Properties

Label 354.2.e.a.139.2
Level $354$
Weight $2$
Character 354.139
Analytic conductor $2.827$
Analytic rank $0$
Dimension $56$
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] = [354,2,Mod(7,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 354.e (of order \(29\), degree \(28\), 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: \(2.82670423155\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(2\) over \(\Q(\zeta_{29})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 139.2
Character \(\chi\) \(=\) 354.139
Dual form 354.2.e.a.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.856857 - 0.515554i) q^{2} +(-0.370138 + 0.928977i) q^{3} +(0.468408 + 0.883512i) q^{4} +(3.11390 + 0.338657i) q^{5} +(0.796093 - 0.605174i) q^{6} +(2.05914 + 0.693803i) q^{7} +(0.0541389 - 0.998533i) q^{8} +(-0.725995 - 0.687699i) q^{9} +O(q^{10})\) \(q+(-0.856857 - 0.515554i) q^{2} +(-0.370138 + 0.928977i) q^{3} +(0.468408 + 0.883512i) q^{4} +(3.11390 + 0.338657i) q^{5} +(0.796093 - 0.605174i) q^{6} +(2.05914 + 0.693803i) q^{7} +(0.0541389 - 0.998533i) q^{8} +(-0.725995 - 0.687699i) q^{9} +(-2.49357 - 1.89557i) q^{10} +(-0.557034 - 0.821564i) q^{11} +(-0.994138 + 0.108119i) q^{12} +(-1.28635 + 1.21850i) q^{13} +(-1.40669 - 1.65609i) q^{14} +(-1.46718 + 2.76739i) q^{15} +(-0.561187 + 0.827689i) q^{16} +(1.74059 - 0.586475i) q^{17} +(0.267528 + 0.963550i) q^{18} +(-0.606126 + 3.69721i) q^{19} +(1.15937 + 2.90980i) q^{20} +(-1.40669 + 1.65609i) q^{21} +(0.0537383 + 0.991144i) q^{22} +(0.574951 - 2.07079i) q^{23} +(0.907575 + 0.419889i) q^{24} +(4.69860 + 1.03424i) q^{25} +(1.73042 - 0.380895i) q^{26} +(0.907575 - 0.419889i) q^{27} +(0.351533 + 2.14425i) q^{28} +(6.78229 - 4.08077i) q^{29} +(2.68390 - 1.61485i) q^{30} +(0.950438 + 5.79742i) q^{31} +(0.907575 - 0.419889i) q^{32} +(0.969393 - 0.213380i) q^{33} +(-1.79380 - 0.394845i) q^{34} +(6.17699 + 2.85778i) q^{35} +(0.267528 - 0.963550i) q^{36} +(0.0190960 + 0.352205i) q^{37} +(2.42547 - 2.85549i) q^{38} +(-0.655829 - 1.64601i) q^{39} +(0.506744 - 3.09100i) q^{40} +(0.700608 + 2.52336i) q^{41} +(2.05914 - 0.693803i) q^{42} +(-1.72676 + 2.54679i) q^{43} +(0.464942 - 0.876974i) q^{44} +(-2.02779 - 2.38729i) q^{45} +(-1.56025 + 1.47795i) q^{46} +(-7.75183 + 0.843062i) q^{47} +(-0.561187 - 0.827689i) q^{48} +(-1.81398 - 1.37895i) q^{49} +(-3.49283 - 3.30858i) q^{50} +(-0.0994392 + 1.83405i) q^{51} +(-1.67910 - 0.565754i) q^{52} +(9.67245 - 7.35281i) q^{53} +(-0.994138 - 0.108119i) q^{54} +(-1.45632 - 2.74691i) q^{55} +(0.804265 - 2.01855i) q^{56} +(-3.21027 - 1.93155i) q^{57} -7.91531 q^{58} +(-7.65953 - 0.575876i) q^{59} -3.13227 q^{60} +(1.81807 + 1.09390i) q^{61} +(2.17449 - 5.45756i) q^{62} +(-1.01779 - 1.91976i) q^{63} +(-0.994138 - 0.108119i) q^{64} +(-4.41824 + 3.35866i) q^{65} +(-0.940640 - 0.316939i) q^{66} +(-0.708395 + 13.0656i) q^{67} +(1.33347 + 1.26313i) q^{68} +(1.71090 + 1.30059i) q^{69} +(-3.81946 - 5.63328i) q^{70} +(6.21527 - 0.675951i) q^{71} +(-0.725995 + 0.687699i) q^{72} +(-10.6342 - 12.5196i) q^{73} +(0.165218 - 0.311634i) q^{74} +(-2.69992 + 3.98208i) q^{75} +(-3.55044 + 1.19628i) q^{76} +(-0.577005 - 2.07818i) q^{77} +(-0.286653 + 1.74851i) q^{78} +(-2.39183 - 6.00303i) q^{79} +(-2.02779 + 2.38729i) q^{80} +(0.0541389 + 0.998533i) q^{81} +(0.700608 - 2.52336i) q^{82} +(-14.3587 - 6.64306i) q^{83} +(-2.12208 - 0.467105i) q^{84} +(5.61866 - 1.23676i) q^{85} +(2.79260 - 1.29199i) q^{86} +(1.28055 + 7.81103i) q^{87} +(-0.850516 + 0.511739i) q^{88} +(3.03286 - 1.82481i) q^{89} +(0.506744 + 3.09100i) q^{90} +(-3.49418 + 1.61658i) q^{91} +(2.09888 - 0.461998i) q^{92} +(-5.73746 - 1.26291i) q^{93} +(7.07686 + 3.27410i) q^{94} +(-3.13951 + 11.3075i) q^{95} +(0.0541389 + 0.998533i) q^{96} +(5.06980 - 5.96863i) q^{97} +(0.843397 + 2.11677i) q^{98} +(-0.160585 + 0.979524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{5}{29}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.856857 0.515554i −0.605890 0.364552i
\(3\) −0.370138 + 0.928977i −0.213699 + 0.536345i
\(4\) 0.468408 + 0.883512i 0.234204 + 0.441756i
\(5\) 3.11390 + 0.338657i 1.39258 + 0.151452i 0.773460 0.633845i \(-0.218524\pi\)
0.619120 + 0.785297i \(0.287490\pi\)
\(6\) 0.796093 0.605174i 0.325004 0.247061i
\(7\) 2.05914 + 0.693803i 0.778280 + 0.262233i 0.680279 0.732953i \(-0.261859\pi\)
0.0980009 + 0.995186i \(0.468755\pi\)
\(8\) 0.0541389 0.998533i 0.0191410 0.353035i
\(9\) −0.725995 0.687699i −0.241998 0.229233i
\(10\) −2.49357 1.89557i −0.788537 0.599431i
\(11\) −0.557034 0.821564i −0.167952 0.247711i 0.734394 0.678724i \(-0.237467\pi\)
−0.902346 + 0.431013i \(0.858156\pi\)
\(12\) −0.994138 + 0.108119i −0.286983 + 0.0312113i
\(13\) −1.28635 + 1.21850i −0.356771 + 0.337951i −0.845002 0.534763i \(-0.820401\pi\)
0.488231 + 0.872714i \(0.337642\pi\)
\(14\) −1.40669 1.65609i −0.375954 0.442607i
\(15\) −1.46718 + 2.76739i −0.378824 + 0.714538i
\(16\) −0.561187 + 0.827689i −0.140297 + 0.206922i
\(17\) 1.74059 0.586475i 0.422156 0.142241i −0.100202 0.994967i \(-0.531949\pi\)
0.522358 + 0.852726i \(0.325052\pi\)
\(18\) 0.267528 + 0.963550i 0.0630570 + 0.227111i
\(19\) −0.606126 + 3.69721i −0.139055 + 0.848197i 0.821521 + 0.570179i \(0.193126\pi\)
−0.960576 + 0.278019i \(0.910322\pi\)
\(20\) 1.15937 + 2.90980i 0.259243 + 0.650651i
\(21\) −1.40669 + 1.65609i −0.306965 + 0.361387i
\(22\) 0.0537383 + 0.991144i 0.0114570 + 0.211313i
\(23\) 0.574951 2.07079i 0.119886 0.431789i −0.879109 0.476621i \(-0.841861\pi\)
0.998995 + 0.0448320i \(0.0142752\pi\)
\(24\) 0.907575 + 0.419889i 0.185258 + 0.0857095i
\(25\) 4.69860 + 1.03424i 0.939721 + 0.206848i
\(26\) 1.73042 0.380895i 0.339364 0.0746997i
\(27\) 0.907575 0.419889i 0.174663 0.0808077i
\(28\) 0.351533 + 2.14425i 0.0664334 + 0.405226i
\(29\) 6.78229 4.08077i 1.25944 0.757779i 0.280093 0.959973i \(-0.409635\pi\)
0.979346 + 0.202193i \(0.0648070\pi\)
\(30\) 2.68390 1.61485i 0.490012 0.294830i
\(31\) 0.950438 + 5.79742i 0.170704 + 1.04125i 0.923670 + 0.383188i \(0.125174\pi\)
−0.752967 + 0.658059i \(0.771378\pi\)
\(32\) 0.907575 0.419889i 0.160438 0.0742266i
\(33\) 0.969393 0.213380i 0.168750 0.0371446i
\(34\) −1.79380 0.394845i −0.307634 0.0677154i
\(35\) 6.17699 + 2.85778i 1.04410 + 0.483053i
\(36\) 0.267528 0.963550i 0.0445881 0.160592i
\(37\) 0.0190960 + 0.352205i 0.00313936 + 0.0579021i 0.999683 0.0251651i \(-0.00801115\pi\)
−0.996544 + 0.0830672i \(0.973528\pi\)
\(38\) 2.42547 2.85549i 0.393464 0.463221i
\(39\) −0.655829 1.64601i −0.105017 0.263572i
\(40\) 0.506744 3.09100i 0.0801233 0.488730i
\(41\) 0.700608 + 2.52336i 0.109417 + 0.394083i 0.997896 0.0648334i \(-0.0206516\pi\)
−0.888480 + 0.458916i \(0.848238\pi\)
\(42\) 2.05914 0.693803i 0.317731 0.107056i
\(43\) −1.72676 + 2.54679i −0.263329 + 0.388381i −0.936251 0.351332i \(-0.885729\pi\)
0.672922 + 0.739714i \(0.265039\pi\)
\(44\) 0.464942 0.876974i 0.0700927 0.132209i
\(45\) −2.02779 2.38729i −0.302284 0.355877i
\(46\) −1.56025 + 1.47795i −0.230047 + 0.217912i
\(47\) −7.75183 + 0.843062i −1.13072 + 0.122973i −0.654294 0.756241i \(-0.727034\pi\)
−0.476427 + 0.879214i \(0.658068\pi\)
\(48\) −0.561187 0.827689i −0.0810004 0.119467i
\(49\) −1.81398 1.37895i −0.259140 0.196993i
\(50\) −3.49283 3.30858i −0.493960 0.467904i
\(51\) −0.0994392 + 1.83405i −0.0139243 + 0.256818i
\(52\) −1.67910 0.565754i −0.232849 0.0784560i
\(53\) 9.67245 7.35281i 1.32861 1.00999i 0.330813 0.943696i \(-0.392677\pi\)
0.997800 0.0662898i \(-0.0211162\pi\)
\(54\) −0.994138 0.108119i −0.135285 0.0147131i
\(55\) −1.45632 2.74691i −0.196370 0.370394i
\(56\) 0.804265 2.01855i 0.107474 0.269741i
\(57\) −3.21027 1.93155i −0.425210 0.255841i
\(58\) −7.91531 −1.03933
\(59\) −7.65953 0.575876i −0.997186 0.0749727i
\(60\) −3.13227 −0.404374
\(61\) 1.81807 + 1.09390i 0.232780 + 0.140059i 0.627166 0.778886i \(-0.284215\pi\)
−0.394385 + 0.918945i \(0.629042\pi\)
\(62\) 2.17449 5.45756i 0.276161 0.693111i
\(63\) −1.01779 1.91976i −0.128230 0.241868i
\(64\) −0.994138 0.108119i −0.124267 0.0135149i
\(65\) −4.41824 + 3.35866i −0.548015 + 0.416590i
\(66\) −0.940640 0.316939i −0.115785 0.0390124i
\(67\) −0.708395 + 13.0656i −0.0865443 + 1.59622i 0.556805 + 0.830643i \(0.312027\pi\)
−0.643350 + 0.765572i \(0.722456\pi\)
\(68\) 1.33347 + 1.26313i 0.161707 + 0.153177i
\(69\) 1.71090 + 1.30059i 0.205968 + 0.156573i
\(70\) −3.81946 5.63328i −0.456512 0.673305i
\(71\) 6.21527 0.675951i 0.737616 0.0802206i 0.268405 0.963306i \(-0.413504\pi\)
0.469212 + 0.883086i \(0.344538\pi\)
\(72\) −0.725995 + 0.687699i −0.0855594 + 0.0810462i
\(73\) −10.6342 12.5196i −1.24464 1.46530i −0.832351 0.554249i \(-0.813005\pi\)
−0.412289 0.911053i \(-0.635270\pi\)
\(74\) 0.165218 0.311634i 0.0192062 0.0362267i
\(75\) −2.69992 + 3.98208i −0.311760 + 0.459811i
\(76\) −3.55044 + 1.19628i −0.407264 + 0.137223i
\(77\) −0.577005 2.07818i −0.0657558 0.236831i
\(78\) −0.286653 + 1.74851i −0.0324571 + 0.197980i
\(79\) −2.39183 6.00303i −0.269102 0.675394i 0.730873 0.682513i \(-0.239113\pi\)
−0.999975 + 0.00711944i \(0.997734\pi\)
\(80\) −2.02779 + 2.38729i −0.226713 + 0.266908i
\(81\) 0.0541389 + 0.998533i 0.00601543 + 0.110948i
\(82\) 0.700608 2.52336i 0.0773692 0.278659i
\(83\) −14.3587 6.64306i −1.57608 0.729170i −0.579748 0.814796i \(-0.696849\pi\)
−0.996327 + 0.0856253i \(0.972711\pi\)
\(84\) −2.12208 0.467105i −0.231538 0.0509653i
\(85\) 5.61866 1.23676i 0.609429 0.134145i
\(86\) 2.79260 1.29199i 0.301133 0.139319i
\(87\) 1.28055 + 7.81103i 0.137290 + 0.837431i
\(88\) −0.850516 + 0.511739i −0.0906653 + 0.0545515i
\(89\) 3.03286 1.82481i 0.321482 0.193430i −0.345660 0.938360i \(-0.612345\pi\)
0.667142 + 0.744930i \(0.267517\pi\)
\(90\) 0.506744 + 3.09100i 0.0534155 + 0.325820i
\(91\) −3.49418 + 1.61658i −0.366289 + 0.169463i
\(92\) 2.09888 0.461998i 0.218823 0.0481666i
\(93\) −5.73746 1.26291i −0.594947 0.130958i
\(94\) 7.07686 + 3.27410i 0.729922 + 0.337698i
\(95\) −3.13951 + 11.3075i −0.322106 + 1.16012i
\(96\) 0.0541389 + 0.998533i 0.00552553 + 0.101912i
\(97\) 5.06980 5.96863i 0.514760 0.606022i −0.441959 0.897035i \(-0.645716\pi\)
0.956719 + 0.291013i \(0.0939922\pi\)
\(98\) 0.843397 + 2.11677i 0.0851959 + 0.213826i
\(99\) −0.160585 + 0.979524i −0.0161394 + 0.0984458i
\(100\) 1.28710 + 4.63572i 0.128710 + 0.463572i
\(101\) −9.42406 + 3.17534i −0.937729 + 0.315958i −0.746346 0.665558i \(-0.768194\pi\)
−0.191383 + 0.981515i \(0.561297\pi\)
\(102\) 1.03076 1.52025i 0.102060 0.150527i
\(103\) 4.25593 8.02754i 0.419350 0.790977i −0.580377 0.814348i \(-0.697095\pi\)
0.999727 + 0.0233704i \(0.00743971\pi\)
\(104\) 1.14707 + 1.35044i 0.112480 + 0.132421i
\(105\) −4.94115 + 4.68050i −0.482207 + 0.456770i
\(106\) −12.0787 + 1.31364i −1.17319 + 0.127592i
\(107\) −4.43868 6.54657i −0.429104 0.632880i 0.550258 0.834994i \(-0.314529\pi\)
−0.979362 + 0.202114i \(0.935219\pi\)
\(108\) 0.796093 + 0.605174i 0.0766041 + 0.0582329i
\(109\) 6.22711 + 5.89863i 0.596449 + 0.564987i 0.925224 0.379422i \(-0.123877\pi\)
−0.328775 + 0.944408i \(0.606636\pi\)
\(110\) −0.168322 + 3.10453i −0.0160489 + 0.296005i
\(111\) −0.334258 0.112625i −0.0317264 0.0106899i
\(112\) −1.72981 + 1.31497i −0.163452 + 0.124253i
\(113\) −11.2608 1.22469i −1.05933 0.115209i −0.438169 0.898893i \(-0.644373\pi\)
−0.621160 + 0.783684i \(0.713338\pi\)
\(114\) 1.75492 + 3.31013i 0.164363 + 0.310022i
\(115\) 2.49163 6.25352i 0.232346 0.583144i
\(116\) 6.78229 + 4.08077i 0.629720 + 0.378890i
\(117\) 1.77185 0.163808
\(118\) 6.26623 + 4.44234i 0.576853 + 0.408951i
\(119\) 3.99102 0.365856
\(120\) 2.68390 + 1.61485i 0.245006 + 0.147415i
\(121\) 3.70684 9.30347i 0.336985 0.845770i
\(122\) −0.993866 1.87463i −0.0899804 0.169721i
\(123\) −2.60347 0.283144i −0.234747 0.0255302i
\(124\) −4.67689 + 3.55528i −0.419998 + 0.319274i
\(125\) −0.560758 0.188941i −0.0501557 0.0168994i
\(126\) −0.117637 + 2.16969i −0.0104800 + 0.193291i
\(127\) −4.21098 3.98885i −0.373664 0.353953i 0.477705 0.878520i \(-0.341469\pi\)
−0.851369 + 0.524567i \(0.824227\pi\)
\(128\) 0.796093 + 0.605174i 0.0703654 + 0.0534903i
\(129\) −1.72676 2.54679i −0.152033 0.224232i
\(130\) 5.51737 0.600050i 0.483905 0.0526279i
\(131\) −0.305134 + 0.289038i −0.0266596 + 0.0252534i −0.700913 0.713246i \(-0.747224\pi\)
0.674254 + 0.738500i \(0.264465\pi\)
\(132\) 0.642595 + 0.756522i 0.0559308 + 0.0658468i
\(133\) −3.81323 + 7.19252i −0.330649 + 0.623670i
\(134\) 7.34301 10.8301i 0.634339 0.935580i
\(135\) 2.96830 1.00014i 0.255471 0.0860781i
\(136\) −0.491381 1.76979i −0.0421355 0.151759i
\(137\) −1.63185 + 9.95381i −0.139418 + 0.850412i 0.820811 + 0.571199i \(0.193522\pi\)
−0.960229 + 0.279212i \(0.909927\pi\)
\(138\) −0.795472 1.99648i −0.0677151 0.169952i
\(139\) 9.76676 11.4983i 0.828405 0.975274i −0.171545 0.985176i \(-0.554876\pi\)
0.999951 + 0.00990186i \(0.00315191\pi\)
\(140\) 0.368471 + 6.79605i 0.0311415 + 0.574371i
\(141\) 2.08606 7.51332i 0.175678 0.632736i
\(142\) −5.67408 2.62511i −0.476159 0.220294i
\(143\) 1.71762 + 0.378077i 0.143635 + 0.0316163i
\(144\) 0.976621 0.214970i 0.0813850 0.0179142i
\(145\) 22.5014 10.4102i 1.86864 0.864524i
\(146\) 2.65749 + 16.2100i 0.219935 + 1.34155i
\(147\) 1.95243 1.17474i 0.161034 0.0968910i
\(148\) −0.302232 + 0.181847i −0.0248433 + 0.0149477i
\(149\) −1.26982 7.74554i −0.104028 0.634540i −0.986447 0.164077i \(-0.947535\pi\)
0.882420 0.470463i \(-0.155913\pi\)
\(150\) 4.36642 2.02012i 0.356517 0.164942i
\(151\) 6.23628 1.37271i 0.507502 0.111710i 0.0461634 0.998934i \(-0.485301\pi\)
0.461338 + 0.887224i \(0.347369\pi\)
\(152\) 3.65897 + 0.805400i 0.296782 + 0.0653266i
\(153\) −1.66698 0.771228i −0.134768 0.0623501i
\(154\) −0.577005 + 2.07818i −0.0464964 + 0.167465i
\(155\) 0.996235 + 18.3745i 0.0800195 + 1.47587i
\(156\) 1.14707 1.35044i 0.0918392 0.108121i
\(157\) −2.54233 6.38077i −0.202900 0.509241i 0.791951 0.610584i \(-0.209065\pi\)
−0.994852 + 0.101343i \(0.967686\pi\)
\(158\) −1.04543 + 6.37686i −0.0831702 + 0.507315i
\(159\) 3.25044 + 11.7070i 0.257777 + 0.928429i
\(160\) 2.96830 1.00014i 0.234665 0.0790678i
\(161\) 2.62062 3.86513i 0.206534 0.304615i
\(162\) 0.468408 0.883512i 0.0368016 0.0694153i
\(163\) −9.51086 11.1970i −0.744948 0.877021i 0.250904 0.968012i \(-0.419272\pi\)
−0.995852 + 0.0909914i \(0.970996\pi\)
\(164\) −1.90125 + 1.80096i −0.148463 + 0.140631i
\(165\) 3.09086 0.336151i 0.240623 0.0261693i
\(166\) 8.87853 + 13.0949i 0.689108 + 1.01636i
\(167\) −11.0037 8.36482i −0.851494 0.647289i 0.0856138 0.996328i \(-0.472715\pi\)
−0.937108 + 0.349039i \(0.886508\pi\)
\(168\) 1.57750 + 1.49429i 0.121707 + 0.115287i
\(169\) −0.533839 + 9.84609i −0.0410646 + 0.757391i
\(170\) −5.45200 1.83699i −0.418150 0.140891i
\(171\) 2.98261 2.26732i 0.228086 0.173386i
\(172\) −3.05895 0.332681i −0.233243 0.0253667i
\(173\) −7.12791 13.4447i −0.541925 1.02218i −0.991643 0.129009i \(-0.958821\pi\)
0.449718 0.893170i \(-0.351524\pi\)
\(174\) 2.92976 7.35314i 0.222104 0.557440i
\(175\) 8.95750 + 5.38955i 0.677123 + 0.407412i
\(176\) 0.992600 0.0748200
\(177\) 3.37006 6.90237i 0.253309 0.518814i
\(178\) −3.53951 −0.265298
\(179\) 16.7771 + 10.0944i 1.25398 + 0.754494i 0.978387 0.206781i \(-0.0662988\pi\)
0.275591 + 0.961275i \(0.411126\pi\)
\(180\) 1.15937 2.90980i 0.0864144 0.216884i
\(181\) 4.03749 + 7.61550i 0.300104 + 0.566056i 0.987004 0.160696i \(-0.0513738\pi\)
−0.686900 + 0.726752i \(0.741029\pi\)
\(182\) 3.82744 + 0.416260i 0.283709 + 0.0308552i
\(183\) −1.68914 + 1.28405i −0.124865 + 0.0949200i
\(184\) −2.03662 0.686218i −0.150142 0.0505887i
\(185\) −0.0598137 + 1.10320i −0.00439759 + 0.0811087i
\(186\) 4.26508 + 4.04010i 0.312731 + 0.296235i
\(187\) −1.45140 1.10332i −0.106137 0.0806830i
\(188\) −4.37588 6.45394i −0.319144 0.470702i
\(189\) 2.16014 0.234929i 0.157127 0.0170886i
\(190\) 8.51972 8.07031i 0.618085 0.585482i
\(191\) 3.80882 + 4.48409i 0.275596 + 0.324457i 0.882495 0.470322i \(-0.155862\pi\)
−0.606898 + 0.794779i \(0.707587\pi\)
\(192\) 0.468408 0.883512i 0.0338045 0.0637620i
\(193\) −5.66145 + 8.35001i −0.407520 + 0.601047i −0.974963 0.222366i \(-0.928622\pi\)
0.567444 + 0.823412i \(0.307933\pi\)
\(194\) −7.42124 + 2.50051i −0.532814 + 0.179526i
\(195\) −1.48476 5.34761i −0.106326 0.382950i
\(196\) 0.368636 2.24858i 0.0263312 0.160613i
\(197\) 5.01974 + 12.5986i 0.357642 + 0.897613i 0.992191 + 0.124731i \(0.0398066\pi\)
−0.634549 + 0.772883i \(0.718814\pi\)
\(198\) 0.642595 0.756522i 0.0456673 0.0537637i
\(199\) −0.229243 4.22814i −0.0162506 0.299725i −0.995349 0.0963369i \(-0.969287\pi\)
0.979098 0.203388i \(-0.0651954\pi\)
\(200\) 1.28710 4.63572i 0.0910118 0.327795i
\(201\) −11.8754 5.49415i −0.837628 0.387528i
\(202\) 9.71213 + 2.13780i 0.683343 + 0.150415i
\(203\) 16.7969 3.69728i 1.17891 0.259498i
\(204\) −1.66698 + 0.771228i −0.116712 + 0.0539968i
\(205\) 1.32707 + 8.09477i 0.0926866 + 0.565363i
\(206\) −7.78536 + 4.68429i −0.542432 + 0.326370i
\(207\) −1.84149 + 1.10799i −0.127992 + 0.0770105i
\(208\) −0.286653 1.74851i −0.0198758 0.121237i
\(209\) 3.37512 1.56150i 0.233462 0.108011i
\(210\) 6.64691 1.46310i 0.458680 0.100963i
\(211\) 12.8405 + 2.82641i 0.883976 + 0.194578i 0.633684 0.773592i \(-0.281542\pi\)
0.250293 + 0.968170i \(0.419473\pi\)
\(212\) 11.0270 + 5.10161i 0.757334 + 0.350380i
\(213\) −1.67256 + 6.02403i −0.114602 + 0.412760i
\(214\) 0.428209 + 7.89785i 0.0292718 + 0.539886i
\(215\) −6.23947 + 7.34567i −0.425528 + 0.500970i
\(216\) −0.370138 0.928977i −0.0251847 0.0632089i
\(217\) −2.06519 + 12.5971i −0.140194 + 0.855146i
\(218\) −2.29468 8.26470i −0.155415 0.559756i
\(219\) 15.5665 5.24496i 1.05189 0.354422i
\(220\) 1.74478 2.57336i 0.117633 0.173496i
\(221\) −1.52440 + 2.87533i −0.102542 + 0.193416i
\(222\) 0.228347 + 0.268831i 0.0153257 + 0.0180428i
\(223\) −16.9128 + 16.0206i −1.13256 + 1.07282i −0.135939 + 0.990717i \(0.543405\pi\)
−0.996624 + 0.0821029i \(0.973836\pi\)
\(224\) 2.16014 0.234929i 0.144330 0.0156969i
\(225\) −2.69992 3.98208i −0.179995 0.265472i
\(226\) 9.01752 + 6.85494i 0.599837 + 0.455984i
\(227\) 6.46439 + 6.12340i 0.429057 + 0.406424i 0.871518 0.490363i \(-0.163136\pi\)
−0.442461 + 0.896788i \(0.645895\pi\)
\(228\) 0.202835 3.74107i 0.0134331 0.247758i
\(229\) 18.6128 + 6.27139i 1.22997 + 0.414425i 0.857918 0.513787i \(-0.171758\pi\)
0.372051 + 0.928212i \(0.378654\pi\)
\(230\) −5.35900 + 4.07380i −0.353362 + 0.268619i
\(231\) 2.14416 + 0.233191i 0.141075 + 0.0153428i
\(232\) −3.70760 6.99327i −0.243416 0.459131i
\(233\) 7.81978 19.6262i 0.512291 1.28575i −0.414457 0.910069i \(-0.636029\pi\)
0.926748 0.375684i \(-0.122592\pi\)
\(234\) −1.51822 0.913484i −0.0992493 0.0597163i
\(235\) −24.4240 −1.59324
\(236\) −3.07899 7.03703i −0.200425 0.458072i
\(237\) 6.46198 0.419751
\(238\) −3.41973 2.05758i −0.221668 0.133373i
\(239\) 6.53083 16.3912i 0.422445 1.06026i −0.551642 0.834081i \(-0.685999\pi\)
0.974087 0.226175i \(-0.0726221\pi\)
\(240\) −1.46718 2.76739i −0.0947060 0.178635i
\(241\) −12.1619 1.32269i −0.783417 0.0852017i −0.292336 0.956316i \(-0.594433\pi\)
−0.491081 + 0.871114i \(0.663398\pi\)
\(242\) −7.97267 + 6.06067i −0.512503 + 0.389594i
\(243\) −0.947653 0.319302i −0.0607920 0.0204832i
\(244\) −0.114872 + 2.11868i −0.00735390 + 0.135635i
\(245\) −5.18156 4.90823i −0.331038 0.313576i
\(246\) 2.08482 + 1.58484i 0.132923 + 0.101046i
\(247\) −3.72535 5.49448i −0.237038 0.349606i
\(248\) 5.84037 0.635179i 0.370864 0.0403339i
\(249\) 11.4860 10.8801i 0.727893 0.689497i
\(250\) 0.383080 + 0.450997i 0.0242281 + 0.0285235i
\(251\) −7.41939 + 13.9945i −0.468308 + 0.883322i 0.531045 + 0.847344i \(0.321800\pi\)
−0.999353 + 0.0359783i \(0.988545\pi\)
\(252\) 1.21939 1.79847i 0.0768144 0.113293i
\(253\) −2.02155 + 0.681140i −0.127094 + 0.0428229i
\(254\) 1.55174 + 5.58886i 0.0973648 + 0.350676i
\(255\) −0.930758 + 5.67738i −0.0582864 + 0.355531i
\(256\) −0.370138 0.928977i −0.0231336 0.0580610i
\(257\) −14.0546 + 16.5463i −0.876700 + 1.03213i 0.122514 + 0.992467i \(0.460905\pi\)
−0.999213 + 0.0396637i \(0.987371\pi\)
\(258\) 0.166585 + 3.07247i 0.0103711 + 0.191284i
\(259\) −0.205040 + 0.738486i −0.0127405 + 0.0458873i
\(260\) −5.03695 2.33034i −0.312379 0.144522i
\(261\) −7.73025 1.70156i −0.478491 0.105324i
\(262\) 0.410470 0.0903514i 0.0253589 0.00558193i
\(263\) −22.2144 + 10.2775i −1.36980 + 0.633738i −0.960402 0.278618i \(-0.910124\pi\)
−0.409399 + 0.912355i \(0.634262\pi\)
\(264\) −0.160585 0.979524i −0.00988331 0.0602855i
\(265\) 32.6092 19.6203i 2.00317 1.20526i
\(266\) 6.97552 4.19703i 0.427697 0.257337i
\(267\) 0.572630 + 3.49289i 0.0350444 + 0.213761i
\(268\) −11.8754 + 5.49415i −0.725407 + 0.335609i
\(269\) −13.6884 + 3.01304i −0.834596 + 0.183708i −0.611656 0.791124i \(-0.709496\pi\)
−0.222940 + 0.974832i \(0.571565\pi\)
\(270\) −3.05903 0.673344i −0.186167 0.0409784i
\(271\) −4.04332 1.87064i −0.245614 0.113633i 0.293220 0.956045i \(-0.405273\pi\)
−0.538834 + 0.842412i \(0.681135\pi\)
\(272\) −0.491381 + 1.76979i −0.0297943 + 0.107309i
\(273\) −0.208436 3.84437i −0.0126151 0.232672i
\(274\) 6.52999 7.68769i 0.394491 0.464431i
\(275\) −1.76759 4.43631i −0.106590 0.267520i
\(276\) −0.347689 + 2.12081i −0.0209284 + 0.127658i
\(277\) 1.83719 + 6.61697i 0.110386 + 0.397575i 0.998014 0.0629854i \(-0.0200621\pi\)
−0.887628 + 0.460561i \(0.847648\pi\)
\(278\) −14.2967 + 4.81712i −0.857460 + 0.288912i
\(279\) 3.29687 4.86251i 0.197378 0.291111i
\(280\) 3.18800 6.01321i 0.190520 0.359358i
\(281\) −8.69634 10.2381i −0.518780 0.610755i 0.438919 0.898527i \(-0.355362\pi\)
−0.957699 + 0.287771i \(0.907086\pi\)
\(282\) −5.66098 + 5.36236i −0.337106 + 0.319324i
\(283\) −23.0893 + 2.51112i −1.37252 + 0.149270i −0.764485 0.644641i \(-0.777007\pi\)
−0.608033 + 0.793911i \(0.708041\pi\)
\(284\) 3.50849 + 5.17464i 0.208191 + 0.307058i
\(285\) −9.34233 7.10186i −0.553392 0.420678i
\(286\) −1.27684 1.20948i −0.0755009 0.0715182i
\(287\) −0.308070 + 5.68203i −0.0181848 + 0.335399i
\(288\) −0.947653 0.319302i −0.0558410 0.0188150i
\(289\) −10.8479 + 8.24633i −0.638110 + 0.485078i
\(290\) −24.6475 2.68058i −1.44735 0.157409i
\(291\) 3.66819 + 6.91894i 0.215033 + 0.405596i
\(292\) 6.08002 15.2597i 0.355807 0.893007i
\(293\) 15.9404 + 9.59104i 0.931250 + 0.560314i 0.898415 0.439147i \(-0.144719\pi\)
0.0328341 + 0.999461i \(0.489547\pi\)
\(294\) −2.27860 −0.132891
\(295\) −23.6560 4.38718i −1.37731 0.255431i
\(296\) 0.352722 0.0205015
\(297\) −0.850516 0.511739i −0.0493520 0.0296941i
\(298\) −2.90519 + 7.29148i −0.168293 + 0.422384i
\(299\) 1.78366 + 3.36434i 0.103152 + 0.194565i
\(300\) −4.78288 0.520170i −0.276140 0.0300320i
\(301\) −5.32261 + 4.04614i −0.306790 + 0.233216i
\(302\) −6.05131 2.03892i −0.348214 0.117327i
\(303\) 0.538391 9.93005i 0.0309298 0.570466i
\(304\) −2.71999 2.57651i −0.156002 0.147773i
\(305\) 5.29085 + 4.02200i 0.302953 + 0.230299i
\(306\) 1.03076 + 1.52025i 0.0589244 + 0.0869070i
\(307\) 26.5238 2.88464i 1.51380 0.164635i 0.686801 0.726845i \(-0.259014\pi\)
0.826994 + 0.562210i \(0.190049\pi\)
\(308\) 1.56583 1.48323i 0.0892212 0.0845148i
\(309\) 5.88212 + 6.92496i 0.334622 + 0.393947i
\(310\) 8.61940 16.2579i 0.489549 0.923387i
\(311\) −5.84629 + 8.62263i −0.331513 + 0.488944i −0.956517 0.291677i \(-0.905787\pi\)
0.625004 + 0.780621i \(0.285097\pi\)
\(312\) −1.67910 + 0.565754i −0.0950602 + 0.0320295i
\(313\) −5.98583 21.5590i −0.338339 1.21859i −0.915621 0.402043i \(-0.868300\pi\)
0.577281 0.816545i \(-0.304114\pi\)
\(314\) −1.11122 + 6.77812i −0.0627096 + 0.382511i
\(315\) −2.51917 6.32264i −0.141939 0.356241i
\(316\) 4.18340 4.92508i 0.235335 0.277057i
\(317\) −1.42269 26.2400i −0.0799064 1.47379i −0.713791 0.700359i \(-0.753023\pi\)
0.633885 0.773428i \(-0.281459\pi\)
\(318\) 3.25044 11.7070i 0.182276 0.656498i
\(319\) −7.13058 3.29896i −0.399236 0.184706i
\(320\) −3.05903 0.673344i −0.171005 0.0376411i
\(321\) 7.72453 1.70030i 0.431141 0.0949014i
\(322\) −4.23818 + 1.96079i −0.236184 + 0.109271i
\(323\) 1.11330 + 6.79082i 0.0619455 + 0.377851i
\(324\) −0.856857 + 0.515554i −0.0476032 + 0.0286419i
\(325\) −7.30429 + 4.39485i −0.405169 + 0.243782i
\(326\) 2.37677 + 14.4976i 0.131637 + 0.802950i
\(327\) −7.78459 + 3.60153i −0.430489 + 0.199165i
\(328\) 2.55759 0.562968i 0.141219 0.0310847i
\(329\) −16.5470 3.64227i −0.912265 0.200805i
\(330\) −2.82173 1.30547i −0.155331 0.0718638i
\(331\) 0.0533024 0.191978i 0.00292977 0.0105521i −0.962071 0.272800i \(-0.912050\pi\)
0.965000 + 0.262248i \(0.0844639\pi\)
\(332\) −0.856531 15.7978i −0.0470082 0.867016i
\(333\) 0.228347 0.268831i 0.0125134 0.0147319i
\(334\) 5.11611 + 12.8405i 0.279941 + 0.702599i
\(335\) −6.63063 + 40.4451i −0.362270 + 2.20975i
\(336\) −0.581307 2.09368i −0.0317129 0.114219i
\(337\) 25.5518 8.60940i 1.39190 0.468984i 0.479229 0.877690i \(-0.340916\pi\)
0.912666 + 0.408706i \(0.134020\pi\)
\(338\) 5.53361 8.16147i 0.300989 0.443925i
\(339\) 5.30577 10.0077i 0.288170 0.543546i
\(340\) 3.72452 + 4.38484i 0.201990 + 0.237802i
\(341\) 4.23352 4.01020i 0.229258 0.217165i
\(342\) −3.72460 + 0.405075i −0.201403 + 0.0219039i
\(343\) −11.3142 16.6873i −0.610912 0.901027i
\(344\) 2.44957 + 1.86211i 0.132072 + 0.100398i
\(345\) 4.88713 + 4.62933i 0.263114 + 0.249235i
\(346\) −0.823848 + 15.1950i −0.0442903 + 0.816887i
\(347\) 31.8785 + 10.7411i 1.71133 + 0.576613i 0.992896 0.118987i \(-0.0379647\pi\)
0.718430 + 0.695600i \(0.244861\pi\)
\(348\) −6.30132 + 4.79014i −0.337786 + 0.256778i
\(349\) −15.1770 1.65060i −0.812406 0.0883545i −0.307521 0.951541i \(-0.599500\pi\)
−0.504885 + 0.863187i \(0.668465\pi\)
\(350\) −4.89670 9.23615i −0.261739 0.493693i
\(351\) −0.655829 + 1.64601i −0.0350056 + 0.0878573i
\(352\) −0.850516 0.511739i −0.0453327 0.0272758i
\(353\) −26.7582 −1.42420 −0.712098 0.702080i \(-0.752255\pi\)
−0.712098 + 0.702080i \(0.752255\pi\)
\(354\) −6.44620 + 4.17690i −0.342612 + 0.222000i
\(355\) 19.5827 1.03934
\(356\) 3.03286 + 1.82481i 0.160741 + 0.0967148i
\(357\) −1.47723 + 3.70756i −0.0781832 + 0.196225i
\(358\) −9.17134 17.2990i −0.484721 0.914280i
\(359\) −3.22229 0.350445i −0.170066 0.0184958i 0.0226899 0.999743i \(-0.492777\pi\)
−0.192756 + 0.981247i \(0.561742\pi\)
\(360\) −2.49357 + 1.89557i −0.131423 + 0.0999051i
\(361\) 4.70346 + 1.58478i 0.247551 + 0.0834095i
\(362\) 0.466655 8.60694i 0.0245268 0.452371i
\(363\) 7.27066 + 6.88714i 0.381611 + 0.361481i
\(364\) −3.06497 2.32993i −0.160648 0.122121i
\(365\) −28.8740 42.5860i −1.51134 2.22905i
\(366\) 2.10935 0.229406i 0.110258 0.0119913i
\(367\) −7.99992 + 7.57793i −0.417593 + 0.395565i −0.867441 0.497540i \(-0.834237\pi\)
0.449848 + 0.893105i \(0.351478\pi\)
\(368\) 1.39131 + 1.63798i 0.0725272 + 0.0853856i
\(369\) 1.22668 2.31376i 0.0638582 0.120449i
\(370\) 0.620010 0.914446i 0.0322328 0.0475398i
\(371\) 25.0183 8.42964i 1.29889 0.437645i
\(372\) −1.57168 5.66067i −0.0814877 0.293492i
\(373\) −3.49308 + 21.3068i −0.180865 + 1.10323i 0.727828 + 0.685760i \(0.240530\pi\)
−0.908693 + 0.417466i \(0.862918\pi\)
\(374\) 0.674817 + 1.69366i 0.0348940 + 0.0875773i
\(375\) 0.383080 0.450997i 0.0197822 0.0232894i
\(376\) 0.422150 + 7.78610i 0.0217707 + 0.401538i
\(377\) −3.75201 + 13.5135i −0.193238 + 0.695982i
\(378\) −1.97205 0.912368i −0.101431 0.0469271i
\(379\) 36.3446 + 8.00004i 1.86689 + 0.410934i 0.996657 0.0816986i \(-0.0260345\pi\)
0.870237 + 0.492633i \(0.163966\pi\)
\(380\) −11.4609 + 2.52273i −0.587930 + 0.129413i
\(381\) 5.26419 2.43548i 0.269693 0.124773i
\(382\) −0.951824 5.80587i −0.0486996 0.297054i
\(383\) 14.4103 8.67037i 0.736330 0.443035i −0.0973732 0.995248i \(-0.531044\pi\)
0.833703 + 0.552213i \(0.186216\pi\)
\(384\) −0.856857 + 0.515554i −0.0437263 + 0.0263092i
\(385\) −1.09294 6.66667i −0.0557016 0.339765i
\(386\) 9.15593 4.23598i 0.466025 0.215606i
\(387\) 3.00505 0.661461i 0.152755 0.0336239i
\(388\) 7.64809 + 1.68347i 0.388273 + 0.0854654i
\(389\) 18.4313 + 8.52722i 0.934503 + 0.432347i 0.827218 0.561881i \(-0.189922\pi\)
0.107285 + 0.994228i \(0.465784\pi\)
\(390\) −1.48476 + 5.34761i −0.0751835 + 0.270787i
\(391\) −0.213707 3.94160i −0.0108076 0.199335i
\(392\) −1.47513 + 1.73666i −0.0745055 + 0.0877147i
\(393\) −0.155568 0.390446i −0.00784736 0.0196954i
\(394\) 2.19406 13.3832i 0.110535 0.674233i
\(395\) −5.41495 19.5029i −0.272456 0.981296i
\(396\) −0.940640 + 0.316939i −0.0472690 + 0.0159268i
\(397\) 2.75373 4.06146i 0.138206 0.203839i −0.752287 0.658836i \(-0.771049\pi\)
0.890493 + 0.454997i \(0.150360\pi\)
\(398\) −1.98341 + 3.74110i −0.0994192 + 0.187525i
\(399\) −5.27026 6.20463i −0.263843 0.310620i
\(400\) −3.49283 + 3.30858i −0.174641 + 0.165429i
\(401\) 21.1932 2.30490i 1.05834 0.115101i 0.437639 0.899151i \(-0.355815\pi\)
0.620698 + 0.784050i \(0.286849\pi\)
\(402\) 7.34301 + 10.8301i 0.366236 + 0.540158i
\(403\) −8.28675 6.29943i −0.412793 0.313797i
\(404\) −7.21976 6.83892i −0.359196 0.340249i
\(405\) −0.169577 + 3.12767i −0.00842637 + 0.155415i
\(406\) −16.2987 5.49167i −0.808890 0.272547i
\(407\) 0.278721 0.211879i 0.0138157 0.0105024i
\(408\) 1.82598 + 0.198587i 0.0903993 + 0.00983151i
\(409\) 13.9390 + 26.2917i 0.689237 + 1.30004i 0.943006 + 0.332774i \(0.107985\pi\)
−0.253769 + 0.967265i \(0.581670\pi\)
\(410\) 3.03618 7.62024i 0.149946 0.376337i
\(411\) −8.64285 5.20023i −0.426321 0.256509i
\(412\) 9.08595 0.447632
\(413\) −15.3725 6.50001i −0.756429 0.319845i
\(414\) 2.14912 0.105624
\(415\) −42.4620 25.5485i −2.08438 1.25413i
\(416\) −0.655829 + 1.64601i −0.0321547 + 0.0807021i
\(417\) 7.06662 + 13.3291i 0.346054 + 0.652727i
\(418\) −3.69704 0.402077i −0.180828 0.0196662i
\(419\) 7.65625 5.82013i 0.374032 0.284332i −0.401223 0.915981i \(-0.631415\pi\)
0.775255 + 0.631649i \(0.217622\pi\)
\(420\) −6.44976 2.17318i −0.314716 0.106040i
\(421\) −2.00503 + 36.9807i −0.0977194 + 1.80233i 0.381225 + 0.924482i \(0.375502\pi\)
−0.478944 + 0.877845i \(0.658980\pi\)
\(422\) −9.54531 9.04180i −0.464658 0.440148i
\(423\) 6.20757 + 4.71887i 0.301822 + 0.229439i
\(424\) −6.81837 10.0563i −0.331129 0.488379i
\(425\) 8.78492 0.955418i 0.426131 0.0463446i
\(426\) 4.53886 4.29944i 0.219909 0.208308i
\(427\) 2.98471 + 3.51387i 0.144440 + 0.170048i
\(428\) 3.70485 6.98810i 0.179081 0.337782i
\(429\) −0.986981 + 1.45569i −0.0476519 + 0.0702813i
\(430\) 9.13342 3.07741i 0.440453 0.148406i
\(431\) −5.78545 20.8373i −0.278675 1.00370i −0.961880 0.273471i \(-0.911828\pi\)
0.683205 0.730227i \(-0.260586\pi\)
\(432\) −0.161782 + 0.986827i −0.00778374 + 0.0474787i
\(433\) 6.27489 + 15.7488i 0.301552 + 0.756838i 0.999184 + 0.0403823i \(0.0128576\pi\)
−0.697632 + 0.716456i \(0.745763\pi\)
\(434\) 8.26404 9.72919i 0.396687 0.467016i
\(435\) 1.34226 + 24.7565i 0.0643563 + 1.18698i
\(436\) −2.29468 + 8.26470i −0.109895 + 0.395807i
\(437\) 7.30763 + 3.38087i 0.349572 + 0.161729i
\(438\) −16.0423 3.53118i −0.766532 0.168726i
\(439\) −32.9140 + 7.24492i −1.57090 + 0.345781i −0.913204 0.407502i \(-0.866400\pi\)
−0.657696 + 0.753283i \(0.728469\pi\)
\(440\) −2.82173 + 1.30547i −0.134521 + 0.0622359i
\(441\) 0.368636 + 2.24858i 0.0175541 + 0.107075i
\(442\) 2.78858 1.67783i 0.132639 0.0798065i
\(443\) 9.50246 5.71744i 0.451476 0.271644i −0.271603 0.962409i \(-0.587554\pi\)
0.723079 + 0.690765i \(0.242726\pi\)
\(444\) −0.0570640 0.348075i −0.00270814 0.0165189i
\(445\) 10.0620 4.65518i 0.476985 0.220677i
\(446\) 22.7513 5.00794i 1.07731 0.237133i
\(447\) 7.66544 + 1.68729i 0.362563 + 0.0798061i
\(448\) −1.97205 0.912368i −0.0931707 0.0431053i
\(449\) −8.96196 + 32.2780i −0.422941 + 1.52330i 0.378717 + 0.925512i \(0.376365\pi\)
−0.801658 + 0.597783i \(0.796049\pi\)
\(450\) 0.260467 + 4.80403i 0.0122785 + 0.226464i
\(451\) 1.68284 1.98119i 0.0792418 0.0932907i
\(452\) −4.19264 10.5227i −0.197205 0.494947i
\(453\) −1.03307 + 6.30146i −0.0485379 + 0.296068i
\(454\) −2.38212 8.57962i −0.111798 0.402662i
\(455\) −11.4280 + 3.85054i −0.535753 + 0.180516i
\(456\) −2.10252 + 3.10099i −0.0984596 + 0.145217i
\(457\) 7.70797 14.5388i 0.360564 0.680095i −0.635170 0.772373i \(-0.719070\pi\)
0.995733 + 0.0922774i \(0.0294147\pi\)
\(458\) −12.7153 14.9696i −0.594146 0.699483i
\(459\) 1.33347 1.26313i 0.0622409 0.0589577i
\(460\) 6.69216 0.727816i 0.312024 0.0339346i
\(461\) 3.77740 + 5.57125i 0.175931 + 0.259479i 0.905423 0.424511i \(-0.139554\pi\)
−0.729492 + 0.683989i \(0.760243\pi\)
\(462\) −1.71701 1.30524i −0.0798826 0.0607252i
\(463\) 21.9730 + 20.8139i 1.02117 + 0.967305i 0.999473 0.0324600i \(-0.0103342\pi\)
0.0216979 + 0.999765i \(0.493093\pi\)
\(464\) −0.428526 + 7.90370i −0.0198938 + 0.366920i
\(465\) −17.4382 5.87561i −0.808677 0.272475i
\(466\) −16.8188 + 12.7853i −0.779115 + 0.592268i
\(467\) 18.6361 + 2.02679i 0.862374 + 0.0937888i 0.528607 0.848867i \(-0.322715\pi\)
0.333767 + 0.942656i \(0.391680\pi\)
\(468\) 0.829949 + 1.56545i 0.0383644 + 0.0723630i
\(469\) −10.5236 + 26.4123i −0.485936 + 1.21961i
\(470\) 20.9278 + 12.5919i 0.965330 + 0.580820i
\(471\) 6.86860 0.316489
\(472\) −0.989710 + 7.61712i −0.0455551 + 0.350606i
\(473\) 3.05421 0.140433
\(474\) −5.53700 3.33150i −0.254323 0.153021i
\(475\) −6.67175 + 16.7448i −0.306121 + 0.768305i
\(476\) 1.86943 + 3.52611i 0.0856850 + 0.161619i
\(477\) −12.0787 1.31364i −0.553045 0.0601472i
\(478\) −14.0465 + 10.6779i −0.642473 + 0.488395i
\(479\) −4.84317 1.63186i −0.221290 0.0745614i 0.206473 0.978452i \(-0.433802\pi\)
−0.427763 + 0.903891i \(0.640698\pi\)
\(480\) −0.169577 + 3.12767i −0.00774011 + 0.142758i
\(481\) −0.453725 0.429792i −0.0206881 0.0195968i
\(482\) 9.73909 + 7.40347i 0.443604 + 0.337219i
\(483\) 2.62062 + 3.86513i 0.119242 + 0.175869i
\(484\) 9.95604 1.08278i 0.452547 0.0492175i
\(485\) 17.8082 16.8688i 0.808628 0.765973i
\(486\) 0.647386 + 0.762162i 0.0293660 + 0.0345724i
\(487\) 1.51037 2.84886i 0.0684414 0.129094i −0.846930 0.531704i \(-0.821552\pi\)
0.915372 + 0.402610i \(0.131897\pi\)
\(488\) 1.19072 1.75618i 0.0539015 0.0794987i
\(489\) 13.9221 4.69091i 0.629581 0.212130i
\(490\) 1.90940 + 6.87703i 0.0862578 + 0.310672i
\(491\) 1.33071 8.11698i 0.0600542 0.366314i −0.939653 0.342128i \(-0.888852\pi\)
0.999707 0.0241861i \(-0.00769943\pi\)
\(492\) −0.969324 2.43282i −0.0437005 0.109680i
\(493\) 9.41195 11.0806i 0.423893 0.499045i
\(494\) 0.359393 + 6.62861i 0.0161698 + 0.298235i
\(495\) −0.831768 + 2.99576i −0.0373852 + 0.134649i
\(496\) −5.33183 2.46677i −0.239406 0.110761i
\(497\) 13.2670 + 2.92030i 0.595108 + 0.130993i
\(498\) −15.4511 + 3.40104i −0.692380 + 0.152404i
\(499\) −11.4038 + 5.27598i −0.510506 + 0.236185i −0.658193 0.752849i \(-0.728679\pi\)
0.147688 + 0.989034i \(0.452817\pi\)
\(500\) −0.0957318 0.583938i −0.00428126 0.0261145i
\(501\) 11.8436 7.12607i 0.529134 0.318369i
\(502\) 13.5723 8.16615i 0.605759 0.364473i
\(503\) −1.21958 7.43910i −0.0543783 0.331693i −0.999980 0.00636568i \(-0.997974\pi\)
0.945601 0.325328i \(-0.105475\pi\)
\(504\) −1.97205 + 0.912368i −0.0878421 + 0.0406401i
\(505\) −30.4210 + 6.69616i −1.35372 + 0.297975i
\(506\) 2.08334 + 0.458579i 0.0926160 + 0.0203863i
\(507\) −8.94919 4.14034i −0.397448 0.183879i
\(508\) 1.55174 5.58886i 0.0688473 0.247966i
\(509\) 1.21377 + 22.3867i 0.0537996 + 0.992275i 0.893454 + 0.449154i \(0.148275\pi\)
−0.839655 + 0.543121i \(0.817243\pi\)
\(510\) 3.72452 4.38484i 0.164925 0.194164i
\(511\) −13.2112 33.1575i −0.584427 1.46680i
\(512\) −0.161782 + 0.986827i −0.00714982 + 0.0436120i
\(513\) 1.00231 + 3.61000i 0.0442531 + 0.159385i
\(514\) 20.5733 6.93194i 0.907448 0.305755i
\(515\) 15.9712 23.5557i 0.703773 1.03799i
\(516\) 1.44129 2.71855i 0.0634491 0.119678i
\(517\) 5.01066 + 5.89901i 0.220369 + 0.259438i
\(518\) 0.556419 0.527068i 0.0244476 0.0231580i
\(519\) 15.1281 1.64528i 0.664050 0.0722197i
\(520\) 3.11453 + 4.59359i 0.136581 + 0.201442i
\(521\) 19.4756 + 14.8049i 0.853240 + 0.648616i 0.937560 0.347823i \(-0.113079\pi\)
−0.0843207 + 0.996439i \(0.526872\pi\)
\(522\) 5.74648 + 5.44335i 0.251516 + 0.238249i
\(523\) 0.679182 12.5268i 0.0296986 0.547758i −0.945390 0.325942i \(-0.894319\pi\)
0.975088 0.221816i \(-0.0711985\pi\)
\(524\) −0.398296 0.134201i −0.0173996 0.00586262i
\(525\) −8.32228 + 6.32643i −0.363214 + 0.276108i
\(526\) 24.3332 + 2.64640i 1.06098 + 0.115388i
\(527\) 5.05437 + 9.53355i 0.220172 + 0.415288i
\(528\) −0.367399 + 0.922102i −0.0159890 + 0.0401293i
\(529\) 15.7501 + 9.47654i 0.684788 + 0.412023i
\(530\) −38.0567 −1.65308
\(531\) 5.16475 + 5.68554i 0.224131 + 0.246731i
\(532\) −8.14082 −0.352949
\(533\) −3.97595 2.39225i −0.172217 0.103620i
\(534\) 1.31011 3.28813i 0.0566940 0.142291i
\(535\) −11.6046 21.8886i −0.501710 0.946325i
\(536\) 13.0081 + 1.41471i 0.561863 + 0.0611063i
\(537\) −15.5873 + 11.8492i −0.672643 + 0.511330i
\(538\) 13.2824 + 4.47535i 0.572644 + 0.192946i
\(539\) −0.122448 + 2.25842i −0.00527421 + 0.0972771i
\(540\) 2.27401 + 2.15406i 0.0978578 + 0.0926959i
\(541\) 16.2428 + 12.3475i 0.698333 + 0.530859i 0.893026 0.450005i \(-0.148578\pi\)
−0.194693 + 0.980864i \(0.562371\pi\)
\(542\) 2.50013 + 3.68742i 0.107390 + 0.158388i
\(543\) −8.56905 + 0.931941i −0.367733 + 0.0399934i
\(544\) 1.33347 1.26313i 0.0571719 0.0541561i
\(545\) 17.3930 + 20.4766i 0.745035 + 0.877123i
\(546\) −1.80338 + 3.40153i −0.0771775 + 0.145572i
\(547\) 4.46511 6.58554i 0.190914 0.281577i −0.720170 0.693798i \(-0.755936\pi\)
0.911084 + 0.412220i \(0.135247\pi\)
\(548\) −9.55868 + 3.22070i −0.408327 + 0.137581i
\(549\) −0.567640 2.04445i −0.0242263 0.0872552i
\(550\) −0.772587 + 4.71257i −0.0329432 + 0.200945i
\(551\) 10.9765 + 27.5490i 0.467615 + 1.17363i
\(552\) 1.39131 1.63798i 0.0592182 0.0697170i
\(553\) −0.760170 14.0205i −0.0323257 0.596213i
\(554\) 1.83719 6.61697i 0.0780549 0.281128i
\(555\) −1.00271 0.463901i −0.0425625 0.0196915i
\(556\) 14.7337 + 3.24314i 0.624849 + 0.137540i
\(557\) 13.6158 2.99706i 0.576919 0.126989i 0.0830800 0.996543i \(-0.473524\pi\)
0.493839 + 0.869553i \(0.335593\pi\)
\(558\) −5.33183 + 2.46677i −0.225714 + 0.104427i
\(559\) −0.882028 5.38013i −0.0373058 0.227555i
\(560\) −5.83180 + 3.50888i −0.246438 + 0.148277i
\(561\) 1.56218 0.939932i 0.0659553 0.0396840i
\(562\) 2.17322 + 13.2560i 0.0916717 + 0.559172i
\(563\) 23.2574 10.7600i 0.980181 0.453480i 0.136684 0.990615i \(-0.456355\pi\)
0.843497 + 0.537135i \(0.180493\pi\)
\(564\) 7.61524 1.67624i 0.320659 0.0705825i
\(565\) −34.6504 7.62712i −1.45775 0.320875i
\(566\) 21.0789 + 9.75213i 0.886012 + 0.409913i
\(567\) −0.581307 + 2.09368i −0.0244126 + 0.0879262i
\(568\) −0.338472 6.24275i −0.0142020 0.261940i
\(569\) −18.6178 + 21.9186i −0.780498 + 0.918874i −0.998368 0.0571041i \(-0.981813\pi\)
0.217870 + 0.975978i \(0.430089\pi\)
\(570\) 4.34365 + 10.9018i 0.181936 + 0.456624i
\(571\) 5.13905 31.3468i 0.215062 1.31182i −0.629766 0.776785i \(-0.716849\pi\)
0.844828 0.535038i \(-0.179703\pi\)
\(572\) 0.470512 + 1.69463i 0.0196731 + 0.0708561i
\(573\) −5.57540 + 1.87857i −0.232916 + 0.0784784i
\(574\) 3.19336 4.70986i 0.133288 0.196586i
\(575\) 4.84316 9.13517i 0.201974 0.380963i
\(576\) 0.647386 + 0.762162i 0.0269744 + 0.0317568i
\(577\) −29.9075 + 28.3299i −1.24506 + 1.17939i −0.268708 + 0.963222i \(0.586597\pi\)
−0.976357 + 0.216166i \(0.930645\pi\)
\(578\) 13.5465 1.47327i 0.563460 0.0612800i
\(579\) −5.66145 8.35001i −0.235282 0.347015i
\(580\) 19.7374 + 15.0040i 0.819551 + 0.623007i
\(581\) −24.9576 23.6411i −1.03542 0.980798i
\(582\) 0.423972 7.81969i 0.0175742 0.324137i
\(583\) −11.4287 3.85077i −0.473328 0.159483i
\(584\) −13.0769 + 9.94081i −0.541127 + 0.411354i
\(585\) 5.51737 + 0.600050i 0.228115 + 0.0248090i
\(586\) −8.71397 16.4363i −0.359971 0.678977i
\(587\) −3.91079 + 9.81534i −0.161416 + 0.405122i −0.987332 0.158671i \(-0.949279\pi\)
0.825916 + 0.563793i \(0.190658\pi\)
\(588\) 1.95243 + 1.17474i 0.0805170 + 0.0484455i
\(589\) −22.0103 −0.906920
\(590\) 18.0080 + 15.9551i 0.741377 + 0.656862i
\(591\) −13.5618 −0.557858
\(592\) −0.302232 0.181847i −0.0124217 0.00747387i
\(593\) 5.40962 13.5771i 0.222147 0.557546i −0.775089 0.631852i \(-0.782295\pi\)
0.997235 + 0.0743063i \(0.0236743\pi\)
\(594\) 0.464942 + 0.876974i 0.0190768 + 0.0359827i
\(595\) 12.4276 + 1.35159i 0.509484 + 0.0554097i
\(596\) 6.24849 4.74998i 0.255948 0.194567i
\(597\) 4.01270 + 1.35204i 0.164229 + 0.0553351i
\(598\) 0.206157 3.80234i 0.00843037 0.155489i
\(599\) −28.2395 26.7498i −1.15383 1.09297i −0.994392 0.105762i \(-0.966272\pi\)
−0.159442 0.987207i \(-0.550969\pi\)
\(600\) 3.83007 + 2.91154i 0.156362 + 0.118863i
\(601\) 6.28467 + 9.26920i 0.256357 + 0.378098i 0.933988 0.357303i \(-0.116304\pi\)
−0.677631 + 0.735402i \(0.736993\pi\)
\(602\) 6.64672 0.722875i 0.270900 0.0294622i
\(603\) 9.49949 8.99839i 0.386849 0.366443i
\(604\) 4.13393 + 4.86684i 0.168207 + 0.198029i
\(605\) 14.6934 27.7147i 0.597373 1.12676i
\(606\) −5.58080 + 8.23106i −0.226704 + 0.334364i
\(607\) 1.53034 0.515632i 0.0621146 0.0209288i −0.288073 0.957609i \(-0.593014\pi\)
0.350187 + 0.936680i \(0.386118\pi\)
\(608\) 1.00231 + 3.61000i 0.0406491 + 0.146405i
\(609\) −2.78249 + 16.9724i −0.112752 + 0.687757i
\(610\) −2.45994 6.17400i −0.0996003 0.249978i
\(611\) 8.94433 10.5301i 0.361849 0.426002i
\(612\) −0.0994392 1.83405i −0.00401959 0.0741370i
\(613\) −7.01515 + 25.2663i −0.283339 + 1.02050i 0.675689 + 0.737187i \(0.263846\pi\)
−0.959028 + 0.283310i \(0.908568\pi\)
\(614\) −24.2143 11.2027i −0.977211 0.452106i
\(615\) −8.01105 1.76337i −0.323037 0.0711058i
\(616\) −2.10637 + 0.463648i −0.0848682 + 0.0186809i
\(617\) −26.5069 + 12.2634i −1.06713 + 0.493706i −0.873226 0.487315i \(-0.837976\pi\)
−0.193902 + 0.981021i \(0.562114\pi\)
\(618\) −1.46994 8.96625i −0.0591298 0.360676i
\(619\) 39.6883 23.8797i 1.59521 0.959804i 0.609217 0.793004i \(-0.291484\pi\)
0.985991 0.166801i \(-0.0533437\pi\)
\(620\) −15.7674 + 9.48694i −0.633235 + 0.381005i
\(621\) −0.347689 2.12081i −0.0139523 0.0851052i
\(622\) 9.45486 4.37429i 0.379105 0.175393i
\(623\) 7.51113 1.65332i 0.300927 0.0662390i
\(624\) 1.73042 + 0.380895i 0.0692724 + 0.0152480i
\(625\) −23.5143 10.8789i −0.940571 0.435154i
\(626\) −5.98583 + 21.5590i −0.239242 + 0.861672i
\(627\) 0.201334 + 3.71338i 0.00804049 + 0.148298i
\(628\) 4.44664 5.23499i 0.177440 0.208899i
\(629\) 0.239797 + 0.601846i 0.00956135 + 0.0239972i
\(630\) −1.10109 + 6.71637i −0.0438686 + 0.267587i
\(631\) −5.02608 18.1023i −0.200085 0.720642i −0.993685 0.112202i \(-0.964210\pi\)
0.793600 0.608440i \(-0.208204\pi\)
\(632\) −6.12372 + 2.06332i −0.243588 + 0.0820745i
\(633\) −7.37843 + 10.8824i −0.293266 + 0.432535i
\(634\) −12.3091 + 23.2174i −0.488857 + 0.922082i
\(635\) −11.7617 13.8470i −0.466750 0.549501i
\(636\) −8.82078 + 8.35548i −0.349767 + 0.331316i
\(637\) 4.01367 0.436513i 0.159027 0.0172953i
\(638\) 4.40910 + 6.50293i 0.174558 + 0.257453i
\(639\) −4.97711 3.78350i −0.196891 0.149673i
\(640\) 2.27401 + 2.15406i 0.0898882 + 0.0851466i
\(641\) 2.63866 48.6672i 0.104221 1.92224i −0.218660 0.975801i \(-0.570169\pi\)
0.322881 0.946440i \(-0.395349\pi\)
\(642\) −7.49542 2.52550i −0.295820 0.0996735i
\(643\) 0.233696 0.177651i 0.00921607 0.00700587i −0.600556 0.799583i \(-0.705054\pi\)
0.609772 + 0.792577i \(0.291261\pi\)
\(644\) 4.64241 + 0.504892i 0.182936 + 0.0198955i
\(645\) −4.51449 8.51523i −0.177758 0.335287i
\(646\) 2.54709 6.39272i 0.100214 0.251518i
\(647\) 31.0054 + 18.6553i 1.21895 + 0.733417i 0.971856 0.235575i \(-0.0756975\pi\)
0.247092 + 0.968992i \(0.420525\pi\)
\(648\) 1.00000 0.0392837
\(649\) 3.79350 + 6.61357i 0.148908 + 0.259605i
\(650\) 8.52452 0.334359
\(651\) −10.9380 6.58117i −0.428694 0.257936i
\(652\) 5.43776 13.6478i 0.212959 0.534487i
\(653\) −7.27745 13.7267i −0.284789 0.537168i 0.699304 0.714824i \(-0.253493\pi\)
−0.984093 + 0.177656i \(0.943149\pi\)
\(654\) 8.52706 + 0.927374i 0.333435 + 0.0362632i
\(655\) −1.04804 + 0.796700i −0.0409504 + 0.0311297i
\(656\) −2.48173 0.836192i −0.0968953 0.0326478i
\(657\) −0.889305 + 16.4023i −0.0346951 + 0.639914i
\(658\) 12.3006 + 11.6518i 0.479528 + 0.454233i
\(659\) −15.8602 12.0566i −0.617827 0.469660i 0.248841 0.968544i \(-0.419950\pi\)
−0.866669 + 0.498884i \(0.833743\pi\)
\(660\) 1.74478 + 2.57336i 0.0679154 + 0.100168i
\(661\) 41.2816 4.48964i 1.60567 0.174627i 0.739068 0.673631i \(-0.235266\pi\)
0.866600 + 0.499004i \(0.166301\pi\)
\(662\) −0.144648 + 0.137017i −0.00562189 + 0.00532533i
\(663\) −2.10687 2.48040i −0.0818242 0.0963309i
\(664\) −7.41068 + 13.9780i −0.287590 + 0.542453i
\(665\) −14.3098 + 21.1054i −0.554911 + 0.818433i
\(666\) −0.334258 + 0.112625i −0.0129522 + 0.00436412i
\(667\) −4.55091 16.3909i −0.176212 0.634659i
\(668\) 2.23618 13.6401i 0.0865203 0.527751i
\(669\) −8.62273 21.6414i −0.333374 0.836705i
\(670\) 26.5331 31.2372i 1.02506 1.20680i
\(671\) −0.114021 2.10300i −0.00440175 0.0811855i
\(672\) −0.581307 + 2.09368i −0.0224244 + 0.0807653i
\(673\) 8.31465 + 3.84677i 0.320506 + 0.148282i 0.573545 0.819174i \(-0.305568\pi\)
−0.253039 + 0.967456i \(0.581430\pi\)
\(674\) −26.3329 5.79630i −1.01430 0.223265i
\(675\) 4.69860 1.03424i 0.180849 0.0398080i
\(676\) −8.94919 + 4.14034i −0.344200 + 0.159244i
\(677\) 2.21331 + 13.5006i 0.0850645 + 0.518870i 0.994646 + 0.103344i \(0.0329543\pi\)
−0.909581 + 0.415526i \(0.863597\pi\)
\(678\) −9.70581 + 5.83979i −0.372749 + 0.224276i
\(679\) 14.5805 8.77277i 0.559546 0.336668i
\(680\) −0.930758 5.67738i −0.0356930 0.217717i
\(681\) −8.08121 + 3.73877i −0.309673 + 0.143270i
\(682\) −5.69500 + 1.25356i −0.218073 + 0.0480015i
\(683\) 29.6954 + 6.53645i 1.13626 + 0.250110i 0.742984 0.669309i \(-0.233410\pi\)
0.393278 + 0.919419i \(0.371341\pi\)
\(684\) 3.40029 + 1.57314i 0.130013 + 0.0601505i
\(685\) −8.45234 + 30.4426i −0.322947 + 1.16315i
\(686\) 1.09151 + 20.1317i 0.0416740 + 0.768632i
\(687\) −12.7153 + 14.9696i −0.485118 + 0.571125i
\(688\) −1.13891 2.85845i −0.0434205 0.108977i
\(689\) −3.48281 + 21.2442i −0.132685 + 0.809340i
\(690\) −1.80090 6.48625i −0.0685591 0.246927i
\(691\) −9.37483 + 3.15875i −0.356635 + 0.120164i −0.491915 0.870643i \(-0.663703\pi\)
0.135280 + 0.990807i \(0.456807\pi\)
\(692\) 8.53975 12.5952i 0.324633 0.478797i
\(693\) −1.01026 + 1.90556i −0.0383767 + 0.0723861i
\(694\) −21.7777 25.6387i −0.826669 0.973230i
\(695\) 34.3067 32.4971i 1.30133 1.23268i
\(696\) 7.86891 0.855795i 0.298270 0.0324388i
\(697\) 2.69936 + 3.98126i 0.102246 + 0.150801i
\(698\) 12.1535 + 9.23889i 0.460019 + 0.349697i
\(699\) 15.3379 + 14.5288i 0.580131 + 0.549529i
\(700\) −0.565963 + 10.4386i −0.0213914 + 0.394541i
\(701\) 25.6249 + 8.63405i 0.967840 + 0.326103i 0.758452 0.651729i \(-0.225956\pi\)
0.209389 + 0.977833i \(0.432853\pi\)
\(702\) 1.41056 1.07228i 0.0532380 0.0404705i
\(703\) −1.31375 0.142879i −0.0495489 0.00538877i
\(704\) 0.464942 + 0.876974i 0.0175232 + 0.0330522i
\(705\) 9.04024 22.6893i 0.340475 0.854528i
\(706\) 22.9280 + 13.7953i 0.862906 + 0.519193i
\(707\) −21.6085 −0.812670
\(708\) 7.67689 0.255641i 0.288515 0.00960756i
\(709\) −40.5059 −1.52123 −0.760616 0.649202i \(-0.775103\pi\)
−0.760616 + 0.649202i \(0.775103\pi\)
\(710\) −16.7795 10.0959i −0.629725 0.378893i
\(711\) −2.39183 + 6.00303i −0.0897005 + 0.225131i
\(712\) −1.65794 3.12720i −0.0621339 0.117197i
\(713\) 12.5517 + 1.36508i 0.470064 + 0.0511225i
\(714\) 3.17722 2.41526i 0.118905 0.0903889i
\(715\) 5.22046 + 1.75898i 0.195234 + 0.0657821i
\(716\) −1.06003 + 19.5511i −0.0396151 + 0.730658i
\(717\) 12.8097 + 12.1340i 0.478387 + 0.453152i
\(718\) 2.58037 + 1.96154i 0.0962984 + 0.0732041i
\(719\) −16.6529 24.5611i −0.621047 0.915976i 0.378908 0.925434i \(-0.376300\pi\)
−0.999955 + 0.00945834i \(0.996989\pi\)
\(720\) 3.11390 0.338657i 0.116048 0.0126210i
\(721\) 14.3331 13.5770i 0.533792 0.505634i
\(722\) −3.21316 3.78282i −0.119581 0.140782i
\(723\) 5.73033 10.8085i 0.213113 0.401974i
\(724\) −4.83720 + 7.13433i −0.179773 + 0.265145i
\(725\) 36.0878 12.1594i 1.34027 0.451588i
\(726\) −2.67923 9.64971i −0.0994355 0.358134i
\(727\) −5.85488 + 35.7132i −0.217146 + 1.32453i 0.623023 + 0.782204i \(0.285904\pi\)
−0.840168 + 0.542326i \(0.817544\pi\)
\(728\) 1.42504 + 3.57657i 0.0528154 + 0.132557i
\(729\) 0.647386 0.762162i 0.0239773 0.0282282i
\(730\) 2.78554 + 51.3763i 0.103097 + 1.90152i
\(731\) −1.51197 + 5.44563i −0.0559223 + 0.201414i
\(732\) −1.92569 0.890918i −0.0711754 0.0329293i
\(733\) −34.6270 7.62198i −1.27898 0.281524i −0.477013 0.878896i \(-0.658281\pi\)
−0.801964 + 0.597372i \(0.796212\pi\)
\(734\) 10.7616 2.36881i 0.397219 0.0874345i
\(735\) 6.47753 2.99682i 0.238927 0.110539i
\(736\) −0.347689 2.12081i −0.0128160 0.0781741i
\(737\) 11.1288 6.69599i 0.409935 0.246650i
\(738\) −2.24395 + 1.35014i −0.0826010 + 0.0496994i
\(739\) −1.74423 10.6393i −0.0641626 0.391375i −0.999311 0.0371180i \(-0.988182\pi\)
0.935148 0.354257i \(-0.115266\pi\)
\(740\) −1.00271 + 0.463901i −0.0368602 + 0.0170533i
\(741\) 6.48314 1.42705i 0.238164 0.0524239i
\(742\) −25.7830 5.67528i −0.946525 0.208346i
\(743\) −16.5546 7.65897i −0.607329 0.280980i 0.0920238 0.995757i \(-0.470666\pi\)
−0.699353 + 0.714776i \(0.746528\pi\)
\(744\) −1.57168 + 5.66067i −0.0576205 + 0.207530i
\(745\) −1.33100 24.5489i −0.0487642 0.899403i
\(746\) 13.9779 16.4560i 0.511767 0.602498i
\(747\) 5.85595 + 14.6973i 0.214258 + 0.537747i
\(748\) 0.294953 1.79913i 0.0107845 0.0657828i
\(749\) −4.59782 16.5598i −0.168001 0.605083i
\(750\) −0.560758 + 0.188941i −0.0204760 + 0.00689917i
\(751\) −17.6366 + 26.0120i −0.643569 + 0.949193i 0.356321 + 0.934363i \(0.384031\pi\)
−0.999890 + 0.0148293i \(0.995280\pi\)
\(752\) 3.65243 6.88922i 0.133191 0.251224i
\(753\) −10.2543 12.0723i −0.373688 0.439940i
\(754\) 10.1819 9.64480i 0.370803 0.351243i
\(755\) 19.8841 2.16252i 0.723655 0.0787023i
\(756\) 1.21939 + 1.79847i 0.0443488 + 0.0654096i
\(757\) 23.8915 + 18.1619i 0.868352 + 0.660104i 0.941425 0.337223i \(-0.109488\pi\)
−0.0730733 + 0.997327i \(0.523281\pi\)
\(758\) −27.0176 25.5925i −0.981325 0.929560i
\(759\) 0.115490 2.13009i 0.00419203 0.0773174i
\(760\) 11.1209 + 3.74708i 0.403398 + 0.135921i
\(761\) −14.2998 + 10.8704i −0.518367 + 0.394052i −0.831387 0.555694i \(-0.812453\pi\)
0.313020 + 0.949747i \(0.398659\pi\)
\(762\) −5.76628 0.627121i −0.208890 0.0227182i
\(763\) 8.72997 + 16.4665i 0.316046 + 0.596126i
\(764\) −2.17766 + 5.46552i −0.0787850 + 0.197736i
\(765\) −4.92964 2.96607i −0.178232 0.107238i
\(766\) −16.8176 −0.607644
\(767\) 10.5546 8.59235i 0.381104 0.310252i
\(768\) 1.00000 0.0360844
\(769\) −29.7175 17.8804i −1.07164 0.644784i −0.133502 0.991048i \(-0.542622\pi\)
−0.938137 + 0.346265i \(0.887450\pi\)
\(770\) −2.50053 + 6.27586i −0.0901128 + 0.226166i
\(771\) −10.1690 19.1808i −0.366228 0.690779i
\(772\) −10.0292 1.09074i −0.360959 0.0392566i
\(773\) −3.70186 + 2.81408i −0.133147 + 0.101215i −0.669628 0.742697i \(-0.733546\pi\)
0.536481 + 0.843912i \(0.319753\pi\)
\(774\) −2.91591 0.982486i −0.104810 0.0353147i
\(775\) −1.53019 + 28.2227i −0.0549662 + 1.01379i
\(776\) −5.68540 5.38550i −0.204094 0.193328i
\(777\) −0.610143 0.463819i −0.0218888 0.0166394i
\(778\) −11.3967 16.8089i −0.408593 0.602629i
\(779\) −9.75404 + 1.06082i −0.349475 + 0.0380077i
\(780\) 4.02920 3.81666i 0.144269 0.136659i
\(781\) −4.01745 4.72971i −0.143756 0.169242i
\(782\) −1.84899 + 3.48756i −0.0661197 + 0.124715i
\(783\) 4.44197 6.55141i 0.158743 0.234128i
\(784\) 2.15932 0.727560i 0.0771186 0.0259843i
\(785\) −5.75568 20.7301i −0.205429 0.739889i
\(786\) −0.0679964 + 0.414760i −0.00242535 + 0.0147940i
\(787\) 10.7708 + 27.0327i 0.383938 + 0.963613i 0.986236 + 0.165342i \(0.0528726\pi\)
−0.602298 + 0.798271i \(0.705748\pi\)
\(788\) −8.77973 + 10.3363i −0.312765 + 0.368215i
\(789\) −1.32514 24.4408i −0.0471763 0.870115i
\(790\) −5.41495 + 19.5029i −0.192655 + 0.693881i
\(791\) −22.3379 10.3346i −0.794243 0.367456i
\(792\) 0.969393 + 0.213380i 0.0344459 + 0.00758211i
\(793\) −3.67160 + 0.808181i −0.130382 + 0.0286993i
\(794\) −4.45346 + 2.06039i −0.158047 + 0.0731204i
\(795\) 6.15689 + 37.5554i 0.218362 + 1.33195i
\(796\) 3.62824 2.18304i 0.128599 0.0773757i
\(797\) −21.3270 + 12.8320i −0.755440 + 0.454533i −0.840479 0.541845i \(-0.817726\pi\)
0.0850389 + 0.996378i \(0.472899\pi\)
\(798\) 1.31704 + 8.03358i 0.0466227 + 0.284386i
\(799\) −12.9984 + 6.01368i −0.459849 + 0.212749i
\(800\) 4.69860 1.03424i 0.166121 0.0365659i
\(801\) −3.45676 0.760891i −0.122139 0.0268848i
\(802\) −19.3478 8.95126i −0.683196 0.316080i
\(803\) −4.36200 + 15.7105i −0.153932 + 0.554411i
\(804\) −0.708395 13.0656i −0.0249832 0.460788i
\(805\) 9.46932 11.1481i 0.333750 0.392920i
\(806\) 3.85287 + 9.66998i 0.135712 + 0.340610i
\(807\) 2.26755 13.8314i 0.0798215 0.486890i
\(808\) 2.66047 + 9.58215i 0.0935950 + 0.337099i
\(809\) −44.1485 + 14.8754i −1.55218 + 0.522990i −0.959321 0.282317i \(-0.908897\pi\)
−0.592858 + 0.805307i \(0.702000\pi\)
\(810\) 1.75779 2.59254i 0.0617623 0.0910926i
\(811\) −1.82101 + 3.43479i −0.0639444 + 0.120612i −0.913424 0.407010i \(-0.866571\pi\)
0.849479 + 0.527622i \(0.176916\pi\)
\(812\) 11.1344 + 13.1084i 0.390741 + 0.460015i
\(813\) 3.23437 3.06376i 0.113434 0.107451i
\(814\) −0.348059 + 0.0378537i −0.0121995 + 0.00132677i
\(815\) −25.8239 38.0875i −0.904573 1.33415i
\(816\) −1.46222 1.11155i −0.0511879 0.0389120i
\(817\) −8.36936 7.92788i −0.292807 0.277361i
\(818\) 1.61107 29.7145i 0.0563298 1.03894i
\(819\) 3.64848 + 1.22932i 0.127488 + 0.0429557i
\(820\) −6.53022 + 4.96414i −0.228045 + 0.173355i
\(821\) −12.0710 1.31280i −0.421280 0.0458170i −0.104976 0.994475i \(-0.533477\pi\)
−0.316304 + 0.948658i \(0.602442\pi\)
\(822\) 4.72469 + 8.91171i 0.164793 + 0.310832i
\(823\) −12.6888 + 31.8465i −0.442304 + 1.11010i 0.523776 + 0.851856i \(0.324523\pi\)
−0.966080 + 0.258243i \(0.916856\pi\)
\(824\) −7.78536 4.68429i −0.271216 0.163185i
\(825\) 4.77548 0.166261
\(826\) 9.82089 + 13.4949i 0.341713 + 0.469548i
\(827\) −45.4289 −1.57972 −0.789859 0.613288i \(-0.789846\pi\)
−0.789859 + 0.613288i \(0.789846\pi\)
\(828\) −1.84149 1.10799i −0.0639962 0.0385053i
\(829\) −13.0936 + 32.8626i −0.454761 + 1.14136i 0.505641 + 0.862744i \(0.331256\pi\)
−0.960402 + 0.278619i \(0.910123\pi\)
\(830\) 23.2122 + 43.7829i 0.805708 + 1.51973i
\(831\) −6.82703 0.742484i −0.236827 0.0257565i
\(832\) 1.41056 1.07228i 0.0489023 0.0371745i
\(833\) −3.96612 1.33634i −0.137418 0.0463015i
\(834\) 0.816764 15.0643i 0.0282822 0.521635i
\(835\) −31.4318 29.7737i −1.08774 1.03036i
\(836\) 2.96054 + 2.25054i 0.102392 + 0.0778367i
\(837\) 3.29687 + 4.86251i 0.113956 + 0.168073i
\(838\) −9.56090 + 1.03981i −0.330276 + 0.0359197i
\(839\) −15.3605 + 14.5503i −0.530305 + 0.502331i −0.905345 0.424677i \(-0.860388\pi\)
0.375040 + 0.927009i \(0.377629\pi\)
\(840\) 4.40613 + 5.18730i 0.152026 + 0.178979i
\(841\) 15.7629 29.7320i 0.543549 1.02524i
\(842\) 20.7836 30.6535i 0.716249 1.05639i
\(843\) 12.7298 4.28918i 0.438439 0.147727i
\(844\) 3.51743 + 12.6686i 0.121075 + 0.436073i
\(845\) −4.99678 + 30.4790i −0.171894 + 1.04851i
\(846\) −2.88617 7.24373i −0.0992285 0.249045i
\(847\) 14.0877 16.5853i 0.484058 0.569877i
\(848\) 0.657783 + 12.1321i 0.0225883 + 0.416618i
\(849\) 6.21348 22.3789i 0.213246 0.768043i
\(850\) −8.01999 3.71044i −0.275083 0.127267i
\(851\) 0.740320 + 0.162957i 0.0253778 + 0.00558608i
\(852\) −6.10575 + 1.34398i −0.209179 + 0.0460439i
\(853\) −28.6177 + 13.2400i −0.979851 + 0.453327i −0.843381 0.537317i \(-0.819438\pi\)
−0.136471 + 0.990644i \(0.543576\pi\)
\(854\) −0.745879 4.54966i −0.0255235 0.155686i
\(855\) 10.0554 6.05014i 0.343888 0.206910i
\(856\) −6.77727 + 4.07775i −0.231642 + 0.139375i
\(857\) −3.69149 22.5171i −0.126099 0.769170i −0.971852 0.235594i \(-0.924296\pi\)
0.845753 0.533575i \(-0.179152\pi\)
\(858\) 1.59619 0.738475i 0.0544929 0.0252111i
\(859\) 43.6316 9.60403i 1.48869 0.327685i 0.605177 0.796091i \(-0.293103\pi\)
0.883513 + 0.468406i \(0.155171\pi\)
\(860\) −9.41260 2.07187i −0.320967 0.0706502i
\(861\) −5.16444 2.38932i −0.176004 0.0814280i
\(862\) −5.78545 + 20.8373i −0.197053 + 0.709722i
\(863\) 0.550980 + 10.1622i 0.0187556 + 0.345926i 0.992817 + 0.119643i \(0.0381749\pi\)
−0.974061 + 0.226284i \(0.927342\pi\)
\(864\) 0.647386 0.762162i 0.0220245 0.0259293i
\(865\) −17.6425 44.2793i −0.599863 1.50554i
\(866\) 2.74266 16.7295i 0.0931995 0.568492i
\(867\) −3.64544 13.1297i −0.123806 0.445908i
\(868\) −12.0970 + 4.07596i −0.410600 + 0.138347i
\(869\) −3.59955 + 5.30893i −0.122106 + 0.180093i
\(870\) 11.6132 21.9048i 0.393723 0.742641i
\(871\) −15.0092 17.6702i −0.508566 0.598730i
\(872\) 6.22711 5.89863i 0.210877 0.199753i
\(873\) −7.78527 + 0.846699i −0.263492 + 0.0286564i
\(874\) −4.51858 6.66440i −0.152843 0.225427i
\(875\) −1.02359 0.778112i −0.0346036 0.0263050i
\(876\) 11.9255 + 11.2964i 0.402924 + 0.381670i
\(877\) 2.18628 40.3236i 0.0738255 1.36163i −0.693538 0.720420i \(-0.743949\pi\)
0.767364 0.641212i \(-0.221568\pi\)
\(878\) 31.9378 + 10.7611i 1.07785 + 0.363169i
\(879\) −14.8100 + 11.2583i −0.499529 + 0.379732i
\(880\) 3.09086 + 0.336151i 0.104193 + 0.0113317i
\(881\) 7.51952 + 14.1833i 0.253339 + 0.477848i 0.977263 0.212032i \(-0.0680081\pi\)
−0.723924 + 0.689880i \(0.757663\pi\)
\(882\) 0.843397 2.11677i 0.0283986 0.0712752i
\(883\) −21.4008 12.8764i −0.720194 0.433326i 0.107720 0.994181i \(-0.465645\pi\)
−0.827914 + 0.560855i \(0.810472\pi\)
\(884\) −3.25443 −0.109458
\(885\) 12.8316 20.3520i 0.431329 0.684126i
\(886\) −11.0899 −0.372572
\(887\) −49.5172 29.7935i −1.66262 1.00037i −0.956259 0.292521i \(-0.905506\pi\)
−0.706366 0.707847i \(-0.749666\pi\)
\(888\) −0.130556 + 0.327670i −0.00438117 + 0.0109959i
\(889\) −5.90350 11.1352i −0.197997 0.373462i
\(890\) −11.0217 1.19868i −0.369448 0.0401799i
\(891\) 0.790202 0.600696i 0.0264728 0.0201241i
\(892\) −22.0765 7.43844i −0.739176 0.249057i
\(893\) 1.58161 29.1711i 0.0529266 0.976174i
\(894\) −5.69830 5.39771i −0.190580 0.180527i
\(895\) 48.8237 + 37.1148i 1.63200 + 1.24061i
\(896\) 1.21939 + 1.79847i 0.0407370 + 0.0600826i
\(897\) −3.78560 + 0.411709i −0.126397 + 0.0137466i
\(898\) 24.3202 23.0373i 0.811575 0.768765i
\(899\) 30.1041 + 35.4412i 1.00403 + 1.18203i
\(900\) 2.25355 4.25065i 0.0751184 0.141688i
\(901\) 12.5236 18.4709i 0.417221 0.615355i
\(902\) −2.46336 + 0.830004i −0.0820211 + 0.0276361i
\(903\) −1.78867 6.44221i −0.0595233 0.214383i
\(904\) −1.83254 + 11.1780i −0.0609494 + 0.371775i
\(905\) 9.99329 + 25.0813i 0.332188 + 0.833730i
\(906\) 4.13393 4.86684i 0.137341 0.161690i
\(907\) 1.32716 + 24.4781i 0.0440678 + 0.812782i 0.934128 + 0.356939i \(0.116179\pi\)
−0.890060 + 0.455843i \(0.849338\pi\)
\(908\) −2.38212 + 8.57962i −0.0790534 + 0.284725i
\(909\) 9.02550 + 4.17564i 0.299357 + 0.138497i
\(910\) 11.7773 + 2.59238i 0.390414 + 0.0859367i
\(911\) −19.8574 + 4.37095i −0.657906 + 0.144816i −0.531362 0.847145i \(-0.678319\pi\)
−0.126544 + 0.991961i \(0.540388\pi\)
\(912\) 3.40029 1.57314i 0.112595 0.0520919i
\(913\) 2.54061 + 15.4970i 0.0840819 + 0.512877i
\(914\) −14.1002 + 8.48378i −0.466392 + 0.280618i
\(915\) −5.69469 + 3.42638i −0.188261 + 0.113273i
\(916\) 3.17755 + 19.3822i 0.104989 + 0.640406i
\(917\) −0.828847 + 0.383465i −0.0273709 + 0.0126631i
\(918\) −1.79380 + 0.394845i −0.0592042 + 0.0130318i
\(919\) 25.1669 + 5.53966i 0.830180 + 0.182736i 0.609677 0.792650i \(-0.291299\pi\)
0.220503 + 0.975386i \(0.429230\pi\)
\(920\) −6.10945 2.82653i −0.201423 0.0931881i
\(921\) −7.13772 + 25.7077i −0.235196 + 0.847099i
\(922\) −0.364414 6.72121i −0.0120013 0.221351i
\(923\) −7.17139 + 8.44281i −0.236049 + 0.277899i
\(924\) 0.798313 + 2.00362i 0.0262626 + 0.0659141i
\(925\) −0.274540 + 1.67462i −0.00902682 + 0.0550611i
\(926\) −8.09701 29.1628i −0.266084 0.958349i
\(927\) −8.61033 + 2.90116i −0.282800 + 0.0952865i
\(928\) 4.44197 6.55141i 0.145815 0.215061i
\(929\) −1.57868 + 2.97770i −0.0517947 + 0.0976951i −0.908058 0.418844i \(-0.862435\pi\)
0.856263 + 0.516540i \(0.172780\pi\)
\(930\) 11.9129 + 14.0249i 0.390638 + 0.459894i
\(931\) 6.19776 5.87083i 0.203123 0.192409i
\(932\) 21.0028 2.28419i 0.687970 0.0748212i
\(933\) −5.84629 8.62263i −0.191399 0.282292i
\(934\) −14.9235 11.3446i −0.488312 0.371205i
\(935\) −4.14586 3.92717i −0.135584 0.128432i
\(936\) 0.0959260 1.76925i 0.00313544 0.0578298i
\(937\) 33.3020 + 11.2208i 1.08793 + 0.366566i 0.805424 0.592700i \(-0.201938\pi\)
0.282506 + 0.959266i \(0.408834\pi\)
\(938\) 22.6342 17.2061i 0.739034 0.561799i
\(939\) 22.2434 + 2.41912i 0.725887 + 0.0789449i
\(940\) −11.4404 21.5789i −0.373144 0.703825i
\(941\) −5.94320 + 14.9163i −0.193743 + 0.486257i −0.993468 0.114108i \(-0.963599\pi\)
0.799726 + 0.600366i \(0.204978\pi\)
\(942\) −5.88541 3.54114i −0.191757 0.115376i
\(943\) 5.62816 0.183278
\(944\) 4.77507 6.01653i 0.155415 0.195821i
\(945\) 6.80603 0.221400
\(946\) −2.61703 1.57461i −0.0850869 0.0511951i
\(947\) 4.48544 11.2576i 0.145757 0.365823i −0.837913 0.545804i \(-0.816224\pi\)
0.983670 + 0.179981i \(0.0576036\pi\)
\(948\) 3.02685 + 5.70924i 0.0983074 + 0.185428i
\(949\) 28.9344 + 3.14681i 0.939251 + 0.102150i
\(950\) 14.3496 10.9083i 0.465562 0.353911i
\(951\) 24.9030 + 8.39078i 0.807534 + 0.272090i
\(952\) 0.216069 3.98516i 0.00700285 0.129160i
\(953\) 20.8967 + 19.7944i 0.676909 + 0.641202i 0.946850 0.321674i \(-0.104246\pi\)
−0.269941 + 0.962877i \(0.587004\pi\)
\(954\) 9.67245 + 7.35281i 0.313157 + 0.238056i
\(955\) 10.3417 + 15.2529i 0.334650 + 0.493572i
\(956\) 17.5409 1.90769i 0.567313 0.0616990i
\(957\) 5.70395 5.40307i 0.184383 0.174656i
\(958\) 3.30860 + 3.89518i 0.106896 + 0.125848i
\(959\) −10.2662 + 19.3641i −0.331512 + 0.625298i
\(960\) 1.75779 2.59254i 0.0567323 0.0836739i
\(961\) −3.32946 + 1.12183i −0.107402 + 0.0361880i
\(962\) 0.167197 + 0.602190i 0.00539065 + 0.0194154i
\(963\) −1.27961 + 7.80526i −0.0412348 + 0.251521i
\(964\) −4.52813 11.3647i −0.145841 0.366034i
\(965\) −20.4570 + 24.0838i −0.658534 + 0.775286i
\(966\) −0.252817 4.66293i −0.00813425 0.150027i
\(967\) 9.64099 34.7237i 0.310033 1.11664i −0.630291 0.776359i \(-0.717064\pi\)
0.940324 0.340280i \(-0.110522\pi\)
\(968\) −9.08914 4.20508i −0.292136 0.135156i
\(969\) −6.72058 1.47931i −0.215896 0.0475224i
\(970\) −23.9558 + 5.27308i −0.769176 + 0.169308i
\(971\) −27.5537 + 12.7477i −0.884242 + 0.409094i −0.808819 0.588058i \(-0.799893\pi\)
−0.0754227 + 0.997152i \(0.524031\pi\)
\(972\) −0.161782 0.986827i −0.00518916 0.0316525i
\(973\) 28.0886 16.9004i 0.900480 0.541801i
\(974\) −2.76291 + 1.66239i −0.0885294 + 0.0532664i
\(975\) −1.37911 8.41222i −0.0441670 0.269407i
\(976\) −1.92569 + 0.890918i −0.0616397 + 0.0285176i
\(977\) −7.24973 + 1.59579i −0.231939 + 0.0510537i −0.329419 0.944184i \(-0.606853\pi\)
0.0974797 + 0.995238i \(0.468922\pi\)
\(978\) −14.3477 3.15817i −0.458789 0.100987i
\(979\) −3.18860 1.47521i −0.101908 0.0471478i
\(980\) 1.90940 6.87703i 0.0609935 0.219679i
\(981\) −0.464368 8.56476i −0.0148261 0.273452i
\(982\) −5.32497 + 6.26904i −0.169927 + 0.200053i
\(983\) 21.0693 + 52.8799i 0.672006 + 1.68661i 0.725665 + 0.688048i \(0.241532\pi\)
−0.0536590 + 0.998559i \(0.517088\pi\)
\(984\) −0.423677 + 2.58432i −0.0135063 + 0.0823851i
\(985\) 11.3644 + 40.9308i 0.362099 + 1.30416i
\(986\) −13.7773 + 4.64213i −0.438760 + 0.147835i
\(987\) 9.50825 14.0236i 0.302651 0.446377i
\(988\) 3.10946 5.86506i 0.0989250 0.186592i
\(989\) 4.28105 + 5.04004i 0.136129 + 0.160264i
\(990\) 2.25718 2.13812i 0.0717380 0.0679538i
\(991\) 22.6602 2.46444i 0.719824 0.0782856i 0.259127 0.965843i \(-0.416565\pi\)
0.460697 + 0.887558i \(0.347600\pi\)
\(992\) 3.29687 + 4.86251i 0.104676 + 0.154385i
\(993\) 0.158614 + 0.120575i 0.00503346 + 0.00382634i
\(994\) −9.86239 9.34216i −0.312816 0.296315i
\(995\) 0.718051 13.2437i 0.0227637 0.419852i
\(996\) 14.9928 + 5.05166i 0.475065 + 0.160068i
\(997\) 4.35881 3.31348i 0.138045 0.104939i −0.533873 0.845565i \(-0.679264\pi\)
0.671918 + 0.740626i \(0.265471\pi\)
\(998\) 12.4915 + 1.35853i 0.395412 + 0.0430036i
\(999\) 0.165218 + 0.311634i 0.00522726 + 0.00985966i
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 354.2.e.a.139.2 56
59.45 even 29 inner 354.2.e.a.163.2 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.2.e.a.139.2 56 1.1 even 1 trivial
354.2.e.a.163.2 yes 56 59.45 even 29 inner