2.53159i 0.0190514 0.108046i
\(550\) 3.43534 0.146483
\(551\) 20.8530 3.38976i 0.888370 0.144409i
\(552\) 0.151191 0.00643511
\(553\) −3.10217 + 17.5933i −0.131918 + 0.748141i
\(554\) −8.37954 7.03127i −0.356013 0.298730i
\(555\) −11.3194 4.11993i −0.480483 0.174881i
\(556\) 6.00722 2.18645i 0.254763 0.0927261i
\(557\) 7.31960 6.14187i 0.310141 0.260240i −0.474409 0.880305i \(-0.657338\pi\)
0.784550 + 0.620065i \(0.212894\pi\)
\(558\) 1.71287 + 2.96678i 0.0725117 + 0.125594i
\(559\) −0.494918 + 0.857223i −0.0209328 + 0.0362567i
\(560\) −0.515288 2.92234i −0.0217749 0.123492i
\(561\) −0.156421 0.887109i −0.00660411 0.0374538i
\(562\) 2.10552 3.64687i 0.0888160 0.153834i
\(563\) 7.09246 + 12.2845i 0.298911 + 0.517730i 0.975887 0.218275i \(-0.0700431\pi\)
−0.676976 + 0.736005i \(0.736710\pi\)
\(564\) 2.56932 2.15592i 0.108188 0.0907804i
\(565\) 5.80555 2.11305i 0.244241 0.0888966i
\(566\) −24.7580 9.01118i −1.04066 0.378768i
\(567\) −2.27318 1.90742i −0.0954646 0.0801043i
\(568\) −0.802455 + 4.55095i −0.0336703 + 0.190954i
\(569\) 5.90923 0.247728 0.123864 0.992299i \(-0.460471\pi\)
0.123864 + 0.992299i \(0.460471\pi\)
\(570\) −3.74540 2.22979i −0.156878 0.0933957i
\(571\) −7.90141 −0.330664 −0.165332 0.986238i \(-0.552869\pi\)
−0.165332 + 0.986238i \(0.552869\pi\)
\(572\) −0.978377 + 5.54865i −0.0409080 + 0.232001i
\(573\) 16.5604 + 13.8958i 0.691821 + 0.580507i
\(574\) 16.1434 + 5.87572i 0.673813 + 0.245248i
\(575\) −0.142073 + 0.0517103i −0.00592485 + 0.00215647i
\(576\) 0.766044 0.642788i 0.0319185 0.0267828i
\(577\) −16.8929 29.2593i −0.703259 1.21808i −0.967316 0.253573i \(-0.918394\pi\)
0.264057 0.964507i \(-0.414939\pi\)
\(578\) 8.46562 14.6629i 0.352123 0.609896i
\(579\) −4.25127 24.1102i −0.176677 1.00198i
\(580\) −0.841640 4.77318i −0.0349472 0.198195i
\(581\) 11.2316 19.4537i 0.465966 0.807077i
\(582\) 3.69315 + 6.39673i 0.153086 + 0.265153i
\(583\) 31.1956 26.1762i 1.29199 1.08411i
\(584\) 5.99788 2.18305i 0.248194 0.0903352i
\(585\) 1.54118 + 0.560943i 0.0637198 + 0.0231921i
\(586\) 25.1081 + 21.0682i 1.03721 + 0.870321i
\(587\) 1.33561 7.57462i 0.0551265 0.312638i −0.944759 0.327766i \(-0.893704\pi\)
0.999886 + 0.0151276i \(0.00481544\pi\)
\(588\) 1.80562 0.0744623
\(589\) −13.0307 + 7.29244i −0.536921 + 0.300480i
\(590\) 2.72813 0.112315
\(591\) −4.33130 + 24.5640i −0.178166 + 1.01043i
\(592\) 9.22768 + 7.74294i 0.379255 + 0.318233i
\(593\) 17.4279 + 6.34324i 0.715679 + 0.260486i 0.674090 0.738649i \(-0.264536\pi\)
0.0415885 + 0.999135i \(0.486758\pi\)
\(594\) −3.22816 + 1.17495i −0.132453 + 0.0482090i
\(595\) 0.596060 0.500154i 0.0244361 0.0205043i
\(596\) 0.602900 + 1.04425i 0.0246958 + 0.0427743i
\(597\) −3.94724 + 6.83682i −0.161550 + 0.279812i
\(598\) −0.0430589 0.244199i −0.00176081 0.00998604i
\(599\) 0.782542 + 4.43802i 0.0319738 + 0.181332i 0.996612 0.0822444i \(-0.0262088\pi\)
−0.964638 + 0.263577i \(0.915098\pi\)
\(600\) −0.500000 + 0.866025i −0.0204124 + 0.0353553i
\(601\) 17.2987 + 29.9622i 0.705628 + 1.22218i 0.966464 + 0.256800i \(0.0826683\pi\)
−0.260837 + 0.965383i \(0.583998\pi\)
\(602\) 1.37192 1.15118i 0.0559155 0.0469187i
\(603\) −0.480870 + 0.175022i −0.0195825 + 0.00712746i
\(604\) −22.7098 8.26568i −0.924048 0.336326i
\(605\) 0.614015 + 0.515220i 0.0249633 + 0.0209467i
\(606\) 1.67796 9.51618i 0.0681624 0.386568i
\(607\) 21.7750 0.883820 0.441910 0.897059i \(-0.354301\pi\)
0.441910 + 0.897059i \(0.354301\pi\)
\(608\) 2.75689 + 3.37632i 0.111807 + 0.136928i
\(609\) 14.3826 0.582810
\(610\) 0.446388 2.53159i 0.0180737 0.102501i
\(611\) −4.21391 3.53589i −0.170476 0.143047i
\(612\) 0.246401 + 0.0896825i 0.00996016 + 0.00362520i
\(613\) 3.27882 1.19339i 0.132430 0.0482007i −0.274955 0.961457i \(-0.588663\pi\)
0.407385 + 0.913256i \(0.366441\pi\)
\(614\) 8.62432 7.23667i 0.348049 0.292048i
\(615\) −2.89467 5.01372i −0.116724 0.202173i
\(616\) 5.09705 8.82836i 0.205366 0.355705i
\(617\) −3.19804 18.1370i −0.128748 0.730167i −0.979011 0.203808i \(-0.934668\pi\)
0.850263 0.526358i \(-0.176443\pi\)
\(618\) 1.79647 + 10.1883i 0.0722645 + 0.409833i
\(619\) 13.8765 24.0348i 0.557743 0.966039i −0.439941 0.898027i \(-0.645001\pi\)
0.997684 0.0680129i \(-0.0216659\pi\)
\(620\) 1.71287 + 2.96678i 0.0687906 + 0.119149i
\(621\) 0.115819 0.0971837i 0.00464766 0.00389985i
\(622\) 5.59310 2.03572i 0.224263 0.0816250i
\(623\) 25.4559 + 9.26518i 1.01987 + 0.371202i
\(624\) −1.25638 1.05423i −0.0502954 0.0422029i
\(625\) 0.173648 0.984808i 0.00694593 0.0393923i
\(626\) −19.8446 −0.793149
\(627\) −4.93267 14.1385i −0.196992 0.564638i
\(628\) 20.6897 0.825610
\(629\) −0.548485 + 3.11061i −0.0218695 + 0.124028i
\(630\) −2.27318 1.90742i −0.0905657 0.0759936i
\(631\) −27.4695 9.99807i −1.09354 0.398017i −0.268610 0.963249i \(-0.586564\pi\)
−0.824932 + 0.565232i \(0.808787\pi\)
\(632\) −5.65719 + 2.05905i −0.225031 + 0.0819046i
\(633\) −10.4853 + 8.79824i −0.416755 + 0.349699i
\(634\) −17.1932 29.7794i −0.682828 1.18269i
\(635\) −6.43375 + 11.1436i −0.255316 + 0.442219i
\(636\) 2.05845 + 11.6741i 0.0816229 + 0.462907i
\(637\) −0.514236 2.91638i −0.0203748 0.115551i
\(638\) 8.32521 14.4197i 0.329598 0.570881i
\(639\) 2.31058 + 4.00204i 0.0914051 + 0.158318i
\(640\) 0.766044 0.642788i 0.0302806 0.0254084i
\(641\) −0.937619 + 0.341265i −0.0370337 + 0.0134792i −0.360471 0.932771i \(-0.617384\pi\)
0.323437 + 0.946250i \(0.395162\pi\)
\(642\) −7.29771 2.65615i −0.288018 0.104830i
\(643\) −25.9538 21.7778i −1.02352 0.858833i −0.0334517 0.999440i \(-0.510650\pi\)
−0.990065 + 0.140607i \(0.955094\pi\)
\(644\) −0.0779069 + 0.441832i −0.00306996 + 0.0174106i
\(645\) −0.603527 −0.0237638
\(646\) −0.405261 + 1.06871i −0.0159448 + 0.0420477i
\(647\) −32.5517 −1.27974 −0.639869 0.768484i \(-0.721011\pi\)
−0.639869 + 0.768484i \(0.721011\pi\)
\(648\) 0.173648 0.984808i 0.00682154 0.0386869i
\(649\) 7.17940 + 6.02423i 0.281816 + 0.236472i
\(650\) 1.54118 + 0.560943i 0.0604499 + 0.0220020i
\(651\) −9.55258 + 3.47686i −0.374395 + 0.136269i
\(652\) −7.13868 + 5.99006i −0.279572 + 0.234589i
\(653\) 9.68172 + 16.7692i 0.378875 + 0.656231i 0.990899 0.134609i \(-0.0429777\pi\)
−0.612024 + 0.790839i \(0.709644\pi\)
\(654\) 3.39283 5.87655i 0.132670 0.229791i
\(655\) 2.45412 + 13.9180i 0.0958906 + 0.543822i
\(656\) 1.00531 + 5.70139i 0.0392507 + 0.222602i
\(657\) 3.19140 5.52767i 0.124508 0.215655i
\(658\) 4.97639 + 8.61936i 0.194000 + 0.336017i
\(659\) −36.0738 + 30.2695i −1.40523 + 1.17913i −0.446515 + 0.894776i \(0.647335\pi\)
−0.958719 + 0.284356i \(0.908220\pi\)
\(660\) −3.22816 + 1.17495i −0.125656 + 0.0457350i
\(661\) −35.5867 12.9525i −1.38416 0.503793i −0.460724 0.887543i \(-0.652410\pi\)
−0.923437 + 0.383750i \(0.874632\pi\)
\(662\) −11.6364 9.76410i −0.452262 0.379493i
\(663\) 0.0746781 0.423520i 0.00290026 0.0164482i
\(664\) 7.56995 0.293771
\(665\) 8.44618 9.79637i 0.327529 0.379887i
\(666\) 12.0459 0.466768
\(667\) −0.127248 + 0.721661i −0.00492707 + 0.0279428i
\(668\) 1.67972 + 1.40946i 0.0649904 + 0.0545335i
\(669\) 24.7865 + 9.02155i 0.958302 + 0.348793i
\(670\) −0.480870 + 0.175022i −0.0185776 + 0.00676170i
\(671\) 6.76497 5.67648i 0.261159 0.219138i
\(672\) 1.48371 + 2.56987i 0.0572355 + 0.0991347i
\(673\) −5.23012 + 9.05883i −0.201606 + 0.349192i −0.949046 0.315137i \(-0.897949\pi\)
0.747440 + 0.664329i \(0.231283\pi\)
\(674\) 2.51812 + 14.2809i 0.0969942 + 0.550081i
\(675\) 0.173648 + 0.984808i 0.00668372 + 0.0379053i
\(676\) 5.15506 8.92882i 0.198271 0.343416i
\(677\) −18.1549 31.4451i −0.697748 1.20853i −0.969246 0.246095i \(-0.920852\pi\)
0.271498 0.962439i \(-0.412481\pi\)
\(678\) −4.73273 + 3.97123i −0.181759 + 0.152514i
\(679\) −20.5965 + 7.49651i −0.790420 + 0.287690i
\(680\) 0.246401 + 0.0896825i 0.00944903 + 0.00343917i
\(681\) 0.176116 + 0.147779i 0.00674880 + 0.00566291i
\(682\) −2.04359 + 11.5898i −0.0782533 + 0.443796i
\(683\) 0.481698 0.0184317 0.00921584 0.999958i \(-0.497066\pi\)
0.00921584 + 0.999958i \(0.497066\pi\)
\(684\) 4.28216 + 0.814315i 0.163732 + 0.0311361i
\(685\) 11.5440 0.441072
\(686\) 2.67660 15.1798i 0.102193 0.579567i
\(687\) −4.34651 3.64715i −0.165830 0.139148i
\(688\) 0.567130 + 0.206418i 0.0216216 + 0.00786962i
\(689\) 18.2693 6.64950i 0.696007 0.253326i
\(690\) 0.115819 0.0971837i 0.00440915 0.00369972i
\(691\) 0.0986815 + 0.170921i 0.00375402 + 0.00650215i 0.867896 0.496745i \(-0.165472\pi\)
−0.864142 + 0.503248i \(0.832138\pi\)
\(692\) 5.62701 9.74627i 0.213907 0.370498i
\(693\) −1.77019 10.0392i −0.0672439 0.381359i
\(694\) 2.43692 + 13.8204i 0.0925040 + 0.524616i
\(695\) 3.19637 5.53628i 0.121245 0.210003i
\(696\) 2.42341 + 4.19746i 0.0918589 + 0.159104i
\(697\) −1.16289 + 0.975783i −0.0440477 + 0.0369604i
\(698\) −11.6179 + 4.22856i −0.439743 + 0.160053i
\(699\) 14.6842 + 5.34460i 0.555406 + 0.202151i
\(700\) −2.27318 1.90742i −0.0859181 0.0720939i
\(701\) 1.00561 5.70310i 0.0379814 0.215403i −0.959910 0.280308i \(-0.909563\pi\)
0.997891 + 0.0649050i \(0.0206744\pi\)
\(702\) −1.64009 −0.0619011
\(703\) −0.702932 + 52.5020i −0.0265116 + 1.98015i
\(704\) 3.43534 0.129474
\(705\) 0.582418 3.30305i 0.0219351 0.124400i
\(706\) 27.0080 + 22.6624i 1.01646 + 0.852911i
\(707\) 26.9449 + 9.80714i 1.01337 + 0.368836i
\(708\) −2.56360 + 0.933074i −0.0963460 + 0.0350671i
\(709\) 16.2536 13.6384i 0.610418 0.512201i −0.284357 0.958718i \(-0.591780\pi\)
0.894775 + 0.446517i \(0.147336\pi\)
\(710\) 2.31058 + 4.00204i 0.0867145 + 0.150194i
\(711\) −3.01013 + 5.21369i −0.112889 + 0.195529i
\(712\) 1.58523 + 8.99029i 0.0594090 + 0.336925i
\(713\) −0.0899396 0.510073i −0.00336827 0.0191024i
\(714\) −0.389050 + 0.673855i −0.0145598 + 0.0252184i
\(715\) 2.81713 + 4.87940i 0.105355 + 0.182479i
\(716\) 9.36197 7.85562i 0.349873 0.293578i
\(717\) −2.82750 + 1.02912i −0.105595 + 0.0384333i
\(718\) −22.1655 8.06758i −0.827209 0.301080i
\(719\) −18.0476 15.1438i −0.673063 0.564767i 0.240907 0.970548i \(-0.422555\pi\)
−0.913970 + 0.405781i \(0.867000\pi\)
\(720\) 0.173648 0.984808i 0.00647149 0.0367016i
\(721\) −30.6993 −1.14330
\(722\) −3.79908 + 18.6163i −0.141387 + 0.692827i
\(723\) 14.8229 0.551269
\(724\) −4.06250 + 23.0396i −0.150982 + 0.856259i
\(725\) −3.71287 3.11547i −0.137893 0.115706i
\(726\) −0.753201 0.274143i −0.0279539 0.0101744i
\(727\) −23.9012 + 8.69934i −0.886448 + 0.322641i −0.744809 0.667278i \(-0.767459\pi\)
−0.141639 + 0.989918i \(0.545237\pi\)
\(728\) 3.72821 3.12834i 0.138177 0.115944i
\(729\) −0.500000 0.866025i −0.0185185 0.0320750i
\(730\) 3.19140 5.52767i 0.118119 0.204588i
\(731\) 0.0274804 + 0.155849i 0.00101640 + 0.00576428i
\(732\) 0.446388 + 2.53159i 0.0164990 + 0.0935704i
\(733\) −8.75751 + 15.1685i −0.323466 + 0.560260i −0.981201 0.192990i \(-0.938182\pi\)
0.657735 + 0.753250i \(0.271515\pi\)
\(734\) −14.8438 25.7102i −0.547893 0.948979i
\(735\) 1.38318 1.16063i 0.0510194 0.0428104i
\(736\) −0.142073 + 0.0517103i −0.00523688 + 0.00190607i
\(737\) −1.65195 0.601261i −0.0608504 0.0221477i
\(738\) 4.43490 + 3.72132i 0.163251 + 0.136984i
\(739\) 1.28169 7.26881i 0.0471476 0.267387i −0.952117 0.305734i \(-0.901098\pi\)
0.999264 + 0.0383469i \(0.0122092\pi\)
\(740\) 12.0459 0.442815
\(741\) 0.0957066 7.14833i 0.00351587 0.262601i
\(742\) −35.1763 −1.29136
\(743\) −3.22662 + 18.2991i −0.118373 + 0.671327i 0.866652 + 0.498914i \(0.166268\pi\)
−0.985025 + 0.172413i \(0.944843\pi\)
\(744\) −2.62427 2.20203i −0.0962105 0.0807302i
\(745\) 1.13308 + 0.412408i 0.0415129 + 0.0151095i
\(746\) −13.5534 + 4.93303i −0.496225 + 0.180611i
\(747\) 5.79892 4.86587i 0.212171 0.178033i
\(748\) 0.450397 + 0.780110i 0.0164681 + 0.0285237i
\(749\) 11.5226 19.9577i 0.421027 0.729240i
\(750\) 0.173648 + 0.984808i 0.00634073 + 0.0359601i
\(751\) −4.81366 27.2996i −0.175653 0.996177i −0.937388 0.348288i \(-0.886763\pi\)
0.761735 0.647889i \(-0.224348\pi\)
\(752\) −1.67700 + 2.90466i −0.0611541 + 0.105922i
\(753\) 14.3342 + 24.8276i 0.522369 + 0.904769i
\(754\) 6.08943 5.10964i 0.221764 0.186082i
\(755\) −22.7098 + 8.26568i −0.826493 + 0.300819i
\(756\) 2.78847 + 1.01492i 0.101416 + 0.0369123i
\(757\) 2.44604 + 2.05247i 0.0889028 + 0.0745983i 0.686156 0.727455i \(-0.259297\pi\)
−0.597253 + 0.802053i \(0.703741\pi\)
\(758\) −2.23580 + 12.6799i −0.0812079 + 0.460553i
\(759\) 0.519392 0.0188527
\(760\) 4.28216 + 0.814315i 0.155330 + 0.0295383i
\(761\) 12.0427 0.436548 0.218274 0.975888i \(-0.429957\pi\)
0.218274 + 0.975888i \(0.429957\pi\)
\(762\) 2.23442 12.6720i 0.0809444 0.459059i
\(763\) 15.4250 + 12.9431i 0.558423 + 0.468573i
\(764\) −20.3144 7.39382i −0.734948 0.267499i
\(765\) 0.246401 0.0896825i 0.00890863 0.00324248i
\(766\) 12.8350 10.7698i 0.463746 0.389129i
\(767\) 2.23718 + 3.87491i 0.0807800 + 0.139915i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) −3.61004 20.4736i −0.130181 0.738295i −0.978095 0.208160i \(-0.933252\pi\)
0.847913 0.530135i \(-0.177859\pi\)
\(770\) −1.77019 10.0392i −0.0637932 0.361789i
\(771\) −4.88454 + 8.46026i −0.175912 + 0.304689i
\(772\) 12.2411 + 21.2021i 0.440565 + 0.763081i
\(773\) −19.7021 + 16.5321i −0.708637 + 0.594617i −0.924216 0.381870i \(-0.875280\pi\)
0.215580 + 0.976486i \(0.430836\pi\)
\(774\) 0.567130 0.206418i 0.0203851 0.00741955i
\(775\) 3.21915 + 1.17167i 0.115635 + 0.0420878i
\(776\) −5.65824 4.74783i −0.203119 0.170437i
\(777\) −6.20710 + 35.2022i −0.222678 + 1.26287i
\(778\) −26.3041 −0.943049
\(779\) −16.4782 + 19.1124i −0.590393 + 0.684772i
\(780\) −1.64009 −0.0587245
\(781\) −2.75670 + 15.6341i −0.0986427 + 0.559430i
\(782\) −0.0303694 0.0254829i −0.00108601 0.000911268i
\(783\) 4.55451 + 1.65771i 0.162765 + 0.0592416i
\(784\) −1.69672 + 0.617557i −0.0605973 + 0.0220556i
\(785\) 15.8493 13.2991i 0.565684 0.474665i
\(786\) −7.06637 12.2393i −0.252049 0.436562i
\(787\) −22.1978 + 38.4478i −0.791267 + 1.37052i 0.133915 + 0.990993i \(0.457245\pi\)
−0.925183 + 0.379522i \(0.876088\pi\)
\(788\) −4.33130 24.5640i −0.154296 0.875057i
\(789\) −1.00272 5.68669i −0.0356976 0.202451i
\(790\) −3.01013 + 5.21369i −0.107096 + 0.185495i
\(791\) −9.16658 15.8770i −0.325926 0.564521i
\(792\) 2.63162 2.20819i 0.0935106 0.0784647i
\(793\) 3.96182 1.44199i 0.140688 0.0512064i
\(794\) 9.73666 + 3.54386i 0.345541 + 0.125767i
\(795\) 9.08081 + 7.61970i 0.322063 + 0.270243i
\(796\) 1.37086 7.77454i 0.0485889 0.275561i
\(797\) 54.8407 1.94256 0.971279 0.237944i \(-0.0764733\pi\)
0.971279 + 0.237944i \(0.0764733\pi\)
\(798\) −4.58625 + 12.0943i −0.162352 + 0.428135i
\(799\) −0.879469 −0.0311134
\(800\) 0.173648 0.984808i 0.00613939 0.0348182i
\(801\) 6.99321 + 5.86800i 0.247093 + 0.207335i
\(802\) 8.92089 + 3.24694i 0.315007 + 0.114653i
\(803\) 20.6047 7.49951i 0.727125 0.264652i
\(804\) 0.392009 0.328934i 0.0138251 0.0116006i
\(805\) 0.224324 + 0.388540i 0.00790638 + 0.0136943i
\(806\) −2.80926 + 4.86578i −0.0989519 + 0.171390i
\(807\) 4.93066 + 27.9632i 0.173568 + 0.984351i
\(808\) 1.67796 + 9.51618i 0.0590304 + 0.334778i
\(809\) 22.7992 39.4894i 0.801578 1.38837i −0.116999 0.993132i \(-0.537328\pi\)
0.918577 0.395242i \(-0.129339\pi\)
\(810\) −0.500000 0.866025i −0.0175682 0.0304290i
\(811\) −39.5132 + 33.1555i −1.38749 + 1.16425i −0.421151 + 0.906990i \(0.638374\pi\)
−0.966343 + 0.257256i \(0.917182\pi\)
\(812\) −13.5152 + 4.91912i −0.474290 + 0.172627i
\(813\) 13.0857 + 4.76279i 0.458934 + 0.167038i
\(814\) 31.7002 + 26.5996i 1.11109 + 0.932316i
\(815\) −1.61821 + 9.17731i −0.0566833 + 0.321467i
\(816\) −0.262214 −0.00917933
\(817\) 0.866581 + 2.48388i 0.0303178 + 0.0869001i
\(818\) 14.9490 0.522681
\(819\) 0.845117 4.79290i 0.0295308 0.167477i
\(820\) 4.43490 + 3.72132i 0.154873 + 0.129954i
\(821\) 4.23286 + 1.54064i 0.147728 + 0.0537685i 0.414826 0.909901i \(-0.363843\pi\)
−0.267098 + 0.963669i \(0.586065\pi\)
\(822\) −10.8478 + 3.94827i −0.378360 + 0.137712i
\(823\) 20.0181 16.7972i 0.697786 0.585512i −0.223357 0.974737i \(-0.571701\pi\)
0.921143 + 0.389225i \(0.127257\pi\)
\(824\) −5.17272 8.95942i −0.180200 0.312116i
\(825\) −1.71767 + 2.97509i −0.0598015 + 0.103579i
\(826\) −1.40577 7.97253i −0.0489130 0.277400i
\(827\) −6.24627 35.4243i −0.217204 1.23182i −0.877041 0.480416i \(-0.840486\pi\)
0.659837 0.751409i \(-0.270625\pi\)
\(828\) −0.0755955 + 0.130935i −0.00262712 + 0.00455031i
\(829\) 13.5963 + 23.5496i 0.472221 + 0.817910i 0.999495 0.0317851i \(-0.0101192\pi\)
−0.527274 + 0.849695i \(0.676786\pi\)
\(830\) 5.79892 4.86587i 0.201283 0.168897i
\(831\) 10.2790 3.74126i 0.356576 0.129783i
\(832\) 1.54118 + 0.560943i 0.0534307 + 0.0194472i
\(833\) −0.362690 0.304333i −0.0125665 0.0105445i
\(834\) −1.11009 + 6.29563i −0.0384392 + 0.218000i
\(835\) 2.19272 0.0758823
\(836\) 9.47086 + 11.5988i 0.327556 + 0.401153i
\(837\) −3.42575 −0.118411
\(838\) −1.07221 + 6.08083i −0.0370390 + 0.210059i
\(839\) 15.2662 + 12.8099i 0.527048 + 0.442246i 0.867081 0.498168i \(-0.165994\pi\)
−0.340032 + 0.940414i \(0.610438\pi\)
\(840\) 2.78847 + 1.01492i 0.0962113 + 0.0350180i
\(841\) 5.17622 1.88399i 0.178490 0.0649652i
\(842\) −0.883431 + 0.741286i −0.0304450 + 0.0255464i
\(843\) 2.10552 + 3.64687i 0.0725179 + 0.125605i
\(844\) 6.84382 11.8538i 0.235574 0.408026i
\(845\) −1.79033 10.1535i −0.0615893 0.349290i
\(846\) 0.582418 + 3.30305i 0.0200239 + 0.113561i
\(847\) 1.18925 2.05985i 0.0408633 0.0707773i
\(848\) −5.92708 10.2660i −0.203537 0.352536i
\(849\) 20.1829 16.9355i 0.692676 0.581224i
\(850\) 0.246401 0.0896825i 0.00845147 0.00307608i
\(851\) −1.71139 0.622896i −0.0586658 0.0213526i
\(852\) −3.54001 2.97042i −0.121279 0.101765i
\(853\) −5.21100 + 29.5530i −0.178421 + 1.01188i 0.755699 + 0.654919i \(0.227297\pi\)
−0.934120 + 0.356958i \(0.883814\pi\)
\(854\) −7.62820 −0.261032
\(855\) 3.80376 2.12872i 0.130086 0.0728006i
\(856\) 7.76606 0.265438
\(857\) 1.41483 8.02388i 0.0483295 0.274090i −0.951061 0.309004i \(-0.900004\pi\)
0.999390 + 0.0349134i \(0.0111155\pi\)
\(858\) −4.31609 3.62163i −0.147349 0.123640i
\(859\) 4.62399 + 1.68299i 0.157768 + 0.0574230i 0.419697 0.907664i \(-0.362136\pi\)
−0.261929 + 0.965087i \(0.584359\pi\)
\(860\) 0.567130 0.206418i 0.0193390 0.00703881i
\(861\) −13.1602 + 11.0427i −0.448499 + 0.376336i
\(862\) 11.7023 + 20.2689i 0.398581 + 0.690362i
\(863\) −2.56539 + 4.44339i −0.0873271 + 0.151255i −0.906380 0.422462i \(-0.861166\pi\)
0.819053 + 0.573717i \(0.194499\pi\)
\(864\) 0.173648 + 0.984808i 0.00590763 + 0.0335038i
\(865\) −1.95424 11.0830i −0.0664462 0.376835i
\(866\) 6.52780 11.3065i 0.221824 0.384210i
\(867\) 8.46562 + 14.6629i 0.287508 + 0.497978i
\(868\) 7.78734 6.53435i 0.264319 0.221790i
\(869\) −19.4344 + 7.07353i −0.659265 + 0.239953i
\(870\) 4.55451 + 1.65771i 0.154412 + 0.0562015i
\(871\) −0.642928 0.539481i −0.0217848 0.0182796i
\(872\) −1.17832 + 6.68257i −0.0399029 + 0.226300i
\(873\) −7.38631 −0.249989
\(874\) −0.566271 0.337124i −0.0191544 0.0114034i
\(875\) −2.96743 −0.100317
\(876\) −1.10836 + 6.28584i −0.0374481 + 0.212379i
\(877\) −20.9188 17.5530i −0.706378 0.592722i 0.217202 0.976127i \(-0.430307\pi\)
−0.923580 + 0.383405i \(0.874751\pi\)
\(878\) 20.9628 + 7.62983i 0.707459 + 0.257494i
\(879\) −30.7997 + 11.2102i −1.03885 + 0.378110i
\(880\) 2.63162 2.20819i 0.0887119 0.0744381i
\(881\) 15.0637 + 26.0912i 0.507510 + 0.879033i 0.999962 + 0.00869372i \(0.00276733\pi\)
−0.492452 + 0.870340i \(0.663899\pi\)
\(882\) −0.902808 + 1.56371i −0.0303991 + 0.0526528i
\(883\) 6.72568 + 38.1433i 0.226337 + 1.28362i 0.860112 + 0.510105i \(0.170393\pi\)
−0.633775 + 0.773518i \(0.718495\pi\)
\(884\) 0.0746781 + 0.423520i 0.00251170 + 0.0142445i
\(885\) −1.36406 + 2.36263i −0.0458525 + 0.0794189i
\(886\) 15.1238 + 26.1952i 0.508095 + 0.880046i
\(887\) 19.3713 16.2544i 0.650424 0.545770i −0.256776 0.966471i \(-0.582660\pi\)
0.907199 + 0.420701i \(0.138216\pi\)
\(888\) −11.3194 + 4.11993i −0.379855 + 0.138256i
\(889\) 35.8806 + 13.0595i 1.20340 + 0.438001i
\(890\) 6.99321 + 5.86800i 0.234413 + 0.196696i
\(891\) 0.596540 3.38315i 0.0199848 0.113340i
\(892\) −26.3773 −0.883176
\(893\) −14.4304 + 2.34572i −0.482894 + 0.0784967i
\(894\) −1.20580 −0.0403280
\(895\) 2.12219 12.0355i 0.0709368 0.402303i
\(896\) −2.27318 1.90742i −0.0759416 0.0637226i
\(897\) 0.233012 + 0.0848094i 0.00778004 + 0.00283170i
\(898\) −29.2736 + 10.6547i −0.976871 + 0.355552i
\(899\) 12.7194 10.6728i 0.424214 0.355958i
\(900\) −0.500000 0.866025i −0.0166667 0.0288675i
\(901\) 1.55416 2.69189i 0.0517767 0.0896798i
\(902\) 3.45358 + 19.5862i 0.114992 + 0.652149i
\(903\) 0.310990 + 1.76371i 0.0103491 + 0.0586927i
\(904\) 3.08907 5.35042i 0.102741 0.177952i
\(905\) 11.6975 + 20.2607i 0.388838 + 0.673488i
\(906\) 18.5132 15.5344i 0.615059 0.516096i
\(907\) −9.35450 + 3.40476i −0.310611 + 0.113053i −0.492622 0.870243i \(-0.663962\pi\)
0.182011 + 0.983296i \(0.441739\pi\)
\(908\) −0.216039 0.0786317i −0.00716950 0.00260948i
\(909\) 7.40227 + 6.21124i 0.245518 + 0.206014i
\(910\) 0.845117 4.79290i 0.0280154 0.158883i
\(911\) 8.60263 0.285018 0.142509 0.989794i \(-0.454483\pi\)
0.142509 + 0.989794i \(0.454483\pi\)
\(912\) −4.30243 + 0.699379i −0.142468 + 0.0231588i
\(913\) 26.0053 0.860650
\(914\) −5.20303 + 29.5078i −0.172101 + 0.976033i
\(915\) 1.96923 + 1.65238i 0.0651007 + 0.0546260i
\(916\) 5.33178 + 1.94061i 0.176167 + 0.0641195i
\(917\) 39.4087 14.3436i 1.30139 0.473667i
\(918\) −0.200868 + 0.168548i −0.00662962 + 0.00556291i
\(919\) −10.3320 17.8956i −0.340823 0.590322i 0.643763 0.765225i \(-0.277372\pi\)
−0.984586 + 0.174903i \(0.944039\pi\)
\(920\) −0.0755955 + 0.130935i −0.00249231 + 0.00431681i
\(921\) 1.95498 + 11.0872i 0.0644186 + 0.365336i
\(922\) 0.167991 + 0.952722i 0.00553247 + 0.0313762i
\(923\) −3.78955 + 6.56369i −0.124735 + 0.216047i
\(924\) 5.09705 + 8.82836i 0.167681 + 0.290432i
\(925\) 9.22768 7.74294i 0.303404 0.254586i
\(926\) −10.3316 + 3.76040i −0.339518 + 0.123574i
\(927\) −9.72154 3.53835i −0.319297 0.116215i
\(928\) −3.71287 3.11547i −0.121881 0.102270i
\(929\) −4.72578 + 26.8013i −0.155048 + 0.879321i 0.803694 + 0.595043i \(0.202865\pi\)
−0.958742 + 0.284278i \(0.908246\pi\)
\(930\) −3.42575 −0.112335
\(931\) −6.76276 4.02615i −0.221640 0.131952i
\(932\) −15.6266 −0.511865
\(933\) −1.03356 + 5.86163i −0.0338373 + 0.191901i
\(934\) 3.35296 + 2.81347i 0.109712 + 0.0920594i
\(935\) 0.846469 + 0.308090i 0.0276825 + 0.0100756i
\(936\) 1.54118 0.560943i 0.0503750 0.0183350i
\(937\) 25.9822 21.8016i 0.848801 0.712228i −0.110724 0.993851i \(-0.535317\pi\)
0.959525 + 0.281623i \(0.0908726\pi\)
\(938\) 0.759262 + 1.31508i 0.0247908 + 0.0429389i
\(939\) 9.92229 17.1859i 0.323802 0.560841i
\(940\) 0.582418 + 3.30305i 0.0189964 + 0.107734i
\(941\) 0.187702 + 1.06451i 0.00611892 + 0.0347021i 0.987714 0.156270i \(-0.0499470\pi\)
−0.981595 + 0.190972i \(0.938836\pi\)
\(942\) −10.3449 + 17.9178i −0.337054 + 0.583794i
\(943\) −0.437648 0.758029i −0.0142518 0.0246848i
\(944\) 2.08987 1.75361i 0.0680194 0.0570750i
\(945\) 2.78847 1.01492i 0.0907089 0.0330153i
\(946\) 1.94828 + 0.709116i 0.0633441 + 0.0230554i
\(947\) −8.33654 6.99519i −0.270901 0.227313i 0.497209 0.867631i \(-0.334358\pi\)
−0.768110 + 0.640318i \(0.778803\pi\)
\(948\) 1.04541 5.92879i 0.0339532 0.192558i
\(949\) 10.4684 0.339817
\(950\) 3.80376 2.12872i 0.123410 0.0690647i
\(951\) 34.3863 1.11505
\(952\) 0.135116 0.766280i 0.00437913 0.0248353i
\(953\) −28.4779 23.8958i −0.922491 0.774062i 0.0519629 0.998649i \(-0.483452\pi\)
−0.974454 + 0.224587i \(0.927897\pi\)
\(954\) −11.1393 4.05436i −0.360647 0.131265i
\(955\) −20.3144 + 7.39382i −0.657357 + 0.239258i
\(956\) 2.30500 1.93412i 0.0745489 0.0625539i
\(957\) 8.32521 + 14.4197i 0.269116 + 0.466123i
\(958\) 7.23209 12.5263i 0.233658 0.404708i
\(959\) −5.94847 33.7354i −0.192086 1.08937i
\(960\) 0.173648 + 0.984808i 0.00560447 + 0.0317845i
\(961\) 9.63213 16.6833i 0.310714 0.538172i
\(962\) 9.87814 + 17.1094i 0.318484 + 0.551630i
\(963\) 5.94915 4.99193i 0.191709 0.160863i
\(964\) −13.9290 + 5.06973i −0.448622 + 0.163285i
\(965\) 23.0057 + 8.37338i 0.740578 + 0.269549i
\(966\) −0.343684 0.288385i −0.0110579 0.00927864i
\(967\) −4.74480 + 26.9091i −0.152582 + 0.865338i 0.808380 + 0.588660i \(0.200344\pi\)
−0.960963 + 0.276677i \(0.910767\pi\)
\(968\) 0.801540 0.0257625
\(969\) −0.722896 0.885319i −0.0232228 0.0284405i
\(970\) −7.38631 −0.237160
\(971\) −1.00978 + 5.72675i −0.0324054 + 0.183780i −0.996714 0.0810005i \(-0.974188\pi\)
0.964309 + 0.264781i \(0.0852996\pi\)
\(972\) 0.766044 + 0.642788i 0.0245709 + 0.0206174i
\(973\) −17.8260 6.48812i −0.571474 0.208000i
\(974\) 16.0414 5.83859i 0.513999 0.187080i
\(975\) −1.25638 + 1.05423i −0.0402363 + 0.0337623i
\(976\) −1.28532 2.22625i −0.0411422 0.0712604i
\(977\) 2.57054 4.45231i 0.0822389 0.142442i −0.821972 0.569527i \(-0.807126\pi\)
0.904211 + 0.427085i \(0.140460\pi\)
\(978\) −1.61821 9.17731i −0.0517445 0.293458i
\(979\) 5.44580 + 30.8847i 0.174049 + 0.987079i
\(980\) −0.902808 + 1.56371i −0.0288391 + 0.0499509i
\(981\) 3.39283 + 5.87655i 0.108325 + 0.187624i
\(982\) −9.51109 + 7.98075i −0.303511 + 0.254676i
\(983\) −17.7836 + 6.47268i −0.567207 + 0.206447i −0.609675 0.792651i \(-0.708700\pi\)
0.0424681 + 0.999098i \(0.486478\pi\)
\(984\) −5.44021 1.98007i −0.173427 0.0631224i
\(985\) −19.1074 16.0330i −0.608813 0.510854i
\(986\) 0.220690 1.25159i 0.00702820 0.0398589i
\(987\) −9.95278 −0.316800
\(988\) 2.35494 + 6.74997i 0.0749206 + 0.214745i
\(989\) −0.0912478 −0.00290151
\(990\) 0.596540 3.38315i 0.0189593 0.107523i
\(991\) 47.9819 + 40.2616i 1.52420 + 1.27895i 0.827261 + 0.561818i \(0.189898\pi\)
0.696935 + 0.717134i \(0.254546\pi\)
\(992\) 3.21915 + 1.17167i 0.102208 + 0.0372007i
\(993\) 14.2742 5.19537i 0.452977 0.164870i
\(994\) 10.5047 8.81451i 0.333190 0.279579i
\(995\) −3.94724 6.83682i −0.125136 0.216742i
\(996\) −3.78497 + 6.55577i −0.119931 + 0.207727i
\(997\) −8.34247 47.3125i −0.264209 1.49840i −0.771279 0.636498i \(-0.780382\pi\)
0.507070 0.861905i \(-0.330729\pi\)
\(998\) 4.18770 + 23.7496i 0.132559 + 0.751782i
\(999\) −6.02294 + 10.4320i −0.190557 + 0.330055i
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 570.2.u.i.511.2 12
19.9 even 9 inner 570.2.u.i.541.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.u.i.511.2 12 1.1 even 1 trivial
570.2.u.i.541.2 yes 12 19.9 even 9 inner