Properties

Label 882.2.y.a.583.25
Level $882$
Weight $2$
Character 882.583
Analytic conductor $7.043$
Analytic rank $0$
Dimension $336$
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] = [882,2,Mod(193,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 22]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.y (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 583.25
Character \(\chi\) \(=\) 882.583
Dual form 882.2.y.a.823.25

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.365341 + 0.930874i) q^{2} +(1.60482 + 0.651566i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(3.48464 - 1.67811i) q^{5} +(-1.19283 + 1.25585i) q^{6} +(-0.638775 + 2.56748i) q^{7} +(0.900969 - 0.433884i) q^{8} +(2.15092 + 2.09130i) q^{9} +O(q^{10})\) \(q+(-0.365341 + 0.930874i) q^{2} +(1.60482 + 0.651566i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(3.48464 - 1.67811i) q^{5} +(-1.19283 + 1.25585i) q^{6} +(-0.638775 + 2.56748i) q^{7} +(0.900969 - 0.433884i) q^{8} +(2.15092 + 2.09130i) q^{9} +(0.289031 + 3.85685i) q^{10} +(-0.807072 - 1.01204i) q^{11} +(-0.733242 - 1.56919i) q^{12} +(-1.91249 + 4.87295i) q^{13} +(-2.15663 - 1.53263i) q^{14} +(6.68564 - 0.422606i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-3.80731 + 3.53267i) q^{17} +(-2.73256 + 1.23820i) q^{18} +(-1.33392 + 2.31042i) q^{19} +(-3.69583 - 1.14001i) q^{20} +(-2.69801 + 3.70415i) q^{21} +(1.23693 - 0.381544i) q^{22} +(1.31637 - 5.76738i) q^{23} +(1.72860 - 0.109266i) q^{24} +(6.20921 - 7.78610i) q^{25} +(-3.83739 - 3.56058i) q^{26} +(2.08924 + 4.75764i) q^{27} +(2.21459 - 1.44762i) q^{28} +(6.91678 + 2.13354i) q^{29} +(-2.04915 + 6.37788i) q^{30} +(1.21373 - 2.10225i) q^{31} +(-0.955573 - 0.294755i) q^{32} +(-0.635800 - 2.15000i) q^{33} +(-1.89750 - 4.83476i) q^{34} +(2.08263 + 10.0187i) q^{35} +(-0.154294 - 2.99603i) q^{36} +(-0.131441 - 0.0405443i) q^{37} +(-1.66337 - 2.08580i) q^{38} +(-6.24427 + 6.57412i) q^{39} +(2.41145 - 3.02386i) q^{40} +(4.08430 + 2.78463i) q^{41} +(-2.46241 - 3.86478i) q^{42} +(5.37327 - 3.66343i) q^{43} +(-0.0967338 + 1.29082i) q^{44} +(11.0046 + 3.67793i) q^{45} +(4.88778 + 3.33243i) q^{46} +(1.44636 - 3.68528i) q^{47} +(-0.529815 + 1.64903i) q^{48} +(-6.18393 - 3.28009i) q^{49} +(4.97940 + 8.62457i) q^{50} +(-8.41183 + 3.18860i) q^{51} +(4.71641 - 2.27130i) q^{52} +(-4.90193 + 1.51205i) q^{53} +(-5.19204 + 0.206655i) q^{54} +(-4.51067 - 2.17222i) q^{55} +(0.538472 + 2.59038i) q^{56} +(-3.64609 + 2.83867i) q^{57} +(-4.51304 + 5.65918i) q^{58} +(8.38128 - 5.71426i) q^{59} +(-5.18837 - 4.23760i) q^{60} +(6.61703 - 6.13971i) q^{61} +(1.51350 + 1.89787i) q^{62} +(-6.74333 + 4.18659i) q^{63} +(0.623490 - 0.781831i) q^{64} +(1.51302 + 20.1899i) q^{65} +(2.23366 + 0.193634i) q^{66} +(3.14270 - 5.44332i) q^{67} +5.19378 q^{68} +(5.87037 - 8.39793i) q^{69} +(-10.0870 - 1.72158i) q^{70} +(1.44429 - 6.32783i) q^{71} +(2.84530 + 0.950944i) q^{72} +(-14.8210 - 2.23391i) q^{73} +(0.0857625 - 0.107543i) q^{74} +(15.0378 - 8.44961i) q^{75} +(2.54931 - 0.786359i) q^{76} +(3.11392 - 1.42568i) q^{77} +(-3.83839 - 8.21442i) q^{78} +(-7.23641 - 12.5338i) q^{79} +(1.93383 + 3.34949i) q^{80} +(0.252942 + 8.99644i) q^{81} +(-4.08430 + 2.78463i) q^{82} +(-4.78162 - 12.1834i) q^{83} +(4.49724 - 0.880227i) q^{84} +(-7.33889 + 18.6992i) q^{85} +(1.44712 + 6.34024i) q^{86} +(9.71007 + 7.93070i) q^{87} +(-1.16625 - 0.561638i) q^{88} +(0.493226 + 1.25672i) q^{89} +(-7.44413 + 8.90023i) q^{90} +(-11.2896 - 8.02301i) q^{91} +(-4.88778 + 3.33243i) q^{92} +(3.31758 - 2.58291i) q^{93} +(2.90211 + 2.69277i) q^{94} +(-0.771087 + 10.2894i) q^{95} +(-1.34147 - 1.09565i) q^{96} +(-5.41140 + 9.37281i) q^{97} +(5.31259 - 4.55811i) q^{98} +(0.380520 - 3.86464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 28 q^{2} - 13 q^{3} + 28 q^{4} - 4 q^{5} - 5 q^{6} - q^{7} + 56 q^{8} + 29 q^{9} - 2 q^{10} + q^{12} - 23 q^{13} + q^{14} + q^{15} + 28 q^{16} + 7 q^{17} - q^{18} + 38 q^{19} + 2 q^{20} + 13 q^{21} + 21 q^{23} - q^{24} - 48 q^{25} + 9 q^{26} - 28 q^{27} + 2 q^{28} + 11 q^{29} - 7 q^{30} + 44 q^{31} - 28 q^{32} - 25 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} - 22 q^{38} - 51 q^{39} + 4 q^{40} + 3 q^{41} + 13 q^{42} + q^{43} - 75 q^{45} - 42 q^{46} - 33 q^{47} - 2 q^{48} - 41 q^{49} + 172 q^{50} + 4 q^{51} + 11 q^{52} - 78 q^{53} + 11 q^{54} + 23 q^{55} + q^{56} - 30 q^{57} - 13 q^{58} + 14 q^{59} - 8 q^{60} + 92 q^{61} - 24 q^{62} - 22 q^{63} - 56 q^{64} + 7 q^{65} + 29 q^{66} + 29 q^{67} + 42 q^{68} + 19 q^{69} - 34 q^{70} + 7 q^{71} - q^{72} - 8 q^{73} - 8 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{77} + 4 q^{78} - 9 q^{79} - 12 q^{80} + 45 q^{81} - 3 q^{82} - 109 q^{83} + 28 q^{84} + 93 q^{85} + 2 q^{86} - 15 q^{87} + 47 q^{89} - 3 q^{90} + 45 q^{91} + 42 q^{92} + 155 q^{93} - 9 q^{94} - 13 q^{95} - q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.365341 + 0.930874i −0.258335 + 0.658227i
\(3\) 1.60482 + 0.651566i 0.926546 + 0.376182i
\(4\) −0.733052 0.680173i −0.366526 0.340086i
\(5\) 3.48464 1.67811i 1.55838 0.750476i 0.561355 0.827575i \(-0.310280\pi\)
0.997023 + 0.0770991i \(0.0245658\pi\)
\(6\) −1.19283 + 1.25585i −0.486972 + 0.512697i
\(7\) −0.638775 + 2.56748i −0.241434 + 0.970417i
\(8\) 0.900969 0.433884i 0.318541 0.153401i
\(9\) 2.15092 + 2.09130i 0.716974 + 0.697099i
\(10\) 0.289031 + 3.85685i 0.0913995 + 1.21964i
\(11\) −0.807072 1.01204i −0.243341 0.305140i 0.645130 0.764073i \(-0.276803\pi\)
−0.888471 + 0.458933i \(0.848232\pi\)
\(12\) −0.733242 1.56919i −0.211669 0.452986i
\(13\) −1.91249 + 4.87295i −0.530430 + 1.35151i 0.375002 + 0.927024i \(0.377642\pi\)
−0.905433 + 0.424490i \(0.860453\pi\)
\(14\) −2.15663 1.53263i −0.576384 0.409611i
\(15\) 6.68564 0.422606i 1.72622 0.109116i
\(16\) 0.0747301 + 0.997204i 0.0186825 + 0.249301i
\(17\) −3.80731 + 3.53267i −0.923409 + 0.856798i −0.990012 0.140981i \(-0.954974\pi\)
0.0666035 + 0.997780i \(0.478784\pi\)
\(18\) −2.73256 + 1.23820i −0.644069 + 0.291847i
\(19\) −1.33392 + 2.31042i −0.306022 + 0.530046i −0.977488 0.210989i \(-0.932331\pi\)
0.671466 + 0.741035i \(0.265665\pi\)
\(20\) −3.69583 1.14001i −0.826413 0.254915i
\(21\) −2.69801 + 3.70415i −0.588753 + 0.808313i
\(22\) 1.23693 0.381544i 0.263715 0.0813454i
\(23\) 1.31637 5.76738i 0.274481 1.20258i −0.630179 0.776449i \(-0.717019\pi\)
0.904661 0.426132i \(-0.140124\pi\)
\(24\) 1.72860 0.109266i 0.352849 0.0223039i
\(25\) 6.20921 7.78610i 1.24184 1.55722i
\(26\) −3.83739 3.56058i −0.752575 0.698287i
\(27\) 2.08924 + 4.75764i 0.402074 + 0.915607i
\(28\) 2.21459 1.44762i 0.418518 0.273575i
\(29\) 6.91678 + 2.13354i 1.28441 + 0.396189i 0.860471 0.509500i \(-0.170170\pi\)
0.423943 + 0.905689i \(0.360646\pi\)
\(30\) −2.04915 + 6.37788i −0.374121 + 1.16444i
\(31\) 1.21373 2.10225i 0.217993 0.377575i −0.736201 0.676762i \(-0.763382\pi\)
0.954194 + 0.299188i \(0.0967157\pi\)
\(32\) −0.955573 0.294755i −0.168923 0.0521058i
\(33\) −0.635800 2.15000i −0.110679 0.374267i
\(34\) −1.89750 4.83476i −0.325419 0.829154i
\(35\) 2.08263 + 10.0187i 0.352028 + 1.69347i
\(36\) −0.154294 2.99603i −0.0257157 0.499338i
\(37\) −0.131441 0.0405443i −0.0216088 0.00666543i 0.283932 0.958844i \(-0.408361\pi\)
−0.305541 + 0.952179i \(0.598837\pi\)
\(38\) −1.66337 2.08580i −0.269834 0.338361i
\(39\) −6.24427 + 6.57412i −0.999883 + 1.05270i
\(40\) 2.41145 3.02386i 0.381283 0.478114i
\(41\) 4.08430 + 2.78463i 0.637861 + 0.434886i 0.838592 0.544760i \(-0.183379\pi\)
−0.200731 + 0.979646i \(0.564332\pi\)
\(42\) −2.46241 3.86478i −0.379958 0.596349i
\(43\) 5.37327 3.66343i 0.819416 0.558668i −0.0794772 0.996837i \(-0.525325\pi\)
0.898893 + 0.438169i \(0.144373\pi\)
\(44\) −0.0967338 + 1.29082i −0.0145832 + 0.194599i
\(45\) 11.0046 + 3.67793i 1.64047 + 0.548273i
\(46\) 4.88778 + 3.33243i 0.720664 + 0.491340i
\(47\) 1.44636 3.68528i 0.210974 0.537553i −0.785740 0.618557i \(-0.787718\pi\)
0.996714 + 0.0810043i \(0.0258127\pi\)
\(48\) −0.529815 + 1.64903i −0.0764723 + 0.238017i
\(49\) −6.18393 3.28009i −0.883419 0.468584i
\(50\) 4.97940 + 8.62457i 0.704193 + 1.21970i
\(51\) −8.41183 + 3.18860i −1.17789 + 0.446493i
\(52\) 4.71641 2.27130i 0.654048 0.314973i
\(53\) −4.90193 + 1.51205i −0.673332 + 0.207695i −0.612522 0.790454i \(-0.709845\pi\)
−0.0608106 + 0.998149i \(0.519369\pi\)
\(54\) −5.19204 + 0.206655i −0.706547 + 0.0281221i
\(55\) −4.51067 2.17222i −0.608219 0.292903i
\(56\) 0.538472 + 2.59038i 0.0719564 + 0.346154i
\(57\) −3.64609 + 2.83867i −0.482937 + 0.375992i
\(58\) −4.51304 + 5.65918i −0.592592 + 0.743086i
\(59\) 8.38128 5.71426i 1.09115 0.743933i 0.122526 0.992465i \(-0.460901\pi\)
0.968624 + 0.248532i \(0.0799482\pi\)
\(60\) −5.18837 4.23760i −0.669815 0.547072i
\(61\) 6.61703 6.13971i 0.847224 0.786109i −0.131494 0.991317i \(-0.541977\pi\)
0.978718 + 0.205208i \(0.0657870\pi\)
\(62\) 1.51350 + 1.89787i 0.192215 + 0.241030i
\(63\) −6.74333 + 4.18659i −0.849579 + 0.527461i
\(64\) 0.623490 0.781831i 0.0779362 0.0977289i
\(65\) 1.51302 + 20.1899i 0.187667 + 2.50425i
\(66\) 2.23366 + 0.193634i 0.274945 + 0.0238347i
\(67\) 3.14270 5.44332i 0.383942 0.665007i −0.607680 0.794182i \(-0.707900\pi\)
0.991622 + 0.129175i \(0.0412329\pi\)
\(68\) 5.19378 0.629839
\(69\) 5.87037 8.39793i 0.706709 1.01099i
\(70\) −10.0870 1.72158i −1.20563 0.205768i
\(71\) 1.44429 6.32783i 0.171405 0.750976i −0.814016 0.580843i \(-0.802723\pi\)
0.985421 0.170133i \(-0.0544197\pi\)
\(72\) 2.84530 + 0.950944i 0.335321 + 0.112070i
\(73\) −14.8210 2.23391i −1.73467 0.261459i −0.795756 0.605617i \(-0.792926\pi\)
−0.938912 + 0.344158i \(0.888164\pi\)
\(74\) 0.0857625 0.107543i 0.00996968 0.0125016i
\(75\) 15.0378 8.44961i 1.73642 0.975677i
\(76\) 2.54931 0.786359i 0.292426 0.0902016i
\(77\) 3.11392 1.42568i 0.354864 0.162471i
\(78\) −3.83839 8.21442i −0.434612 0.930100i
\(79\) −7.23641 12.5338i −0.814159 1.41017i −0.909930 0.414762i \(-0.863865\pi\)
0.0957708 0.995403i \(-0.469468\pi\)
\(80\) 1.93383 + 3.34949i 0.216209 + 0.374485i
\(81\) 0.252942 + 8.99644i 0.0281046 + 0.999605i
\(82\) −4.08430 + 2.78463i −0.451036 + 0.307511i
\(83\) −4.78162 12.1834i −0.524851 1.33730i −0.910063 0.414470i \(-0.863967\pi\)
0.385212 0.922828i \(-0.374128\pi\)
\(84\) 4.49724 0.880227i 0.490690 0.0960407i
\(85\) −7.33889 + 18.6992i −0.796014 + 2.02821i
\(86\) 1.44712 + 6.34024i 0.156047 + 0.683685i
\(87\) 9.71007 + 7.93070i 1.04103 + 0.850260i
\(88\) −1.16625 0.561638i −0.124323 0.0598708i
\(89\) 0.493226 + 1.25672i 0.0522819 + 0.133212i 0.954629 0.297799i \(-0.0962524\pi\)
−0.902347 + 0.431011i \(0.858157\pi\)
\(90\) −7.44413 + 8.90023i −0.784680 + 0.938166i
\(91\) −11.2896 8.02301i −1.18347 0.841040i
\(92\) −4.88778 + 3.33243i −0.509586 + 0.347430i
\(93\) 3.31758 2.58291i 0.344017 0.267835i
\(94\) 2.90211 + 2.69277i 0.299330 + 0.277738i
\(95\) −0.771087 + 10.2894i −0.0791118 + 1.05567i
\(96\) −1.34147 1.09565i −0.136914 0.111824i
\(97\) −5.41140 + 9.37281i −0.549444 + 0.951665i 0.448869 + 0.893598i \(0.351827\pi\)
−0.998313 + 0.0580673i \(0.981506\pi\)
\(98\) 5.31259 4.55811i 0.536653 0.460439i
\(99\) 0.380520 3.86464i 0.0382437 0.388411i
\(100\) −9.84756 + 1.48428i −0.984756 + 0.148428i
\(101\) −12.0347 + 5.79561i −1.19750 + 0.576684i −0.922961 0.384892i \(-0.874239\pi\)
−0.274536 + 0.961577i \(0.588524\pi\)
\(102\) 0.105006 8.99528i 0.0103971 0.890666i
\(103\) −4.83768 + 2.32970i −0.476671 + 0.229553i −0.656763 0.754097i \(-0.728075\pi\)
0.180092 + 0.983650i \(0.442360\pi\)
\(104\) 0.391198 + 5.22018i 0.0383602 + 0.511881i
\(105\) −3.18559 + 17.4352i −0.310881 + 1.70150i
\(106\) 0.383353 5.11549i 0.0372346 0.496861i
\(107\) 5.75340 + 14.6594i 0.556203 + 1.41718i 0.881778 + 0.471665i \(0.156347\pi\)
−0.325575 + 0.945516i \(0.605558\pi\)
\(108\) 1.70450 4.90863i 0.164015 0.472334i
\(109\) −2.50696 + 6.38763i −0.240123 + 0.611824i −0.999234 0.0391378i \(-0.987539\pi\)
0.759111 + 0.650962i \(0.225634\pi\)
\(110\) 3.67000 3.40526i 0.349921 0.324679i
\(111\) −0.184523 0.150709i −0.0175141 0.0143047i
\(112\) −2.60804 0.445121i −0.246437 0.0420600i
\(113\) −11.3292 1.70760i −1.06576 0.160637i −0.407331 0.913280i \(-0.633541\pi\)
−0.658429 + 0.752643i \(0.728779\pi\)
\(114\) −1.31038 4.43114i −0.122728 0.415014i
\(115\) −5.09126 22.3063i −0.474762 2.08007i
\(116\) −3.61918 6.26860i −0.336032 0.582025i
\(117\) −14.3044 + 6.48175i −1.32244 + 0.599238i
\(118\) 2.25723 + 9.88956i 0.207795 + 0.910408i
\(119\) −6.63805 12.0318i −0.608509 1.10295i
\(120\) 5.84019 3.28154i 0.533134 0.299563i
\(121\) 2.07488 9.09063i 0.188625 0.826421i
\(122\) 3.29782 + 8.40271i 0.298571 + 0.760746i
\(123\) 4.74022 + 7.13003i 0.427411 + 0.642893i
\(124\) −2.31962 + 0.715508i −0.208308 + 0.0642545i
\(125\) 4.26771 18.6981i 0.381716 1.67241i
\(126\) −1.43357 7.80672i −0.127713 0.695478i
\(127\) −2.81858 12.3490i −0.250109 1.09580i −0.931461 0.363842i \(-0.881465\pi\)
0.681352 0.731956i \(-0.261392\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 11.0101 2.37813i 0.969387 0.209382i
\(130\) −19.3470 5.96776i −1.69684 0.523407i
\(131\) −2.14227 1.03166i −0.187171 0.0901370i 0.337951 0.941164i \(-0.390266\pi\)
−0.525122 + 0.851027i \(0.675980\pi\)
\(132\) −0.996298 + 2.00852i −0.0867166 + 0.174819i
\(133\) −5.07988 4.90065i −0.440481 0.424940i
\(134\) 3.91889 + 4.91413i 0.338540 + 0.424516i
\(135\) 15.2641 + 13.0727i 1.31372 + 1.12512i
\(136\) −1.89750 + 4.83476i −0.162709 + 0.414577i
\(137\) 6.02857 + 2.90321i 0.515056 + 0.248038i 0.673310 0.739361i \(-0.264872\pi\)
−0.158254 + 0.987398i \(0.550586\pi\)
\(138\) 5.67273 + 8.53268i 0.482895 + 0.726350i
\(139\) 7.65708 + 5.22051i 0.649465 + 0.442798i 0.842721 0.538350i \(-0.180952\pi\)
−0.193256 + 0.981148i \(0.561905\pi\)
\(140\) 5.28777 8.76077i 0.446898 0.740420i
\(141\) 4.72236 4.97182i 0.397695 0.418703i
\(142\) 5.36276 + 3.65626i 0.450032 + 0.306827i
\(143\) 6.47513 1.99731i 0.541477 0.167024i
\(144\) −1.92471 + 2.30119i −0.160393 + 0.191766i
\(145\) 27.6828 4.17251i 2.29893 0.346508i
\(146\) 7.49421 12.9803i 0.620225 1.07426i
\(147\) −7.78693 9.29321i −0.642255 0.766491i
\(148\) 0.0687762 + 0.119124i 0.00565337 + 0.00979192i
\(149\) 6.66043 + 8.35192i 0.545644 + 0.684216i 0.975832 0.218524i \(-0.0701241\pi\)
−0.430188 + 0.902739i \(0.641553\pi\)
\(150\) 2.37158 + 17.0853i 0.193639 + 1.39501i
\(151\) 0.459713 2.01413i 0.0374109 0.163908i −0.952772 0.303687i \(-0.901782\pi\)
0.990183 + 0.139779i \(0.0446394\pi\)
\(152\) −0.199368 + 2.66038i −0.0161709 + 0.215785i
\(153\) −15.5771 0.363725i −1.25933 0.0294054i
\(154\) 0.189484 + 3.41953i 0.0152691 + 0.275553i
\(155\) 0.701612 9.36236i 0.0563548 0.752002i
\(156\) 9.04891 0.571990i 0.724493 0.0457959i
\(157\) −15.9999 + 10.9086i −1.27693 + 0.870597i −0.996019 0.0891360i \(-0.971589\pi\)
−0.280912 + 0.959733i \(0.590637\pi\)
\(158\) 14.3112 2.15706i 1.13853 0.171607i
\(159\) −8.85194 0.767365i −0.702004 0.0608560i
\(160\) −3.82446 + 0.576445i −0.302350 + 0.0455720i
\(161\) 13.9668 + 7.06381i 1.10074 + 0.556706i
\(162\) −8.46696 3.05131i −0.665228 0.239734i
\(163\) −4.84380 + 3.30245i −0.379396 + 0.258668i −0.737970 0.674834i \(-0.764215\pi\)
0.358574 + 0.933501i \(0.383263\pi\)
\(164\) −1.09998 4.81931i −0.0858936 0.376325i
\(165\) −5.82349 6.42504i −0.453358 0.500188i
\(166\) 13.0881 1.01583
\(167\) 5.25306 4.87413i 0.406494 0.377171i −0.450259 0.892898i \(-0.648668\pi\)
0.856753 + 0.515727i \(0.172478\pi\)
\(168\) −0.823647 + 4.50795i −0.0635458 + 0.347796i
\(169\) −10.5584 9.79674i −0.812182 0.753595i
\(170\) −14.7254 13.6632i −1.12939 1.04792i
\(171\) −7.70092 + 2.17990i −0.588904 + 0.166701i
\(172\) −6.43065 0.969265i −0.490332 0.0739057i
\(173\) 4.47314 1.37978i 0.340087 0.104903i −0.120007 0.992773i \(-0.538292\pi\)
0.460094 + 0.887870i \(0.347816\pi\)
\(174\) −10.9300 + 6.14144i −0.828599 + 0.465581i
\(175\) 16.0244 + 20.9156i 1.21133 + 1.58107i
\(176\) 0.948894 0.880445i 0.0715256 0.0663660i
\(177\) 17.1737 3.70943i 1.29085 0.278817i
\(178\) −1.35004 −0.101190
\(179\) 5.26827 4.88824i 0.393769 0.365364i −0.458297 0.888799i \(-0.651540\pi\)
0.852065 + 0.523435i \(0.175350\pi\)
\(180\) −5.56534 10.1812i −0.414816 0.758859i
\(181\) 8.49165 10.6482i 0.631179 0.791474i −0.358690 0.933457i \(-0.616776\pi\)
0.989869 + 0.141983i \(0.0453478\pi\)
\(182\) 11.5930 7.57803i 0.859327 0.561721i
\(183\) 14.6196 5.54172i 1.08071 0.409656i
\(184\) −1.31637 5.76738i −0.0970438 0.425177i
\(185\) −0.526063 + 0.0792913i −0.0386770 + 0.00582961i
\(186\) 1.19231 + 4.03189i 0.0874247 + 0.295633i
\(187\) 6.64796 + 1.00202i 0.486147 + 0.0732749i
\(188\) −3.56689 + 1.71772i −0.260142 + 0.125278i
\(189\) −13.5497 + 2.32502i −0.985595 + 0.169120i
\(190\) −9.29646 4.47694i −0.674436 0.324791i
\(191\) 16.6430 + 11.3470i 1.20424 + 0.821040i 0.987872 0.155271i \(-0.0496251\pi\)
0.216372 + 0.976311i \(0.430577\pi\)
\(192\) 1.51001 0.848457i 0.108975 0.0612321i
\(193\) 1.84855 24.6671i 0.133061 1.77558i −0.387612 0.921822i \(-0.626700\pi\)
0.520674 0.853756i \(-0.325681\pi\)
\(194\) −6.74790 8.46160i −0.484471 0.607508i
\(195\) −10.7269 + 33.3870i −0.768170 + 2.39090i
\(196\) 2.30212 + 6.61062i 0.164437 + 0.472187i
\(197\) −20.4617 −1.45784 −0.728918 0.684601i \(-0.759976\pi\)
−0.728918 + 0.684601i \(0.759976\pi\)
\(198\) 3.45847 + 1.76613i 0.245783 + 0.125513i
\(199\) −11.4172 7.78409i −0.809342 0.551800i 0.0864592 0.996255i \(-0.472445\pi\)
−0.895801 + 0.444456i \(0.853397\pi\)
\(200\) 2.21604 9.70910i 0.156698 0.686537i
\(201\) 8.59017 6.68790i 0.605904 0.471728i
\(202\) −0.998208 13.3202i −0.0702337 0.937203i
\(203\) −9.89610 + 16.3959i −0.694570 + 1.15076i
\(204\) 8.33511 + 3.38409i 0.583574 + 0.236934i
\(205\) 18.9052 + 2.84951i 1.32040 + 0.199018i
\(206\) −0.401257 5.35440i −0.0279569 0.373059i
\(207\) 14.8927 9.65227i 1.03512 0.670879i
\(208\) −5.00225 1.54299i −0.346844 0.106987i
\(209\) 3.41479 0.514697i 0.236206 0.0356023i
\(210\) −15.0662 9.33518i −1.03966 0.644189i
\(211\) −8.18597 1.23384i −0.563546 0.0849408i −0.138910 0.990305i \(-0.544360\pi\)
−0.424636 + 0.905364i \(0.639598\pi\)
\(212\) 4.62182 + 2.22575i 0.317428 + 0.152865i
\(213\) 6.44083 9.21401i 0.441318 0.631334i
\(214\) −15.7480 −1.07651
\(215\) 12.5762 21.7827i 0.857693 1.48557i
\(216\) 3.94660 + 3.38000i 0.268532 + 0.229980i
\(217\) 4.62218 + 4.45910i 0.313774 + 0.302703i
\(218\) −5.03018 4.66733i −0.340687 0.316111i
\(219\) −22.3296 13.2419i −1.50889 0.894804i
\(220\) 1.82907 + 4.66039i 0.123316 + 0.314203i
\(221\) −9.93307 25.3091i −0.668171 1.70247i
\(222\) 0.207705 0.116707i 0.0139402 0.00783288i
\(223\) 9.62140 + 8.92735i 0.644296 + 0.597820i 0.933121 0.359562i \(-0.117074\pi\)
−0.288825 + 0.957382i \(0.593264\pi\)
\(224\) 1.36717 2.26513i 0.0913482 0.151346i
\(225\) 29.6386 3.76200i 1.97591 0.250800i
\(226\) 5.72858 9.92218i 0.381059 0.660014i
\(227\) −18.4522 −1.22471 −0.612357 0.790581i \(-0.709779\pi\)
−0.612357 + 0.790581i \(0.709779\pi\)
\(228\) 4.60356 + 0.399078i 0.304879 + 0.0264296i
\(229\) 21.4956 + 10.3517i 1.42047 + 0.684061i 0.977199 0.212327i \(-0.0681042\pi\)
0.443269 + 0.896388i \(0.353818\pi\)
\(230\) 22.6244 + 3.41007i 1.49181 + 0.224854i
\(231\) 5.92622 0.259039i 0.389917 0.0170435i
\(232\) 7.15751 1.07882i 0.469914 0.0708281i
\(233\) −0.841556 0.259586i −0.0551322 0.0170060i 0.267066 0.963678i \(-0.413946\pi\)
−0.322199 + 0.946672i \(0.604422\pi\)
\(234\) −0.807702 15.6837i −0.0528011 1.02527i
\(235\) −1.14426 15.2690i −0.0746430 0.996042i
\(236\) −10.0306 1.51187i −0.652936 0.0984143i
\(237\) −3.44655 24.8296i −0.223877 1.61285i
\(238\) 13.6252 1.78348i 0.883192 0.115606i
\(239\) 0.313141 + 4.17858i 0.0202554 + 0.270290i 0.998131 + 0.0611044i \(0.0194622\pi\)
−0.977876 + 0.209186i \(0.932919\pi\)
\(240\) 0.921042 + 6.63536i 0.0594530 + 0.428311i
\(241\) 2.86842 12.5674i 0.184771 0.809536i −0.794546 0.607204i \(-0.792291\pi\)
0.979317 0.202332i \(-0.0648520\pi\)
\(242\) 7.70420 + 5.25263i 0.495244 + 0.337652i
\(243\) −5.45585 + 14.6025i −0.349993 + 0.936752i
\(244\) −9.02669 −0.577875
\(245\) −27.0531 1.05258i −1.72836 0.0672468i
\(246\) −8.36895 + 1.80765i −0.533585 + 0.115251i
\(247\) −8.70743 10.9188i −0.554041 0.694745i
\(248\) 0.181405 2.42068i 0.0115192 0.153713i
\(249\) 0.264609 22.6677i 0.0167689 1.43651i
\(250\) 15.8464 + 10.8039i 1.00221 + 0.683297i
\(251\) 4.05628 + 1.95340i 0.256030 + 0.123298i 0.557497 0.830179i \(-0.311762\pi\)
−0.301467 + 0.953477i \(0.597476\pi\)
\(252\) 7.79081 + 1.51764i 0.490775 + 0.0956024i
\(253\) −6.89920 + 3.32248i −0.433749 + 0.208882i
\(254\) 12.5251 + 1.88786i 0.785895 + 0.118455i
\(255\) −23.9614 + 25.2271i −1.50052 + 1.57979i
\(256\) −0.988831 + 0.149042i −0.0618019 + 0.00931514i
\(257\) 2.68294 + 11.7547i 0.167357 + 0.733239i 0.987047 + 0.160432i \(0.0512886\pi\)
−0.819690 + 0.572808i \(0.805854\pi\)
\(258\) −1.80871 + 11.1179i −0.112606 + 0.692168i
\(259\) 0.188058 0.311574i 0.0116854 0.0193603i
\(260\) 12.6235 15.8293i 0.782875 0.981694i
\(261\) 10.4156 + 19.0541i 0.644708 + 1.17942i
\(262\) 1.74301 1.61728i 0.107684 0.0999157i
\(263\) −25.6954 −1.58444 −0.792222 0.610233i \(-0.791076\pi\)
−0.792222 + 0.610233i \(0.791076\pi\)
\(264\) −1.50569 1.66122i −0.0926686 0.102241i
\(265\) −14.5441 + 13.4949i −0.893436 + 0.828988i
\(266\) 6.41777 2.93832i 0.393499 0.180160i
\(267\) −0.0272946 + 2.33819i −0.00167040 + 0.143095i
\(268\) −6.00616 + 1.85266i −0.366885 + 0.113169i
\(269\) −14.9725 2.25674i −0.912889 0.137596i −0.324231 0.945978i \(-0.605106\pi\)
−0.588658 + 0.808382i \(0.700344\pi\)
\(270\) −17.7456 + 9.43296i −1.07996 + 0.574072i
\(271\) 19.2152 + 17.8291i 1.16724 + 1.08304i 0.995191 + 0.0979498i \(0.0312285\pi\)
0.172047 + 0.985089i \(0.444962\pi\)
\(272\) −3.80731 3.53267i −0.230852 0.214200i
\(273\) −12.8903 20.2314i −0.780154 1.22446i
\(274\) −4.90500 + 4.55118i −0.296322 + 0.274947i
\(275\) −12.8911 −0.777362
\(276\) −10.0153 + 2.16326i −0.602852 + 0.130213i
\(277\) 4.11128 + 18.0127i 0.247023 + 1.08228i 0.934470 + 0.356043i \(0.115874\pi\)
−0.687447 + 0.726235i \(0.741269\pi\)
\(278\) −7.65708 + 5.22051i −0.459241 + 0.313105i
\(279\) 7.00707 1.98349i 0.419502 0.118749i
\(280\) 6.22333 + 8.12291i 0.371915 + 0.485437i
\(281\) 12.0685 1.81904i 0.719949 0.108515i 0.221159 0.975238i \(-0.429016\pi\)
0.498790 + 0.866723i \(0.333778\pi\)
\(282\) 2.90286 + 6.21233i 0.172863 + 0.369939i
\(283\) 11.7361 1.76894i 0.697641 0.105152i 0.209359 0.977839i \(-0.432862\pi\)
0.488281 + 0.872686i \(0.337624\pi\)
\(284\) −5.36276 + 3.65626i −0.318221 + 0.216959i
\(285\) −7.94171 + 16.0103i −0.470426 + 0.948370i
\(286\) −0.506384 + 6.75722i −0.0299431 + 0.399563i
\(287\) −9.75843 + 8.70762i −0.576022 + 0.513994i
\(288\) −1.43894 2.63238i −0.0847905 0.155115i
\(289\) 0.745460 9.94748i 0.0438506 0.585146i
\(290\) −6.22959 + 27.2936i −0.365814 + 1.60274i
\(291\) −14.7913 + 11.5158i −0.867084 + 0.675070i
\(292\) 9.34512 + 11.7184i 0.546882 + 0.685768i
\(293\) −7.06160 12.2310i −0.412543 0.714545i 0.582624 0.812742i \(-0.302026\pi\)
−0.995167 + 0.0981965i \(0.968693\pi\)
\(294\) 11.4957 3.85346i 0.670442 0.224738i
\(295\) 19.6166 33.9769i 1.14212 1.97821i
\(296\) −0.136016 + 0.0205011i −0.00790577 + 0.00119160i
\(297\) 3.12874 5.95414i 0.181548 0.345494i
\(298\) −10.2079 + 3.14872i −0.591328 + 0.182401i
\(299\) 25.5866 + 17.4447i 1.47971 + 1.00885i
\(300\) −16.7707 4.03433i −0.968258 0.232922i
\(301\) 5.97349 + 16.1359i 0.344306 + 0.930057i
\(302\) 1.70695 + 1.16378i 0.0982240 + 0.0669680i
\(303\) −23.0898 + 1.45953i −1.32647 + 0.0838477i
\(304\) −2.40364 1.15753i −0.137858 0.0663890i
\(305\) 12.7548 32.4988i 0.730341 1.86088i
\(306\) 6.02954 14.3674i 0.344686 0.821331i
\(307\) −9.72341 12.1928i −0.554945 0.695878i 0.422670 0.906284i \(-0.361093\pi\)
−0.977614 + 0.210405i \(0.932522\pi\)
\(308\) −3.25238 1.07291i −0.185321 0.0611346i
\(309\) −9.28158 + 0.586698i −0.528011 + 0.0333761i
\(310\) 8.45884 + 4.07356i 0.480430 + 0.231363i
\(311\) 24.5521 + 7.57331i 1.39222 + 0.429443i 0.898039 0.439916i \(-0.144992\pi\)
0.494181 + 0.869359i \(0.335468\pi\)
\(312\) −2.77349 + 8.63236i −0.157018 + 0.488711i
\(313\) −15.2890 26.4814i −0.864188 1.49682i −0.867851 0.496824i \(-0.834499\pi\)
0.00366332 0.999993i \(-0.498834\pi\)
\(314\) −4.30906 18.8792i −0.243175 1.06542i
\(315\) −16.4725 + 25.9048i −0.928120 + 1.45957i
\(316\) −3.22050 + 14.1099i −0.181167 + 0.793747i
\(317\) 18.8560 5.81629i 1.05906 0.326676i 0.284168 0.958774i \(-0.408283\pi\)
0.774888 + 0.632099i \(0.217806\pi\)
\(318\) 3.94830 7.95969i 0.221409 0.446357i
\(319\) −3.42312 8.72195i −0.191658 0.488336i
\(320\) 0.860635 3.77069i 0.0481110 0.210788i
\(321\) −0.318387 + 27.2745i −0.0177706 + 1.52232i
\(322\) −11.6782 + 10.4206i −0.650798 + 0.580718i
\(323\) −3.08329 13.5088i −0.171559 0.751648i
\(324\) 5.93372 6.76690i 0.329651 0.375939i
\(325\) 26.0662 + 45.1480i 1.44589 + 2.50436i
\(326\) −1.30452 5.71549i −0.0722508 0.316552i
\(327\) −8.18519 + 8.61757i −0.452642 + 0.476553i
\(328\) 4.88803 + 0.736752i 0.269896 + 0.0406803i
\(329\) 8.53798 + 6.06758i 0.470714 + 0.334516i
\(330\) 8.10846 3.07360i 0.446356 0.169196i
\(331\) −2.47926 + 2.30042i −0.136273 + 0.126443i −0.745365 0.666657i \(-0.767725\pi\)
0.609092 + 0.793100i \(0.291534\pi\)
\(332\) −4.78162 + 12.1834i −0.262425 + 0.668649i
\(333\) −0.197930 0.362090i −0.0108465 0.0198424i
\(334\) 2.61804 + 6.67066i 0.143253 + 0.365002i
\(335\) 1.81667 24.2418i 0.0992555 1.32447i
\(336\) −3.89542 2.41365i −0.212513 0.131675i
\(337\) −0.917795 12.2471i −0.0499955 0.667143i −0.964756 0.263146i \(-0.915240\pi\)
0.914760 0.403997i \(-0.132379\pi\)
\(338\) 12.9769 6.24936i 0.705852 0.339920i
\(339\) −17.0687 10.1221i −0.927047 0.549758i
\(340\) 18.0985 8.71576i 0.981527 0.472679i
\(341\) −3.10712 + 0.468323i −0.168260 + 0.0253611i
\(342\) 0.784249 7.96500i 0.0424073 0.430698i
\(343\) 12.3717 13.7819i 0.668010 0.744153i
\(344\) 3.25164 5.63201i 0.175317 0.303658i
\(345\) 6.36343 39.1149i 0.342595 2.10588i
\(346\) −0.349820 + 4.66802i −0.0188064 + 0.250955i
\(347\) −9.02368 8.37275i −0.484416 0.449473i 0.399764 0.916618i \(-0.369092\pi\)
−0.884181 + 0.467145i \(0.845282\pi\)
\(348\) −1.72374 12.4181i −0.0924021 0.665682i
\(349\) −18.4086 + 12.5508i −0.985391 + 0.671828i −0.944902 0.327352i \(-0.893844\pi\)
−0.0404881 + 0.999180i \(0.512891\pi\)
\(350\) −25.3241 + 7.27535i −1.35363 + 0.388884i
\(351\) −27.1794 + 1.08180i −1.45073 + 0.0577422i
\(352\) 0.472913 + 1.20496i 0.0252064 + 0.0642247i
\(353\) 8.23842 + 3.96741i 0.438487 + 0.211164i 0.640085 0.768304i \(-0.278899\pi\)
−0.201598 + 0.979468i \(0.564613\pi\)
\(354\) −2.82125 + 17.3417i −0.149948 + 0.921704i
\(355\) −5.58601 24.4739i −0.296475 1.29894i
\(356\) 0.493226 1.25672i 0.0261409 0.0666060i
\(357\) −2.81340 23.6340i −0.148901 1.25085i
\(358\) 2.62562 + 6.68997i 0.138768 + 0.353576i
\(359\) −3.64697 + 2.48646i −0.192480 + 0.131230i −0.655725 0.754999i \(-0.727637\pi\)
0.463246 + 0.886230i \(0.346685\pi\)
\(360\) 11.5106 1.46103i 0.606663 0.0770032i
\(361\) 5.94132 + 10.2907i 0.312701 + 0.541614i
\(362\) 6.80978 + 11.7949i 0.357914 + 0.619925i
\(363\) 9.25296 13.2370i 0.485655 0.694760i
\(364\) 2.81880 + 13.5601i 0.147746 + 0.710745i
\(365\) −55.3946 + 17.0870i −2.89949 + 0.894374i
\(366\) −0.182498 + 15.6336i −0.00953930 + 0.817183i
\(367\) −18.0407 + 22.6223i −0.941716 + 1.18087i 0.0416299 + 0.999133i \(0.486745\pi\)
−0.983346 + 0.181742i \(0.941826\pi\)
\(368\) 5.84962 + 0.881689i 0.304933 + 0.0459612i
\(369\) 2.96153 + 14.5310i 0.154171 + 0.756454i
\(370\) 0.118382 0.518667i 0.00615441 0.0269642i
\(371\) −0.750919 13.5515i −0.0389858 0.703558i
\(372\) −4.18878 0.363121i −0.217178 0.0188269i
\(373\) 33.2381 1.72100 0.860501 0.509449i \(-0.170151\pi\)
0.860501 + 0.509449i \(0.170151\pi\)
\(374\) −3.36153 + 5.82234i −0.173820 + 0.301066i
\(375\) 19.0320 27.2264i 0.982806 1.40597i
\(376\) −0.295852 3.94787i −0.0152574 0.203596i
\(377\) −23.6250 + 29.6248i −1.21675 + 1.52575i
\(378\) 2.78596 13.4625i 0.143295 0.692435i
\(379\) −11.8133 14.8134i −0.606808 0.760913i 0.379614 0.925145i \(-0.376057\pi\)
−0.986422 + 0.164232i \(0.947485\pi\)
\(380\) 7.56384 7.01822i 0.388017 0.360027i
\(381\) 3.52287 21.6545i 0.180482 1.10939i
\(382\) −16.6430 + 11.3470i −0.851529 + 0.580563i
\(383\) −3.23108 + 4.05164i −0.165100 + 0.207029i −0.857499 0.514486i \(-0.827983\pi\)
0.692398 + 0.721515i \(0.256554\pi\)
\(384\) 0.238139 + 1.71560i 0.0121525 + 0.0875489i
\(385\) 8.45845 10.1935i 0.431083 0.519509i
\(386\) 22.2866 + 10.7327i 1.13436 + 0.546279i
\(387\) 19.2188 + 3.35735i 0.976947 + 0.170663i
\(388\) 10.3420 3.19007i 0.525034 0.161951i
\(389\) 22.1168 10.6509i 1.12137 0.540021i 0.221052 0.975262i \(-0.429051\pi\)
0.900314 + 0.435241i \(0.143337\pi\)
\(390\) −27.1601 22.1830i −1.37531 1.12328i
\(391\) 15.3624 + 26.6085i 0.776911 + 1.34565i
\(392\) −6.99471 0.272149i −0.353286 0.0137456i
\(393\) −2.76578 3.05147i −0.139515 0.153926i
\(394\) 7.47550 19.0473i 0.376610 0.959587i
\(395\) −46.2495 31.5324i −2.32706 1.58656i
\(396\) −2.90756 + 2.57416i −0.146111 + 0.129357i
\(397\) −1.42206 + 18.9760i −0.0713710 + 0.952379i 0.840476 + 0.541849i \(0.182275\pi\)
−0.911847 + 0.410530i \(0.865344\pi\)
\(398\) 11.4172 7.78409i 0.572291 0.390181i
\(399\) −4.95921 11.1746i −0.248271 0.559428i
\(400\) 8.22834 + 5.60999i 0.411417 + 0.280499i
\(401\) −11.6894 + 14.6581i −0.583743 + 0.731991i −0.982746 0.184959i \(-0.940785\pi\)
0.399003 + 0.916950i \(0.369356\pi\)
\(402\) 3.08725 + 10.4397i 0.153978 + 0.520686i
\(403\) 7.92289 + 9.93499i 0.394667 + 0.494897i
\(404\) 12.7641 + 3.93720i 0.635036 + 0.195883i
\(405\) 15.9785 + 30.9249i 0.793977 + 1.53667i
\(406\) −11.6470 15.2021i −0.578032 0.754468i
\(407\) 0.0650503 + 0.165745i 0.00322442 + 0.00821570i
\(408\) −6.19532 + 6.52259i −0.306714 + 0.322916i
\(409\) −21.8030 6.72533i −1.07809 0.332546i −0.295664 0.955292i \(-0.595541\pi\)
−0.782425 + 0.622745i \(0.786017\pi\)
\(410\) −9.55939 + 16.5574i −0.472105 + 0.817710i
\(411\) 7.78317 + 8.58715i 0.383915 + 0.423573i
\(412\) 5.13087 + 1.58266i 0.252780 + 0.0779723i
\(413\) 9.31751 + 25.1689i 0.458485 + 1.23848i
\(414\) 3.54413 + 17.3896i 0.174184 + 0.854653i
\(415\) −37.1073 34.4305i −1.82153 1.69013i
\(416\) 3.26385 4.09274i 0.160024 0.200663i
\(417\) 8.88677 + 13.3671i 0.435187 + 0.654590i
\(418\) −0.768446 + 3.36678i −0.0375859 + 0.164675i
\(419\) 1.40031 0.431939i 0.0684098 0.0211016i −0.260361 0.965511i \(-0.583842\pi\)
0.328771 + 0.944410i \(0.393366\pi\)
\(420\) 14.1942 10.6142i 0.692604 0.517918i
\(421\) 1.89503 + 0.584538i 0.0923579 + 0.0284886i 0.340590 0.940212i \(-0.389373\pi\)
−0.248232 + 0.968701i \(0.579849\pi\)
\(422\) 4.13922 7.16934i 0.201494 0.348998i
\(423\) 10.8180 4.90197i 0.525991 0.238342i
\(424\) −3.76044 + 3.48918i −0.182623 + 0.169449i
\(425\) 3.86532 + 51.5792i 0.187496 + 2.50196i
\(426\) 6.22398 + 9.36185i 0.301553 + 0.453583i
\(427\) 11.5368 + 20.9110i 0.558305 + 1.01195i
\(428\) 5.75340 14.6594i 0.278101 0.708591i
\(429\) 11.6928 + 1.01364i 0.564535 + 0.0489389i
\(430\) 15.6823 + 19.6650i 0.756269 + 0.948331i
\(431\) 0.850365 + 11.3473i 0.0409607 + 0.546582i 0.979505 + 0.201422i \(0.0645563\pi\)
−0.938544 + 0.345160i \(0.887825\pi\)
\(432\) −4.58820 + 2.43893i −0.220750 + 0.117343i
\(433\) −10.1861 + 4.90537i −0.489513 + 0.235737i −0.662323 0.749218i \(-0.730429\pi\)
0.172810 + 0.984955i \(0.444715\pi\)
\(434\) −5.83953 + 2.67357i −0.280306 + 0.128336i
\(435\) 47.1447 + 11.3410i 2.26042 + 0.543761i
\(436\) 6.18242 2.97730i 0.296084 0.142587i
\(437\) 11.5691 + 10.7346i 0.553426 + 0.513504i
\(438\) 20.4844 15.9482i 0.978784 0.762035i
\(439\) −2.82579 + 7.20001i −0.134868 + 0.343638i −0.982313 0.187245i \(-0.940044\pi\)
0.847445 + 0.530882i \(0.178139\pi\)
\(440\) −5.00647 −0.238674
\(441\) −6.44152 19.9877i −0.306739 0.951794i
\(442\) 27.1885 1.29322
\(443\) −5.64491 + 14.3830i −0.268198 + 0.683357i 0.731801 + 0.681519i \(0.238680\pi\)
−0.999998 + 0.00183780i \(0.999415\pi\)
\(444\) 0.0327566 + 0.235985i 0.00155456 + 0.0111994i
\(445\) 3.82764 + 3.55153i 0.181447 + 0.168359i
\(446\) −11.8253 + 5.69478i −0.559946 + 0.269656i
\(447\) 5.24700 + 17.7431i 0.248175 + 0.839219i
\(448\) 1.60907 + 2.10021i 0.0760214 + 0.0992258i
\(449\) 32.8102 15.8006i 1.54841 0.745674i 0.552286 0.833655i \(-0.313756\pi\)
0.996122 + 0.0879807i \(0.0280414\pi\)
\(450\) −7.32624 + 28.9642i −0.345362 + 1.36538i
\(451\) −0.478179 6.38086i −0.0225166 0.300463i
\(452\) 7.14342 + 8.95756i 0.335998 + 0.421328i
\(453\) 2.05010 2.93280i 0.0963220 0.137795i
\(454\) 6.74134 17.1767i 0.316387 0.806140i
\(455\) −52.8036 9.01213i −2.47547 0.422495i
\(456\) −2.05336 + 4.13954i −0.0961575 + 0.193852i
\(457\) −0.190191 2.53792i −0.00889675 0.118719i 0.990987 0.133957i \(-0.0427684\pi\)
−0.999884 + 0.0152382i \(0.995149\pi\)
\(458\) −17.4894 + 16.2278i −0.817225 + 0.758274i
\(459\) −24.7615 10.7332i −1.15577 0.500984i
\(460\) −11.4400 + 19.8146i −0.533391 + 0.923860i
\(461\) 33.6874 + 10.3912i 1.56898 + 0.483966i 0.952789 0.303633i \(-0.0981996\pi\)
0.616189 + 0.787598i \(0.288676\pi\)
\(462\) −1.92396 + 5.61120i −0.0895107 + 0.261057i
\(463\) −29.1250 + 8.98388i −1.35355 + 0.417516i −0.884865 0.465847i \(-0.845750\pi\)
−0.468689 + 0.883363i \(0.655274\pi\)
\(464\) −1.61069 + 7.05688i −0.0747742 + 0.327607i
\(465\) 7.22616 14.5678i 0.335105 0.675565i
\(466\) 0.549096 0.688545i 0.0254364 0.0318962i
\(467\) −13.5545 12.5767i −0.627226 0.581981i 0.301171 0.953570i \(-0.402623\pi\)
−0.928397 + 0.371589i \(0.878813\pi\)
\(468\) 14.8946 + 4.97802i 0.688503 + 0.230109i
\(469\) 11.9681 + 11.5459i 0.552638 + 0.533140i
\(470\) 14.6316 + 4.51325i 0.674905 + 0.208181i
\(471\) −32.7847 + 7.08132i −1.51064 + 0.326290i
\(472\) 5.07195 8.78487i 0.233455 0.404356i
\(473\) −8.04414 2.48129i −0.369870 0.114090i
\(474\) 24.3724 + 5.86296i 1.11946 + 0.269295i
\(475\) 9.70654 + 24.7319i 0.445367 + 1.13478i
\(476\) −3.31766 + 13.3349i −0.152065 + 0.611206i
\(477\) −13.7058 6.99911i −0.627546 0.320467i
\(478\) −4.00414 1.23511i −0.183145 0.0564927i
\(479\) −14.1058 17.6881i −0.644511 0.808191i 0.347048 0.937847i \(-0.387184\pi\)
−0.991559 + 0.129656i \(0.958613\pi\)
\(480\) −6.51318 1.56680i −0.297285 0.0715142i
\(481\) 0.448951 0.562966i 0.0204704 0.0256691i
\(482\) 10.6507 + 7.26152i 0.485126 + 0.330753i
\(483\) 17.8117 + 20.4365i 0.810460 + 0.929891i
\(484\) −7.70420 + 5.25263i −0.350191 + 0.238756i
\(485\) −3.12812 + 41.7418i −0.142041 + 1.89540i
\(486\) −11.5999 10.4136i −0.526180 0.472371i
\(487\) 0.204169 + 0.139200i 0.00925180 + 0.00630777i 0.567937 0.823072i \(-0.307742\pi\)
−0.558685 + 0.829380i \(0.688694\pi\)
\(488\) 3.29782 8.40271i 0.149285 0.380373i
\(489\) −9.92521 + 2.14379i −0.448834 + 0.0969457i
\(490\) 10.8634 24.7985i 0.490760 1.12028i
\(491\) −8.47218 14.6742i −0.382344 0.662240i 0.609053 0.793130i \(-0.291550\pi\)
−0.991397 + 0.130890i \(0.958216\pi\)
\(492\) 1.37483 8.45085i 0.0619821 0.380994i
\(493\) −33.8714 + 16.3116i −1.52549 + 0.734639i
\(494\) 13.3452 4.11644i 0.600428 0.185208i
\(495\) −5.15934 14.1054i −0.231895 0.633992i
\(496\) 2.18707 + 1.05324i 0.0982023 + 0.0472918i
\(497\) 15.3240 + 7.75024i 0.687376 + 0.347646i
\(498\) 21.0041 + 8.52776i 0.941216 + 0.382138i
\(499\) 2.85598 3.58129i 0.127851 0.160321i −0.713786 0.700364i \(-0.753021\pi\)
0.841637 + 0.540044i \(0.181592\pi\)
\(500\) −15.8464 + 10.8039i −0.708671 + 0.483164i
\(501\) 11.6061 4.39940i 0.518520 0.196551i
\(502\) −3.30030 + 3.06223i −0.147299 + 0.136674i
\(503\) 25.5580 + 32.0487i 1.13957 + 1.42898i 0.887221 + 0.461344i \(0.152633\pi\)
0.252352 + 0.967635i \(0.418796\pi\)
\(504\) −4.25904 + 6.69781i −0.189713 + 0.298344i
\(505\) −32.2109 + 40.3912i −1.43337 + 1.79739i
\(506\) −0.572248 7.63612i −0.0254395 0.339467i
\(507\) −10.5611 22.6015i −0.469035 1.00377i
\(508\) −6.33329 + 10.9696i −0.280994 + 0.486697i
\(509\) 0.508406 0.0225347 0.0112674 0.999937i \(-0.496413\pi\)
0.0112674 + 0.999937i \(0.496413\pi\)
\(510\) −14.7292 31.5215i −0.652220 1.39580i
\(511\) 15.2028 36.6257i 0.672533 1.62023i
\(512\) 0.222521 0.974928i 0.00983413 0.0430861i
\(513\) −13.7790 1.51930i −0.608357 0.0670787i
\(514\) −11.9223 1.79700i −0.525872 0.0792625i
\(515\) −12.9481 + 16.2364i −0.570560 + 0.715460i
\(516\) −9.68852 5.74549i −0.426514 0.252931i
\(517\) −4.89695 + 1.51051i −0.215368 + 0.0664322i
\(518\) 0.221331 + 0.288889i 0.00972473 + 0.0126931i
\(519\) 8.07763 + 0.700241i 0.354569 + 0.0307372i
\(520\) 10.1232 + 17.5340i 0.443934 + 0.768916i
\(521\) 11.1948 + 19.3900i 0.490453 + 0.849490i 0.999940 0.0109890i \(-0.00349798\pi\)
−0.509487 + 0.860479i \(0.670165\pi\)
\(522\) −21.5422 + 2.73434i −0.942878 + 0.119679i
\(523\) −0.522751 + 0.356405i −0.0228583 + 0.0155845i −0.574695 0.818367i \(-0.694879\pi\)
0.551837 + 0.833952i \(0.313927\pi\)
\(524\) 0.868688 + 2.21338i 0.0379488 + 0.0966919i
\(525\) 12.0884 + 44.0068i 0.527582 + 1.92061i
\(526\) 9.38757 23.9191i 0.409318 1.04292i
\(527\) 2.80548 + 12.2916i 0.122209 + 0.535431i
\(528\) 2.09648 0.794692i 0.0912374 0.0345845i
\(529\) −10.8076 5.20465i −0.469894 0.226289i
\(530\) −7.24854 18.4690i −0.314856 0.802241i
\(531\) 29.9777 + 5.23682i 1.30092 + 0.227259i
\(532\) 0.390525 + 7.04762i 0.0169314 + 0.305553i
\(533\) −21.3806 + 14.5770i −0.926095 + 0.631401i
\(534\) −2.16658 0.879643i −0.0937572 0.0380659i
\(535\) 44.6488 + 41.4280i 1.93033 + 1.79109i
\(536\) 0.469709 6.26783i 0.0202883 0.270729i
\(537\) 11.6397 4.41214i 0.502288 0.190398i
\(538\) 7.57081 13.1130i 0.326401 0.565343i
\(539\) 1.67131 + 8.90563i 0.0719885 + 0.383593i
\(540\) −2.29769 19.9652i −0.0988770 0.859164i
\(541\) −43.3872 + 6.53957i −1.86536 + 0.281158i −0.982190 0.187889i \(-0.939835\pi\)
−0.883173 + 0.469048i \(0.844597\pi\)
\(542\) −23.6167 + 11.3732i −1.01442 + 0.488521i
\(543\) 20.5656 11.5556i 0.882555 0.495899i
\(544\) 4.67944 2.25350i 0.200629 0.0966179i
\(545\) 1.98332 + 26.4656i 0.0849561 + 1.13366i
\(546\) 23.5422 4.60783i 1.00752 0.197197i
\(547\) −0.839650 + 11.2044i −0.0359008 + 0.479063i 0.950058 + 0.312074i \(0.101024\pi\)
−0.985959 + 0.166990i \(0.946595\pi\)
\(548\) −2.44457 6.22867i −0.104427 0.266076i
\(549\) 27.0727 + 0.632147i 1.15543 + 0.0269794i
\(550\) 4.70964 12.0000i 0.200820 0.511681i
\(551\) −14.1558 + 13.1347i −0.603057 + 0.559555i
\(552\) 1.64529 10.1133i 0.0700282 0.430452i
\(553\) 36.8028 10.5731i 1.56501 0.449612i
\(554\) −18.2696 2.75369i −0.776199 0.116993i
\(555\) −0.895903 0.215516i −0.0380290 0.00914817i
\(556\) −2.06219 9.03504i −0.0874563 0.383171i
\(557\) 17.7111 + 30.6765i 0.750442 + 1.29980i 0.947609 + 0.319433i \(0.103492\pi\)
−0.197167 + 0.980370i \(0.563174\pi\)
\(558\) −0.713588 + 7.24735i −0.0302086 + 0.306805i
\(559\) 7.57539 + 33.1900i 0.320405 + 1.40379i
\(560\) −9.83504 + 2.82550i −0.415606 + 0.119399i
\(561\) 10.0159 + 5.93965i 0.422873 + 0.250772i
\(562\) −2.71584 + 11.8989i −0.114561 + 0.501923i
\(563\) −4.50254 11.4723i −0.189759 0.483499i 0.804055 0.594555i \(-0.202672\pi\)
−0.993814 + 0.111056i \(0.964577\pi\)
\(564\) −6.84343 + 0.432580i −0.288161 + 0.0182149i
\(565\) −42.3437 + 13.0613i −1.78141 + 0.549493i
\(566\) −2.64103 + 11.5711i −0.111011 + 0.486371i
\(567\) −23.2598 5.09728i −0.976819 0.214066i
\(568\) −1.44429 6.32783i −0.0606009 0.265510i
\(569\) −20.1535 34.9069i −0.844879 1.46337i −0.885726 0.464208i \(-0.846339\pi\)
0.0408472 0.999165i \(-0.486994\pi\)
\(570\) −12.0022 13.2420i −0.502715 0.554644i
\(571\) −1.63026 0.502869i −0.0682243 0.0210444i 0.260455 0.965486i \(-0.416127\pi\)
−0.328679 + 0.944442i \(0.606604\pi\)
\(572\) −6.10512 2.94007i −0.255268 0.122931i
\(573\) 19.3158 + 29.0539i 0.806927 + 1.21375i
\(574\) −4.54054 12.2651i −0.189518 0.511936i
\(575\) −36.7318 46.0602i −1.53182 1.92084i
\(576\) 2.97612 0.377756i 0.124005 0.0157398i
\(577\) 1.28361 3.27058i 0.0534373 0.136156i −0.901662 0.432441i \(-0.857652\pi\)
0.955100 + 0.296285i \(0.0957477\pi\)
\(578\) 8.98750 + 4.32815i 0.373831 + 0.180027i
\(579\) 19.0389 38.3820i 0.791228 1.59510i
\(580\) −23.1310 15.7704i −0.960461 0.654832i
\(581\) 34.3349 4.49429i 1.42445 0.186455i
\(582\) −5.31591 17.9761i −0.220351 0.745133i
\(583\) 5.48646 + 3.74060i 0.227226 + 0.154920i
\(584\) −14.3225 + 4.41791i −0.592670 + 0.182815i
\(585\) −38.9687 + 46.5911i −1.61116 + 1.92630i
\(586\) 13.9654 2.10495i 0.576907 0.0869548i
\(587\) 2.87957 4.98757i 0.118853 0.205859i −0.800461 0.599385i \(-0.795412\pi\)
0.919313 + 0.393526i \(0.128745\pi\)
\(588\) −0.612759 + 12.1089i −0.0252698 + 0.499361i
\(589\) 3.23804 + 5.60845i 0.133421 + 0.231092i
\(590\) 24.4615 + 30.6737i 1.00706 + 1.26282i
\(591\) −32.8374 13.3322i −1.35075 0.548411i
\(592\) 0.0306083 0.134104i 0.00125799 0.00551162i
\(593\) −0.0650259 + 0.867710i −0.00267029 + 0.0356326i −0.998380 0.0569019i \(-0.981878\pi\)
0.995709 + 0.0925345i \(0.0294968\pi\)
\(594\) 4.39949 + 5.08775i 0.180513 + 0.208753i
\(595\) −43.3219 30.7870i −1.77603 1.26215i
\(596\) 0.798305 10.6526i 0.0326998 0.436349i
\(597\) −13.2507 19.9311i −0.542315 0.815727i
\(598\) −25.5866 + 17.4447i −1.04632 + 0.713365i
\(599\) −18.4473 + 2.78049i −0.753737 + 0.113608i −0.514662 0.857393i \(-0.672082\pi\)
−0.239076 + 0.971001i \(0.576844\pi\)
\(600\) 9.88248 14.1375i 0.403450 0.577162i
\(601\) 1.36056 0.205072i 0.0554984 0.00836504i −0.121234 0.992624i \(-0.538685\pi\)
0.176733 + 0.984259i \(0.443447\pi\)
\(602\) −17.2028 0.334536i −0.701135 0.0136347i
\(603\) 18.1433 5.13584i 0.738853 0.209147i
\(604\) −1.70695 + 1.16378i −0.0694548 + 0.0473535i
\(605\) −8.02492 35.1595i −0.326259 1.42944i
\(606\) 7.07702 22.0269i 0.287484 0.894782i
\(607\) 45.7049 1.85511 0.927553 0.373691i \(-0.121908\pi\)
0.927553 + 0.373691i \(0.121908\pi\)
\(608\) 1.95566 1.81459i 0.0793126 0.0735914i
\(609\) −26.5645 + 19.8645i −1.07645 + 0.804950i
\(610\) 25.5924 + 23.7463i 1.03621 + 0.961460i
\(611\) 15.1920 + 14.0961i 0.614603 + 0.570269i
\(612\) 11.1714 + 10.8617i 0.451578 + 0.439060i
\(613\) −24.9934 3.76715i −1.00947 0.152154i −0.376574 0.926387i \(-0.622898\pi\)
−0.632901 + 0.774233i \(0.718136\pi\)
\(614\) 14.9023 4.59675i 0.601408 0.185510i
\(615\) 28.4830 + 16.8910i 1.14854 + 0.681110i
\(616\) 2.18697 2.63557i 0.0881155 0.106190i
\(617\) 27.0168 25.0679i 1.08765 1.00920i 0.0877393 0.996143i \(-0.472036\pi\)
0.999915 0.0130520i \(-0.00415471\pi\)
\(618\) 2.84480 8.85433i 0.114435 0.356173i
\(619\) −15.3667 −0.617640 −0.308820 0.951120i \(-0.599934\pi\)
−0.308820 + 0.951120i \(0.599934\pi\)
\(620\) −6.88234 + 6.38588i −0.276401 + 0.256463i
\(621\) 30.1893 5.78662i 1.21145 0.232209i
\(622\) −16.0197 + 20.0880i −0.642330 + 0.805456i
\(623\) −3.54167 + 0.463589i −0.141894 + 0.0185733i
\(624\) −7.02237 5.73552i −0.281120 0.229605i
\(625\) −5.42586 23.7722i −0.217034 0.950889i
\(626\) 30.2366 4.55743i 1.20850 0.182151i
\(627\) 5.81550 + 1.39896i 0.232249 + 0.0558693i
\(628\) 19.1485 + 2.88617i 0.764107 + 0.115171i
\(629\) 0.643667 0.309974i 0.0256647 0.0123595i
\(630\) −18.0961 24.7979i −0.720964 0.987973i
\(631\) 29.1705 + 14.0478i 1.16126 + 0.559232i 0.912397 0.409307i \(-0.134230\pi\)
0.248861 + 0.968539i \(0.419944\pi\)
\(632\) −11.9580 8.15282i −0.475664 0.324302i
\(633\) −12.3331 7.31379i −0.490198 0.290697i
\(634\) −1.47462 + 19.6774i −0.0585647 + 0.781491i
\(635\) −30.5448 38.3020i −1.21213 1.51997i
\(636\) 5.96699 + 6.58337i 0.236607 + 0.261047i
\(637\) 27.8104 23.8609i 1.10189 0.945402i
\(638\) 9.36964 0.370948
\(639\) 16.3399 10.5902i 0.646398 0.418944i
\(640\) 3.19561 + 2.17873i 0.126318 + 0.0861219i
\(641\) 5.98351 26.2155i 0.236335 1.03545i −0.707935 0.706277i \(-0.750373\pi\)
0.944270 0.329172i \(-0.106770\pi\)
\(642\) −25.2728 10.2609i −0.997439 0.404965i
\(643\) 0.673873 + 8.99221i 0.0265750 + 0.354618i 0.994601 + 0.103770i \(0.0330905\pi\)
−0.968026 + 0.250848i \(0.919290\pi\)
\(644\) −5.43377 14.6780i −0.214120 0.578393i
\(645\) 34.3755 26.7632i 1.35354 1.05380i
\(646\) 13.7014 + 2.06515i 0.539075 + 0.0812524i
\(647\) 0.993298 + 13.2546i 0.0390506 + 0.521094i 0.982090 + 0.188413i \(0.0603342\pi\)
−0.943039 + 0.332681i \(0.892047\pi\)
\(648\) 4.13130 + 7.99577i 0.162293 + 0.314103i
\(649\) −12.5473 3.87034i −0.492526 0.151924i
\(650\) −51.5502 + 7.76994i −2.02196 + 0.304762i
\(651\) 4.51239 + 10.1677i 0.176854 + 0.398505i
\(652\) 5.79699 + 0.873756i 0.227028 + 0.0342189i
\(653\) −23.2360 11.1899i −0.909296 0.437894i −0.0800583 0.996790i \(-0.525511\pi\)
−0.829237 + 0.558896i \(0.811225\pi\)
\(654\) −5.03149 10.7677i −0.196747 0.421052i
\(655\) −9.19631 −0.359329
\(656\) −2.47162 + 4.28098i −0.0965006 + 0.167144i
\(657\) −27.2071 35.8001i −1.06145 1.39670i
\(658\) −8.76743 + 5.73105i −0.341790 + 0.223420i
\(659\) −28.0246 26.0030i −1.09168 1.01293i −0.999853 0.0171597i \(-0.994538\pi\)
−0.0918308 0.995775i \(-0.529272\pi\)
\(660\) −0.101218 + 8.67086i −0.00393992 + 0.337513i
\(661\) 1.01366 + 2.58275i 0.0394266 + 0.100457i 0.949231 0.314580i \(-0.101864\pi\)
−0.909804 + 0.415038i \(0.863768\pi\)
\(662\) −1.23562 3.14832i −0.0480239 0.122363i
\(663\) 0.549685 47.0886i 0.0213480 1.82877i
\(664\) −9.59425 8.90216i −0.372329 0.345471i
\(665\) −25.9254 8.55239i −1.00534 0.331647i
\(666\) 0.409372 0.0519613i 0.0158629 0.00201346i
\(667\) 21.4100 37.0832i 0.828997 1.43587i
\(668\) −7.16602 −0.277261
\(669\) 9.62389 + 20.5958i 0.372081 + 0.796280i
\(670\) 21.9024 + 10.5476i 0.846163 + 0.407490i
\(671\) −11.5540 1.74149i −0.446038 0.0672295i
\(672\) 3.66996 2.74434i 0.141572 0.105865i
\(673\) 12.4606 1.87814i 0.480321 0.0723968i 0.0955811 0.995422i \(-0.469529\pi\)
0.384740 + 0.923025i \(0.374291\pi\)
\(674\) 11.7358 + 3.62002i 0.452047 + 0.139438i
\(675\) 50.0159 + 13.2741i 1.92511 + 0.510922i
\(676\) 1.07636 + 14.3630i 0.0413985 + 0.552424i
\(677\) 32.2722 + 4.86426i 1.24032 + 0.186949i 0.736248 0.676712i \(-0.236596\pi\)
0.504074 + 0.863660i \(0.331834\pi\)
\(678\) 15.6583 12.1908i 0.601354 0.468186i
\(679\) −20.6079 19.8808i −0.790857 0.762955i
\(680\) 1.50116 + 20.0316i 0.0575669 + 0.768177i
\(681\) −29.6125 12.0228i −1.13475 0.460715i
\(682\) 0.699209 3.06343i 0.0267741 0.117305i
\(683\) 35.4173 + 24.1471i 1.35520 + 0.923963i 0.999942 0.0108040i \(-0.00343910\pi\)
0.355263 + 0.934767i \(0.384391\pi\)
\(684\) 7.12789 + 3.63998i 0.272542 + 0.139178i
\(685\) 25.8793 0.988798
\(686\) 8.30932 + 16.5516i 0.317251 + 0.631943i
\(687\) 27.7518 + 30.6185i 1.05880 + 1.16817i
\(688\) 4.05473 + 5.08447i 0.154585 + 0.193844i
\(689\) 2.00678 26.7787i 0.0764524 1.02019i
\(690\) 34.0862 + 20.2138i 1.29764 + 0.769527i
\(691\) −9.66341 6.58840i −0.367614 0.250635i 0.365397 0.930852i \(-0.380933\pi\)
−0.733011 + 0.680217i \(0.761886\pi\)
\(692\) −4.21754 2.03106i −0.160327 0.0772093i
\(693\) 9.67933 + 3.44561i 0.367687 + 0.130888i
\(694\) 11.0907 5.34100i 0.420997 0.202741i
\(695\) 35.4428 + 5.34214i 1.34442 + 0.202639i
\(696\) 12.1895 + 2.93227i 0.462041 + 0.111148i
\(697\) −25.3874 + 3.82653i −0.961615 + 0.144940i
\(698\) −4.95777 21.7214i −0.187654 0.822168i
\(699\) −1.18141 0.964919i −0.0446851 0.0364966i
\(700\) 2.47951 26.2316i 0.0937167 0.991460i
\(701\) 21.4879 26.9450i 0.811587 1.01770i −0.187783 0.982210i \(-0.560130\pi\)
0.999370 0.0354870i \(-0.0112982\pi\)
\(702\) 8.92273 25.6958i 0.336767 0.969826i
\(703\) 0.269006 0.249601i 0.0101458 0.00941388i
\(704\) −1.29444 −0.0487862
\(705\) 8.11246 25.2497i 0.305533 0.950958i
\(706\) −6.70300 + 6.21947i −0.252271 + 0.234073i
\(707\) −7.19265 34.6010i −0.270508 1.30130i
\(708\) −15.1123 8.96188i −0.567954 0.336808i
\(709\) 12.8361 3.95942i 0.482070 0.148699i −0.0441888 0.999023i \(-0.514070\pi\)
0.526259 + 0.850324i \(0.323594\pi\)
\(710\) 24.8229 + 3.74145i 0.931587 + 0.140414i
\(711\) 10.6470 42.0928i 0.399294 1.57860i
\(712\) 0.989652 + 0.918263i 0.0370888 + 0.0344134i
\(713\) −10.5267 9.76738i −0.394229 0.365791i
\(714\) 23.0282 + 6.01556i 0.861807 + 0.225127i
\(715\) 19.2118 17.8259i 0.718479 0.666652i
\(716\) −7.18676 −0.268582
\(717\) −2.22009 + 6.90992i −0.0829106 + 0.258056i
\(718\) −0.982194 4.30327i −0.0366551 0.160597i
\(719\) −19.9094 + 13.5740i −0.742495 + 0.506225i −0.874501 0.485024i \(-0.838811\pi\)
0.132005 + 0.991249i \(0.457858\pi\)
\(720\) −2.84527 + 11.2487i −0.106037 + 0.419215i
\(721\) −2.89128 13.9088i −0.107677 0.517991i
\(722\) −11.7499 + 1.77102i −0.437287 + 0.0659104i
\(723\) 12.7918 18.2995i 0.475732 0.680565i
\(724\) −13.4674 + 2.02989i −0.500513 + 0.0754402i
\(725\) 59.5597 40.6071i 2.21199 1.50811i
\(726\) 8.94144 + 13.4493i 0.331848 + 0.499152i
\(727\) 2.74112 36.5777i 0.101662 1.35659i −0.680148 0.733075i \(-0.738084\pi\)
0.781810 0.623517i \(-0.214297\pi\)
\(728\) −13.6526 2.33013i −0.505999 0.0863602i
\(729\) −18.2702 + 19.8796i −0.676674 + 0.736283i
\(730\) 4.33211 57.8080i 0.160339 2.13957i
\(731\) −7.51601 + 32.9298i −0.277990 + 1.21795i
\(732\) −14.4863 5.88149i −0.535427 0.217386i
\(733\) −10.7426 13.4708i −0.396787 0.497556i 0.542801 0.839861i \(-0.317364\pi\)
−0.939589 + 0.342305i \(0.888792\pi\)
\(734\) −14.4675 25.0585i −0.534006 0.924925i
\(735\) −42.7297 19.3161i −1.57611 0.712486i
\(736\) −2.95785 + 5.12314i −0.109028 + 0.188842i
\(737\) −8.04522 + 1.21262i −0.296350 + 0.0446675i
\(738\) −14.6085 2.55197i −0.537747 0.0939392i
\(739\) 11.1922 3.45234i 0.411712 0.126996i −0.0819781 0.996634i \(-0.526124\pi\)
0.493690 + 0.869638i \(0.335648\pi\)
\(740\) 0.439564 + 0.299689i 0.0161587 + 0.0110168i
\(741\) −6.85960 23.1962i −0.251994 0.852133i
\(742\) 12.8891 + 4.25190i 0.473172 + 0.156092i
\(743\) −1.29235 0.881110i −0.0474118 0.0323248i 0.539382 0.842061i \(-0.318658\pi\)
−0.586794 + 0.809736i \(0.699610\pi\)
\(744\) 1.86835 3.76656i 0.0684972 0.138089i
\(745\) 37.2247 + 17.9265i 1.36381 + 0.656775i
\(746\) −12.1432 + 30.9404i −0.444595 + 1.13281i
\(747\) 15.1942 36.2053i 0.555925 1.32468i
\(748\) −4.19176 5.25630i −0.153266 0.192189i
\(749\) −41.3130 + 5.40768i −1.50954 + 0.197592i
\(750\) 18.3912 + 27.6633i 0.671552 + 1.01012i
\(751\) −0.881916 0.424708i −0.0321816 0.0154978i 0.417724 0.908574i \(-0.362828\pi\)
−0.449905 + 0.893076i \(0.648542\pi\)
\(752\) 3.78306 + 1.16692i 0.137954 + 0.0425532i
\(753\) 5.23685 + 5.77780i 0.190841 + 0.210555i
\(754\) −18.9457 32.8150i −0.689963 1.19505i
\(755\) −1.77801 7.78998i −0.0647085 0.283506i
\(756\) 11.5140 + 7.51178i 0.418762 + 0.273201i
\(757\) −4.25273 + 18.6324i −0.154568 + 0.677206i 0.836955 + 0.547272i \(0.184334\pi\)
−0.991523 + 0.129934i \(0.958523\pi\)
\(758\) 18.1053 5.58474i 0.657613 0.202847i
\(759\) −13.2368 + 0.836712i −0.480466 + 0.0303707i
\(760\) 3.76969 + 9.60502i 0.136741 + 0.348411i
\(761\) 4.02984 17.6559i 0.146082 0.640025i −0.847870 0.530204i \(-0.822115\pi\)
0.993951 0.109821i \(-0.0350276\pi\)
\(762\) 18.8705 + 11.1906i 0.683608 + 0.405393i
\(763\) −14.7987 10.5168i −0.535750 0.380735i
\(764\) −4.48226 19.6380i −0.162162 0.710480i
\(765\) −54.8910 + 24.8727i −1.98459 + 0.899275i
\(766\) −2.59112 4.48796i −0.0936211 0.162156i
\(767\) 11.8162 + 51.7701i 0.426657 + 1.86931i
\(768\) −1.68401 0.405102i −0.0607665 0.0146179i
\(769\) −23.7775 3.58389i −0.857440 0.129238i −0.294414 0.955678i \(-0.595125\pi\)
−0.563025 + 0.826440i \(0.690363\pi\)
\(770\) 6.39864 + 11.5979i 0.230591 + 0.417958i
\(771\) −3.35333 + 20.6124i −0.120767 + 0.742336i
\(772\) −18.1330 + 16.8249i −0.652620 + 0.605543i
\(773\) 3.26585 8.32124i 0.117464 0.299294i −0.860034 0.510236i \(-0.829558\pi\)
0.977499 + 0.210942i \(0.0676531\pi\)
\(774\) −10.1467 + 16.6637i −0.364715 + 0.598965i
\(775\) −8.83198 22.5035i −0.317254 0.808350i
\(776\) −0.808788 + 10.7925i −0.0290338 + 0.387429i
\(777\) 0.504812 0.377490i 0.0181100 0.0135424i
\(778\) 1.83446 + 24.4791i 0.0657685 + 0.877620i
\(779\) −11.8818 + 5.72196i −0.425709 + 0.205011i
\(780\) 30.5723 17.1783i 1.09467 0.615081i
\(781\) −7.56964 + 3.64535i −0.270863 + 0.130441i
\(782\) −30.3817 + 4.57930i −1.08645 + 0.163755i
\(783\) 4.30015 + 37.3650i 0.153675 + 1.33532i
\(784\) 2.80879 6.41176i 0.100314 0.228992i
\(785\) −37.4481 + 64.8621i −1.33658 + 2.31503i
\(786\) 3.85099 1.45976i 0.137360 0.0520679i
\(787\) 1.29991 17.3461i 0.0463367 0.618321i −0.924901 0.380208i \(-0.875852\pi\)
0.971238 0.238112i \(-0.0765287\pi\)
\(788\) 14.9995 + 13.9175i 0.534335 + 0.495790i
\(789\) −41.2366 16.7422i −1.46806 0.596039i
\(790\) 46.2495 31.5324i 1.64548 1.12187i
\(791\) 11.6210 27.9967i 0.413196 0.995449i
\(792\) −1.33397 3.64702i −0.0474005 0.129591i
\(793\) 17.2635 + 43.9866i 0.613044 + 1.56201i
\(794\) −17.1447 8.25647i −0.608444 0.293011i
\(795\) −32.1336 + 12.1806i −1.13966 + 0.432001i
\(796\) 3.07485 + 13.4718i 0.108985 + 0.477495i
\(797\) 1.68681 4.29792i 0.0597498 0.152240i −0.897881 0.440237i \(-0.854894\pi\)
0.957631 + 0.287998i \(0.0929895\pi\)
\(798\) 12.2139 0.533878i 0.432368 0.0188991i
\(799\) 7.51210 + 19.1405i 0.265759 + 0.677143i
\(800\) −8.22834 + 5.60999i −0.290916 + 0.198343i
\(801\) −1.56729 + 3.73459i −0.0553773 + 0.131955i
\(802\) −9.37421 16.2366i −0.331015 0.573334i
\(803\) 9.70082 + 16.8023i 0.342335 + 0.592941i
\(804\) −10.8460 0.940224i −0.382508 0.0331592i
\(805\) 60.5231 + 1.17697i 2.13316 + 0.0414826i
\(806\) −12.1428 + 3.74555i −0.427711 + 0.131931i
\(807\) −22.5578 13.3772i −0.794073 0.470901i
\(808\) −8.32827 + 10.4433i −0.292988 + 0.367395i
\(809\) 37.6292 + 5.67169i 1.32297 + 0.199406i 0.772270 0.635295i \(-0.219122\pi\)
0.550703 + 0.834701i \(0.314360\pi\)
\(810\) −34.6248 + 3.57581i −1.21659 + 0.125641i
\(811\) −3.61528 + 15.8396i −0.126950 + 0.556202i 0.870947 + 0.491377i \(0.163506\pi\)
−0.997897 + 0.0648254i \(0.979351\pi\)
\(812\) 18.4064 5.28795i 0.645937 0.185571i
\(813\) 19.2201 + 41.1325i 0.674080 + 1.44258i
\(814\) −0.178054 −0.00624078
\(815\) −11.3370 + 19.6363i −0.397119 + 0.687830i
\(816\) −3.80830 8.15003i −0.133317 0.285308i
\(817\) 1.29655 + 17.3012i 0.0453604 + 0.605292i
\(818\) 14.2260 17.8388i 0.497399 0.623719i
\(819\) −7.50448 40.8667i −0.262228 1.42800i
\(820\) −11.9204 14.9477i −0.416277 0.521995i
\(821\) −5.90405 + 5.47816i −0.206053 + 0.191189i −0.776448 0.630181i \(-0.782981\pi\)
0.570395 + 0.821370i \(0.306790\pi\)
\(822\) −10.8371 + 4.10791i −0.377986 + 0.143280i
\(823\) −37.4641 + 25.5426i −1.30592 + 0.890359i −0.998132 0.0610972i \(-0.980540\pi\)
−0.307785 + 0.951456i \(0.599588\pi\)
\(824\) −3.34778 + 4.19798i −0.116625 + 0.146244i
\(825\) −20.6879 8.39940i −0.720261 0.292429i
\(826\) −26.8331 0.521812i −0.933645 0.0181562i
\(827\) −32.4208 15.6130i −1.12738 0.542918i −0.225216 0.974309i \(-0.572309\pi\)
−0.902165 + 0.431391i \(0.858023\pi\)
\(828\) −17.4823 3.05400i −0.607554 0.106134i
\(829\) −8.41772 + 2.59652i −0.292359 + 0.0901809i −0.437466 0.899235i \(-0.644124\pi\)
0.145106 + 0.989416i \(0.453648\pi\)
\(830\) 45.6073 21.9633i 1.58305 0.762358i
\(831\) −5.13858 + 31.5860i −0.178255 + 1.09571i
\(832\) 2.61741 + 4.53348i 0.0907423 + 0.157170i
\(833\) 35.1316 9.35747i 1.21724 0.324217i
\(834\) −15.6898 + 3.38891i −0.543293 + 0.117348i
\(835\) 10.1257 25.7998i 0.350414 0.892840i
\(836\) −2.85330 1.94535i −0.0986835 0.0672813i
\(837\) 12.5375 + 1.38241i 0.433359 + 0.0477831i
\(838\) −0.109511 + 1.46132i −0.00378299 + 0.0504804i
\(839\) −23.1675 + 15.7953i −0.799831 + 0.545315i −0.892853 0.450349i \(-0.851300\pi\)
0.0930222 + 0.995664i \(0.470347\pi\)
\(840\) 4.69474 + 17.0908i 0.161984 + 0.589687i
\(841\) 19.3289 + 13.1782i 0.666514 + 0.454421i
\(842\) −1.23646 + 1.55047i −0.0426113 + 0.0534328i
\(843\) 20.5531 + 4.94421i 0.707887 + 0.170288i
\(844\) 5.16152 + 6.47234i 0.177667 + 0.222787i
\(845\) −53.2322 16.4200i −1.83124 0.564864i
\(846\) 0.610842 + 11.8611i 0.0210012 + 0.407793i
\(847\) 22.0147 + 11.1341i 0.756433 + 0.382572i
\(848\) −1.87414 4.77523i −0.0643582 0.163982i
\(849\) 19.9870 + 4.80803i 0.685953 + 0.165011i
\(850\) −49.4259 15.2459i −1.69529 0.522929i
\(851\) −0.406859 + 0.704700i −0.0139469 + 0.0241568i
\(852\) −10.9886 + 2.37347i −0.376463 + 0.0813139i
\(853\) 12.3867 + 3.82079i 0.424113 + 0.130821i 0.499462 0.866336i \(-0.333531\pi\)
−0.0753495 + 0.997157i \(0.524007\pi\)
\(854\) −23.6804 + 3.09966i −0.810326 + 0.106068i
\(855\) −23.1768 + 20.5192i −0.792631 + 0.701742i
\(856\) 11.5441 + 10.7114i 0.394570 + 0.366108i
\(857\) 7.21911 9.05248i 0.246600 0.309227i −0.643091 0.765790i \(-0.722348\pi\)
0.889691 + 0.456563i \(0.150920\pi\)
\(858\) −5.21544 + 10.5142i −0.178052 + 0.358949i
\(859\) −9.57368 + 41.9450i −0.326650 + 1.43115i 0.498823 + 0.866704i \(0.333766\pi\)
−0.825472 + 0.564442i \(0.809091\pi\)
\(860\) −24.0350 + 7.41383i −0.819588 + 0.252809i
\(861\) −21.3342 + 7.61593i −0.727066 + 0.259550i
\(862\) −10.8736 3.35406i −0.370357 0.114240i
\(863\) 7.35116 12.7326i 0.250236 0.433422i −0.713354 0.700803i \(-0.752825\pi\)
0.963591 + 0.267381i \(0.0861583\pi\)
\(864\) −0.594079 5.16208i −0.0202110 0.175618i
\(865\) 13.2719 12.3145i 0.451257 0.418705i
\(866\) −0.844878 11.2741i −0.0287101 0.383110i
\(867\) 7.67777 15.4782i 0.260751 0.525669i
\(868\) −0.355339 6.41263i −0.0120610 0.217659i
\(869\) −6.84438 + 17.4392i −0.232180 + 0.591584i
\(870\) −27.7810 + 39.7425i −0.941863 + 1.34740i
\(871\) 20.5146 + 25.7246i 0.695112 + 0.871643i
\(872\) 0.512796 + 6.84278i 0.0173655 + 0.231726i
\(873\) −31.2408 + 8.84336i −1.05734 + 0.299302i
\(874\) −14.2192 + 6.84761i −0.480972 + 0.231624i
\(875\) 45.2809 + 22.9011i 1.53077 + 0.774200i
\(876\) 7.36196 + 24.8950i 0.248738 + 0.841123i
\(877\) 9.78418 4.71181i 0.330388 0.159107i −0.261334 0.965248i \(-0.584162\pi\)
0.591722 + 0.806142i \(0.298448\pi\)
\(878\) −5.66992 5.26092i −0.191350 0.177547i
\(879\) −3.36329 24.2298i −0.113441 0.817250i
\(880\) 1.82907 4.66039i 0.0616578 0.157102i
\(881\) 41.7340 1.40606 0.703028 0.711163i \(-0.251831\pi\)
0.703028 + 0.711163i \(0.251831\pi\)
\(882\) 20.9593 + 1.30607i 0.705738 + 0.0439776i
\(883\) −7.44387 −0.250506 −0.125253 0.992125i \(-0.539974\pi\)
−0.125253 + 0.992125i \(0.539974\pi\)
\(884\) −9.93307 + 25.3091i −0.334085 + 0.851236i
\(885\) 53.6193 41.7455i 1.80239 1.40326i
\(886\) −11.3264 10.5094i −0.380519 0.353070i
\(887\) −33.1694 + 15.9736i −1.11372 + 0.536340i −0.897947 0.440104i \(-0.854942\pi\)
−0.215774 + 0.976443i \(0.569227\pi\)
\(888\) −0.231640 0.0557227i −0.00777332 0.00186993i
\(889\) 33.5063 + 0.651582i 1.12377 + 0.0218534i
\(890\) −4.70442 + 2.26553i −0.157692 + 0.0759407i
\(891\) 8.90059 7.51677i 0.298181 0.251821i
\(892\) −0.980842 13.0884i −0.0328410 0.438233i
\(893\) 6.58519 + 8.25756i 0.220365 + 0.276329i
\(894\) −18.4335 1.59798i −0.616509 0.0534444i
\(895\) 10.1550 25.8745i 0.339444 0.864890i
\(896\) −2.54289 + 0.730546i −0.0849521 + 0.0244058i
\(897\) 29.6957 + 44.6670i 0.991510 + 1.49139i
\(898\) 2.72141 + 36.3147i 0.0908147 + 1.21184i
\(899\) 12.8804 11.9512i 0.429584 0.398596i
\(900\) −24.2854 17.4016i −0.809514 0.580054i
\(901\) 13.3216 23.0737i 0.443808 0.768698i
\(902\) 6.11447 + 1.88606i 0.203590 + 0.0627991i
\(903\) −0.927192 + 29.7874i −0.0308550 + 0.991262i
\(904\) −10.9481 + 3.37705i −0.364130 + 0.112319i
\(905\) 11.7215 51.3551i 0.389635 1.70710i
\(906\) 1.98108 + 2.97985i 0.0658169 + 0.0989990i
\(907\) 0.433393 0.543458i 0.0143906 0.0180452i −0.774584 0.632471i \(-0.782041\pi\)
0.788975 + 0.614426i \(0.210612\pi\)
\(908\) 13.5264 + 12.5507i 0.448890 + 0.416509i
\(909\) −38.0061 12.7022i −1.26058 0.421307i
\(910\) 27.6805 45.8610i 0.917599 1.52028i
\(911\) −22.2339 6.85824i −0.736641 0.227224i −0.0963407 0.995348i \(-0.530714\pi\)
−0.640300 + 0.768125i \(0.721190\pi\)
\(912\) −3.10321 3.42376i −0.102758 0.113372i
\(913\) −8.47089 + 14.6720i −0.280346 + 0.485573i
\(914\) 2.43197 + 0.750162i 0.0804423 + 0.0248132i
\(915\) 41.6444 43.8443i 1.37672 1.44945i
\(916\) −8.71641 22.2091i −0.287998 0.733808i
\(917\) 4.01721 4.84125i 0.132660 0.159872i
\(918\) 19.0377 19.1286i 0.628337 0.631337i
\(919\) −5.44390 1.67922i −0.179578 0.0553924i 0.203662 0.979041i \(-0.434716\pi\)
−0.383240 + 0.923649i \(0.625192\pi\)
\(920\) −14.2654 17.8882i −0.470316 0.589758i
\(921\) −7.65997 25.9027i −0.252405 0.853523i
\(922\) −21.9803 + 27.5624i −0.723881 + 0.907719i
\(923\) 28.0730 + 19.1399i 0.924035 + 0.629997i
\(924\) −4.52042 3.84097i −0.148711 0.126359i
\(925\) −1.13183 + 0.771667i −0.0372143 + 0.0253722i
\(926\) 2.27771 30.3939i 0.0748501 0.998806i
\(927\) −15.2776 5.10602i −0.501782 0.167704i
\(928\) −5.98061 4.07751i −0.196323 0.133851i
\(929\) −3.02129 + 7.69811i −0.0991252 + 0.252567i −0.971831 0.235680i \(-0.924268\pi\)
0.872706 + 0.488247i \(0.162363\pi\)
\(930\) 10.9208 + 12.0489i 0.358106 + 0.395097i
\(931\) 15.8272 9.91208i 0.518716 0.324855i
\(932\) 0.440341 + 0.762693i 0.0144239 + 0.0249828i
\(933\) 34.4672 + 28.1511i 1.12841 + 0.921626i
\(934\) 16.6593 8.02272i 0.545110 0.262511i
\(935\) 24.8473 7.66437i 0.812593 0.250652i
\(936\) −10.0755 + 12.0463i −0.329328 + 0.393746i
\(937\) 5.68165 + 2.73614i 0.185611 + 0.0893857i 0.524381 0.851483i \(-0.324297\pi\)
−0.338770 + 0.940869i \(0.610011\pi\)
\(938\) −15.1202 + 6.92265i −0.493693 + 0.226032i
\(939\) −7.28185 52.4598i −0.237634 1.71196i
\(940\) −9.54678 + 11.9713i −0.311382 + 0.390460i
\(941\) 27.9751 19.0731i 0.911962 0.621765i −0.0137866 0.999905i \(-0.504389\pi\)
0.925748 + 0.378140i \(0.123436\pi\)
\(942\) 5.38578 33.1055i 0.175478 1.07864i
\(943\) 21.4364 19.8901i 0.698067 0.647711i
\(944\) 6.32461 + 7.93082i 0.205849 + 0.258126i
\(945\) −43.3142 + 30.8398i −1.40901 + 1.00322i
\(946\) 5.24862 6.58156i 0.170647 0.213985i
\(947\) −0.548030 7.31296i −0.0178086 0.237639i −0.999004 0.0446218i \(-0.985792\pi\)
0.981195 0.193017i \(-0.0618273\pi\)
\(948\) −14.3619 + 20.5456i −0.466453 + 0.667291i
\(949\) 39.2308 67.9497i 1.27349 2.20574i
\(950\) −26.5684 −0.861994
\(951\) 34.0502 + 2.95177i 1.10415 + 0.0957178i
\(952\) −11.2011 7.96012i −0.363029 0.257989i
\(953\) −12.4419 + 54.5115i −0.403032 + 1.76580i 0.211972 + 0.977276i \(0.432012\pi\)
−0.615004 + 0.788524i \(0.710846\pi\)
\(954\) 11.5226 10.2013i 0.373057 0.330280i
\(955\) 77.0364 + 11.6114i 2.49284 + 0.375735i
\(956\) 2.61261 3.27611i 0.0844978 0.105957i
\(957\) 0.189431 16.2276i 0.00612344 0.524564i
\(958\) 21.6188 6.66853i 0.698473 0.215450i
\(959\) −11.3048 + 13.6238i −0.365052 + 0.439934i
\(960\) 3.83802 5.49053i 0.123872 0.177206i
\(961\) 12.5537 + 21.7437i 0.404958 + 0.701408i
\(962\) 0.360031 + 0.623591i 0.0116079 + 0.0201054i
\(963\) −18.2821 + 43.5634i −0.589133 + 1.40381i
\(964\) −10.6507 + 7.26152i −0.343036 + 0.233878i
\(965\) −34.9527 89.0581i −1.12517 2.86688i
\(966\) −25.5311 + 9.11417i −0.821450 + 0.293244i
\(967\) 7.22977 18.4212i 0.232494 0.592384i −0.766247 0.642546i \(-0.777878\pi\)
0.998741 + 0.0501613i \(0.0159735\pi\)
\(968\) −2.07488 9.09063i −0.0666891 0.292184i
\(969\) 3.85372 23.6882i 0.123799 0.760973i
\(970\) −37.7135 18.1619i −1.21091 0.583143i
\(971\) 18.0135 + 45.8977i 0.578081 + 1.47293i 0.858380 + 0.513014i \(0.171471\pi\)
−0.280299 + 0.959913i \(0.590434\pi\)
\(972\) 13.9317 6.99349i 0.446858 0.224316i
\(973\) −18.2947 + 16.3247i −0.586502 + 0.523346i
\(974\) −0.204169 + 0.139200i −0.00654201 + 0.00446027i
\(975\) 12.4148 + 89.4385i 0.397592 + 2.86433i
\(976\) 6.61703 + 6.13971i 0.211806 + 0.196527i
\(977\) −1.51497 + 20.2159i −0.0484683 + 0.646765i 0.919079 + 0.394074i \(0.128935\pi\)
−0.967547 + 0.252691i \(0.918684\pi\)
\(978\) 1.63049 10.0223i 0.0521373 0.320479i
\(979\) 0.873777 1.51343i 0.0279260 0.0483693i
\(980\) 19.1154 + 19.1724i 0.610620 + 0.612440i
\(981\) −18.7507 + 8.49650i −0.598664 + 0.271272i
\(982\) 16.7551 2.52543i 0.534677 0.0805896i
\(983\) 30.0232 14.4584i 0.957590 0.461151i 0.111249 0.993793i \(-0.464515\pi\)
0.846341 + 0.532642i \(0.178801\pi\)
\(984\) 7.36439 + 4.36723i 0.234768 + 0.139222i
\(985\) −71.3017 + 34.3371i −2.27186 + 1.09407i
\(986\) −2.80944 37.4893i −0.0894707 1.19390i
\(987\) 9.74854 + 15.3005i 0.310299 + 0.487019i
\(988\) −1.04365 + 13.9266i −0.0332030 + 0.443064i
\(989\) −14.0552 35.8121i −0.446930 1.13876i
\(990\) 15.0153 + 0.350607i 0.477218 + 0.0111430i
\(991\) −1.55107 + 3.95205i −0.0492712 + 0.125541i −0.953391 0.301739i \(-0.902433\pi\)
0.904119 + 0.427280i \(0.140528\pi\)
\(992\) −1.77946 + 1.65110i −0.0564978 + 0.0524223i
\(993\) −5.47766 + 2.07637i −0.173828 + 0.0658915i
\(994\) −12.8130 + 11.4333i −0.406403 + 0.362641i
\(995\) −52.8473 7.96545i −1.67537 0.252522i
\(996\) −15.6119 + 16.4366i −0.494683 + 0.520814i
\(997\) 12.3943 + 54.3031i 0.392533 + 1.71980i 0.655677 + 0.755041i \(0.272383\pi\)
−0.263145 + 0.964756i \(0.584760\pi\)
\(998\) 2.29032 + 3.96695i 0.0724989 + 0.125572i
\(999\) −0.0817169 0.710056i −0.00258541 0.0224652i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 882.2.y.a.583.25 336
9.4 even 3 882.2.bb.b.877.22 yes 336
49.39 even 21 882.2.bb.b.529.22 yes 336
441.382 even 21 inner 882.2.y.a.823.25 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.y.a.583.25 336 1.1 even 1 trivial
882.2.y.a.823.25 yes 336 441.382 even 21 inner
882.2.bb.b.529.22 yes 336 49.39 even 21
882.2.bb.b.877.22 yes 336 9.4 even 3