Properties

Label 570.2.v.a.197.1
Level $570$
Weight $2$
Character 570.197
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(83,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.83");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.v (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 197.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 570.197
Dual form 570.2.v.a.353.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.158919 - 1.72474i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.448288 + 2.19067i) q^{5} +(-0.599900 + 1.62484i) q^{6} +(-2.12132 - 2.12132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.158919 - 1.72474i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.448288 + 2.19067i) q^{5} +(-0.599900 + 1.62484i) q^{6} +(-2.12132 - 2.12132i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.94949 - 0.548188i) q^{9} +(0.133975 - 2.23205i) q^{10} +5.82843i q^{11} +(1.00000 - 1.41421i) q^{12} +(-0.732051 - 2.73205i) q^{13} +(1.50000 + 2.59808i) q^{14} +(3.84959 - 0.425044i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-6.02993 - 1.61571i) q^{17} +(2.70711 + 1.29289i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-0.707107 + 2.12132i) q^{20} +(-3.99585 + 3.32162i) q^{21} +(1.50851 - 5.62983i) q^{22} +(-2.89778 + 0.776457i) q^{23} +(-1.33195 + 1.10721i) q^{24} +(-4.59808 + 1.96410i) q^{25} +2.82843i q^{26} +(-1.41421 + 5.00000i) q^{27} +(-0.776457 - 2.89778i) q^{28} +(4.41421 - 7.64564i) q^{29} +(-3.82843 - 0.585786i) q^{30} -2.24264 q^{31} +(-0.258819 - 0.965926i) q^{32} +(10.0525 + 0.926246i) q^{33} +(5.40629 + 3.12132i) q^{34} +(3.69615 - 5.59808i) q^{35} +(-2.28024 - 1.94949i) q^{36} +(2.12132 + 2.12132i) q^{37} +(4.31199 + 0.637756i) q^{38} +(-4.82843 + 0.828427i) q^{39} +(1.23205 - 1.86603i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(4.71940 - 2.17423i) q^{42} +(-4.09808 - 1.09808i) q^{43} +(-2.91421 + 5.04757i) q^{44} +(-0.121320 - 6.70711i) q^{45} +3.00000 q^{46} +(2.71379 + 10.1280i) q^{47} +(1.57313 - 0.724745i) q^{48} +2.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-3.74496 + 10.1433i) q^{51} +(0.732051 - 2.73205i) q^{52} +(-7.23023 + 1.93733i) q^{53} +(2.66012 - 4.46360i) q^{54} +(-12.7682 + 2.61281i) q^{55} +3.00000i q^{56} +(0.174235 + 7.54782i) q^{57} +(-6.24264 + 6.24264i) q^{58} +(2.82843 + 4.89898i) q^{59} +(3.54636 + 1.55670i) q^{60} +(3.12132 - 5.40629i) q^{61} +(2.16622 + 0.580438i) q^{62} +(5.09393 + 7.41970i) q^{63} +1.00000i q^{64} +(5.65685 - 2.82843i) q^{65} +(-9.47029 - 3.49648i) q^{66} +(5.46410 - 1.46410i) q^{67} +(-4.41421 - 4.41421i) q^{68} +(0.878680 + 5.12132i) q^{69} +(-5.01910 + 4.45069i) q^{70} +(-11.6170 + 6.70711i) q^{71} +(1.69798 + 2.47323i) q^{72} +(7.49303 + 2.00775i) q^{73} +(-1.50000 - 2.59808i) q^{74} +(2.65685 + 8.24264i) q^{75} +(-4.00000 - 1.73205i) q^{76} +(12.3640 - 12.3640i) q^{77} +(4.87832 + 0.449490i) q^{78} +(-9.08052 + 5.24264i) q^{79} +(-1.67303 + 1.48356i) q^{80} +(8.39898 + 3.23375i) q^{81} +(2.89778 - 0.776457i) q^{82} +(-3.00000 - 3.00000i) q^{83} +(-5.12132 + 0.878680i) q^{84} +(0.836355 - 13.9339i) q^{85} +(3.67423 + 2.12132i) q^{86} +(-12.4853 - 8.82843i) q^{87} +(4.12132 - 4.12132i) q^{88} +(3.08579 - 5.34474i) q^{89} +(-1.61874 + 6.50997i) q^{90} +(-4.24264 + 7.34847i) q^{91} +(-2.89778 - 0.776457i) q^{92} +(-0.356397 + 3.86798i) q^{93} -10.4853i q^{94} +(-3.03648 - 9.26174i) q^{95} +(-1.70711 + 0.292893i) q^{96} +(0.643238 - 2.40060i) q^{97} +(0.517638 - 1.93185i) q^{98} +(3.19507 - 17.1909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{6} - 4 q^{9} + 8 q^{10} + 8 q^{12} + 8 q^{13} + 12 q^{14} + 12 q^{15} + 4 q^{16} - 12 q^{17} + 16 q^{18} + 12 q^{21} - 8 q^{22} + 4 q^{24} - 16 q^{25} + 24 q^{29} - 8 q^{30} + 16 q^{31} + 12 q^{33} - 12 q^{35} - 16 q^{39} - 4 q^{40} - 12 q^{43} - 12 q^{44} + 16 q^{45} + 24 q^{46} - 24 q^{47} - 20 q^{51} - 8 q^{52} - 24 q^{53} + 4 q^{54} - 8 q^{55} - 28 q^{57} - 16 q^{58} + 4 q^{60} + 8 q^{61} + 12 q^{62} - 24 q^{63} - 4 q^{66} + 16 q^{67} - 24 q^{68} + 24 q^{69} - 8 q^{72} - 12 q^{73} - 12 q^{74} - 24 q^{75} - 32 q^{76} + 48 q^{77} + 28 q^{81} - 24 q^{83} - 24 q^{84} + 16 q^{85} - 32 q^{87} + 16 q^{88} + 36 q^{89} + 8 q^{90} + 24 q^{93} - 8 q^{96} - 24 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) 0.158919 1.72474i 0.0917517 0.995782i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0.448288 + 2.19067i 0.200480 + 0.979698i
\(6\) −0.599900 + 1.62484i −0.244908 + 0.663340i
\(7\) −2.12132 2.12132i −0.801784 0.801784i 0.181591 0.983374i \(-0.441875\pi\)
−0.983374 + 0.181591i \(0.941875\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −2.94949 0.548188i −0.983163 0.182729i
\(10\) 0.133975 2.23205i 0.0423665 0.705836i
\(11\) 5.82843i 1.75734i 0.477432 + 0.878668i \(0.341568\pi\)
−0.477432 + 0.878668i \(0.658432\pi\)
\(12\) 1.00000 1.41421i 0.288675 0.408248i
\(13\) −0.732051 2.73205i −0.203034 0.757735i −0.990040 0.140788i \(-0.955036\pi\)
0.787005 0.616946i \(-0.211630\pi\)
\(14\) 1.50000 + 2.59808i 0.400892 + 0.694365i
\(15\) 3.84959 0.425044i 0.993960 0.109746i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −6.02993 1.61571i −1.46247 0.391868i −0.562129 0.827049i \(-0.690018\pi\)
−0.900343 + 0.435181i \(0.856684\pi\)
\(18\) 2.70711 + 1.29289i 0.638071 + 0.304738i
\(19\) −4.33013 + 0.500000i −0.993399 + 0.114708i
\(20\) −0.707107 + 2.12132i −0.158114 + 0.474342i
\(21\) −3.99585 + 3.32162i −0.871967 + 0.724837i
\(22\) 1.50851 5.62983i 0.321615 1.20028i
\(23\) −2.89778 + 0.776457i −0.604228 + 0.161903i −0.547948 0.836512i \(-0.684591\pi\)
−0.0562805 + 0.998415i \(0.517924\pi\)
\(24\) −1.33195 + 1.10721i −0.271883 + 0.226008i
\(25\) −4.59808 + 1.96410i −0.919615 + 0.392820i
\(26\) 2.82843i 0.554700i
\(27\) −1.41421 + 5.00000i −0.272166 + 0.962250i
\(28\) −0.776457 2.89778i −0.146737 0.547628i
\(29\) 4.41421 7.64564i 0.819699 1.41976i −0.0862053 0.996277i \(-0.527474\pi\)
0.905904 0.423483i \(-0.139193\pi\)
\(30\) −3.82843 0.585786i −0.698972 0.106949i
\(31\) −2.24264 −0.402790 −0.201395 0.979510i \(-0.564548\pi\)
−0.201395 + 0.979510i \(0.564548\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) 10.0525 + 0.926246i 1.74992 + 0.161239i
\(34\) 5.40629 + 3.12132i 0.927170 + 0.535302i
\(35\) 3.69615 5.59808i 0.624764 0.946248i
\(36\) −2.28024 1.94949i −0.380040 0.324915i
\(37\) 2.12132 + 2.12132i 0.348743 + 0.348743i 0.859641 0.510898i \(-0.170687\pi\)
−0.510898 + 0.859641i \(0.670687\pi\)
\(38\) 4.31199 + 0.637756i 0.699497 + 0.103458i
\(39\) −4.82843 + 0.828427i −0.773167 + 0.132655i
\(40\) 1.23205 1.86603i 0.194804 0.295045i
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 4.71940 2.17423i 0.728219 0.335492i
\(43\) −4.09808 1.09808i −0.624951 0.167455i −0.0675734 0.997714i \(-0.521526\pi\)
−0.557377 + 0.830259i \(0.688192\pi\)
\(44\) −2.91421 + 5.04757i −0.439334 + 0.760949i
\(45\) −0.121320 6.70711i −0.0180854 0.999836i
\(46\) 3.00000 0.442326
\(47\) 2.71379 + 10.1280i 0.395847 + 1.47732i 0.820333 + 0.571887i \(0.193788\pi\)
−0.424486 + 0.905435i \(0.639545\pi\)
\(48\) 1.57313 0.724745i 0.227062 0.104608i
\(49\) 2.00000i 0.285714i
\(50\) 4.94975 0.707107i 0.700000 0.100000i
\(51\) −3.74496 + 10.1433i −0.524400 + 1.42035i
\(52\) 0.732051 2.73205i 0.101517 0.378867i
\(53\) −7.23023 + 1.93733i −0.993148 + 0.266113i −0.718572 0.695452i \(-0.755204\pi\)
−0.274576 + 0.961565i \(0.588537\pi\)
\(54\) 2.66012 4.46360i 0.361997 0.607420i
\(55\) −12.7682 + 2.61281i −1.72166 + 0.352312i
\(56\) 3.00000i 0.400892i
\(57\) 0.174235 + 7.54782i 0.0230779 + 0.999734i
\(58\) −6.24264 + 6.24264i −0.819699 + 0.819699i
\(59\) 2.82843 + 4.89898i 0.368230 + 0.637793i 0.989289 0.145971i \(-0.0466306\pi\)
−0.621059 + 0.783764i \(0.713297\pi\)
\(60\) 3.54636 + 1.55670i 0.457834 + 0.200969i
\(61\) 3.12132 5.40629i 0.399644 0.692204i −0.594038 0.804437i \(-0.702467\pi\)
0.993682 + 0.112233i \(0.0358004\pi\)
\(62\) 2.16622 + 0.580438i 0.275111 + 0.0737157i
\(63\) 5.09393 + 7.41970i 0.641775 + 0.934794i
\(64\) 1.00000i 0.125000i
\(65\) 5.65685 2.82843i 0.701646 0.350823i
\(66\) −9.47029 3.49648i −1.16571 0.430386i
\(67\) 5.46410 1.46410i 0.667546 0.178868i 0.0908970 0.995860i \(-0.471027\pi\)
0.576649 + 0.816992i \(0.304360\pi\)
\(68\) −4.41421 4.41421i −0.535302 0.535302i
\(69\) 0.878680 + 5.12132i 0.105781 + 0.616535i
\(70\) −5.01910 + 4.45069i −0.599897 + 0.531959i
\(71\) −11.6170 + 6.70711i −1.37869 + 0.795987i −0.992002 0.126223i \(-0.959714\pi\)
−0.386688 + 0.922210i \(0.626381\pi\)
\(72\) 1.69798 + 2.47323i 0.200108 + 0.291473i
\(73\) 7.49303 + 2.00775i 0.876993 + 0.234990i 0.669109 0.743164i \(-0.266676\pi\)
0.207884 + 0.978154i \(0.433342\pi\)
\(74\) −1.50000 2.59808i −0.174371 0.302020i
\(75\) 2.65685 + 8.24264i 0.306787 + 0.951778i
\(76\) −4.00000 1.73205i −0.458831 0.198680i
\(77\) 12.3640 12.3640i 1.40900 1.40900i
\(78\) 4.87832 + 0.449490i 0.552360 + 0.0508947i
\(79\) −9.08052 + 5.24264i −1.02164 + 0.589843i −0.914578 0.404409i \(-0.867477\pi\)
−0.107060 + 0.994253i \(0.534144\pi\)
\(80\) −1.67303 + 1.48356i −0.187051 + 0.165867i
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 2.89778 0.776457i 0.320006 0.0857453i
\(83\) −3.00000 3.00000i −0.329293 0.329293i 0.523025 0.852318i \(-0.324804\pi\)
−0.852318 + 0.523025i \(0.824804\pi\)
\(84\) −5.12132 + 0.878680i −0.558782 + 0.0958718i
\(85\) 0.836355 13.9339i 0.0907155 1.51134i
\(86\) 3.67423 + 2.12132i 0.396203 + 0.228748i
\(87\) −12.4853 8.82843i −1.33856 0.946507i
\(88\) 4.12132 4.12132i 0.439334 0.439334i
\(89\) 3.08579 5.34474i 0.327093 0.566541i −0.654841 0.755767i \(-0.727264\pi\)
0.981934 + 0.189226i \(0.0605977\pi\)
\(90\) −1.61874 + 6.50997i −0.170630 + 0.686211i
\(91\) −4.24264 + 7.34847i −0.444750 + 0.770329i
\(92\) −2.89778 0.776457i −0.302114 0.0809513i
\(93\) −0.356397 + 3.86798i −0.0369567 + 0.401091i
\(94\) 10.4853i 1.08147i
\(95\) −3.03648 9.26174i −0.311536 0.950234i
\(96\) −1.70711 + 0.292893i −0.174231 + 0.0298933i
\(97\) 0.643238 2.40060i 0.0653109 0.243744i −0.925551 0.378623i \(-0.876398\pi\)
0.990862 + 0.134879i \(0.0430645\pi\)
\(98\) 0.517638 1.93185i 0.0522893 0.195146i
\(99\) 3.19507 17.1909i 0.321117 1.72775i
\(100\) −4.96410 0.598076i −0.496410 0.0598076i
\(101\) 4.60181 + 2.65685i 0.457897 + 0.264367i 0.711160 0.703031i \(-0.248170\pi\)
−0.253263 + 0.967398i \(0.581504\pi\)
\(102\) 6.24264 8.82843i 0.618114 0.874145i
\(103\) 2.12132 2.12132i 0.209020 0.209020i −0.594831 0.803851i \(-0.702781\pi\)
0.803851 + 0.594831i \(0.202781\pi\)
\(104\) −1.41421 + 2.44949i −0.138675 + 0.240192i
\(105\) −9.06787 7.26456i −0.884933 0.708948i
\(106\) 7.48528 0.727035
\(107\) 6.00000 6.00000i 0.580042 0.580042i −0.354873 0.934915i \(-0.615476\pi\)
0.934915 + 0.354873i \(0.115476\pi\)
\(108\) −3.72474 + 3.62302i −0.358414 + 0.348625i
\(109\) 5.40629 3.12132i 0.517828 0.298968i −0.218217 0.975900i \(-0.570024\pi\)
0.736046 + 0.676932i \(0.236691\pi\)
\(110\) 13.0093 + 0.780861i 1.24039 + 0.0744522i
\(111\) 3.99585 3.32162i 0.379270 0.315274i
\(112\) 0.776457 2.89778i 0.0733683 0.273814i
\(113\) −14.1421 14.1421i −1.33038 1.33038i −0.905028 0.425352i \(-0.860150\pi\)
−0.425352 0.905028i \(-0.639850\pi\)
\(114\) 1.78522 7.33573i 0.167201 0.687054i
\(115\) −3.00000 6.00000i −0.279751 0.559503i
\(116\) 7.64564 4.41421i 0.709880 0.409849i
\(117\) 0.661498 + 8.45946i 0.0611556 + 0.782077i
\(118\) −1.46410 5.46410i −0.134781 0.503011i
\(119\) 9.36396 + 16.2189i 0.858393 + 1.48678i
\(120\) −3.02262 2.42152i −0.275926 0.221053i
\(121\) −22.9706 −2.08823
\(122\) −4.41421 + 4.41421i −0.399644 + 0.399644i
\(123\) 2.17423 + 4.71940i 0.196044 + 0.425534i
\(124\) −1.94218 1.12132i −0.174413 0.100698i
\(125\) −6.36396 9.19239i −0.569210 0.822192i
\(126\) −3.00000 8.48528i −0.267261 0.755929i
\(127\) 8.36188 2.24056i 0.741997 0.198817i 0.132031 0.991246i \(-0.457850\pi\)
0.609965 + 0.792428i \(0.291183\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) −2.54516 + 6.89363i −0.224089 + 0.606950i
\(130\) −6.19615 + 1.26795i −0.543439 + 0.111207i
\(131\) 12.9904 7.50000i 1.13497 0.655278i 0.189794 0.981824i \(-0.439218\pi\)
0.945181 + 0.326546i \(0.105885\pi\)
\(132\) 8.24264 + 5.82843i 0.717430 + 0.507299i
\(133\) 10.2462 + 8.12493i 0.888462 + 0.704520i
\(134\) −5.65685 −0.488678
\(135\) −11.5873 0.856638i −0.997278 0.0737276i
\(136\) 3.12132 + 5.40629i 0.267651 + 0.463585i
\(137\) −0.909676 3.39496i −0.0777189 0.290051i 0.916117 0.400911i \(-0.131306\pi\)
−0.993836 + 0.110860i \(0.964640\pi\)
\(138\) 0.476756 5.17423i 0.0405842 0.440460i
\(139\) −12.1244 7.00000i −1.02837 0.593732i −0.111856 0.993724i \(-0.535679\pi\)
−0.916519 + 0.399992i \(0.869013\pi\)
\(140\) 6.00000 3.00000i 0.507093 0.253546i
\(141\) 17.8995 3.07107i 1.50741 0.258631i
\(142\) 12.9571 3.47185i 1.08734 0.291352i
\(143\) 15.9236 4.26670i 1.33159 0.356800i
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 18.7279 + 6.24264i 1.55527 + 0.518423i
\(146\) −6.71807 3.87868i −0.555991 0.321002i
\(147\) 3.44949 + 0.317837i 0.284509 + 0.0262148i
\(148\) 0.776457 + 2.89778i 0.0638244 + 0.238196i
\(149\) −5.65685 9.79796i −0.463428 0.802680i 0.535701 0.844407i \(-0.320047\pi\)
−0.999129 + 0.0417274i \(0.986714\pi\)
\(150\) −0.432972 8.64942i −0.0353520 0.706223i
\(151\) 14.7279 1.19854 0.599271 0.800546i \(-0.295457\pi\)
0.599271 + 0.800546i \(0.295457\pi\)
\(152\) 3.41542 + 2.70831i 0.277027 + 0.219673i
\(153\) 16.8995 + 8.07107i 1.36624 + 0.652507i
\(154\) −15.1427 + 8.74264i −1.22023 + 0.704502i
\(155\) −1.00535 4.91289i −0.0807515 0.394613i
\(156\) −4.59575 1.69677i −0.367955 0.135851i
\(157\) −1.59732 + 5.96128i −0.127480 + 0.475762i −0.999916 0.0129665i \(-0.995873\pi\)
0.872436 + 0.488729i \(0.162539\pi\)
\(158\) 10.1280 2.71379i 0.805741 0.215898i
\(159\) 2.19239 + 12.7782i 0.173868 + 1.01338i
\(160\) 2.00000 1.00000i 0.158114 0.0790569i
\(161\) 7.79423 + 4.50000i 0.614271 + 0.354650i
\(162\) −7.27583 5.29738i −0.571644 0.416201i
\(163\) −5.75736 + 5.75736i −0.450951 + 0.450951i −0.895670 0.444719i \(-0.853304\pi\)
0.444719 + 0.895670i \(0.353304\pi\)
\(164\) −3.00000 −0.234261
\(165\) 2.47734 + 22.4371i 0.192860 + 1.74672i
\(166\) 2.12132 + 3.67423i 0.164646 + 0.285176i
\(167\) −1.68613 6.29273i −0.130477 0.486946i 0.869499 0.493935i \(-0.164442\pi\)
−0.999976 + 0.00698883i \(0.997775\pi\)
\(168\) 5.17423 + 0.476756i 0.399201 + 0.0367825i
\(169\) 4.33013 2.50000i 0.333087 0.192308i
\(170\) −4.41421 + 13.2426i −0.338555 + 1.01566i
\(171\) 13.0458 + 0.898979i 0.997634 + 0.0687467i
\(172\) −3.00000 3.00000i −0.228748 0.228748i
\(173\) −3.61585 + 13.4945i −0.274908 + 1.02597i 0.680995 + 0.732288i \(0.261547\pi\)
−0.955903 + 0.293682i \(0.905119\pi\)
\(174\) 9.77489 + 11.7590i 0.741033 + 0.891450i
\(175\) 13.9205 + 5.58750i 1.05229 + 0.422376i
\(176\) −5.04757 + 2.91421i −0.380475 + 0.219667i
\(177\) 8.89898 4.09978i 0.668888 0.308158i
\(178\) −4.36396 + 4.36396i −0.327093 + 0.327093i
\(179\) −20.6569 −1.54397 −0.771983 0.635643i \(-0.780735\pi\)
−0.771983 + 0.635643i \(0.780735\pi\)
\(180\) 3.24849 5.86919i 0.242128 0.437463i
\(181\) 1.24264 2.15232i 0.0923648 0.159980i −0.816141 0.577853i \(-0.803891\pi\)
0.908506 + 0.417872i \(0.137224\pi\)
\(182\) 6.00000 6.00000i 0.444750 0.444750i
\(183\) −8.82843 6.24264i −0.652616 0.461469i
\(184\) 2.59808 + 1.50000i 0.191533 + 0.110581i
\(185\) −3.69615 + 5.59808i −0.271747 + 0.411579i
\(186\) 1.34536 3.64394i 0.0986467 0.267187i
\(187\) 9.41707 35.1450i 0.688645 2.57006i
\(188\) −2.71379 + 10.1280i −0.197924 + 0.738661i
\(189\) 13.6066 7.60660i 0.989735 0.553299i
\(190\) 0.535898 + 9.73205i 0.0388782 + 0.706037i
\(191\) 13.4142i 0.970618i −0.874343 0.485309i \(-0.838707\pi\)
0.874343 0.485309i \(-0.161293\pi\)
\(192\) 1.72474 + 0.158919i 0.124473 + 0.0114690i
\(193\) −11.5911 3.10583i −0.834346 0.223562i −0.183737 0.982975i \(-0.558820\pi\)
−0.650609 + 0.759413i \(0.725486\pi\)
\(194\) −1.24264 + 2.15232i −0.0892164 + 0.154527i
\(195\) −3.97934 10.2061i −0.284966 0.730875i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) −18.0208 + 18.0208i −1.28393 + 1.28393i −0.345518 + 0.938412i \(0.612297\pi\)
−0.938412 + 0.345518i \(0.887703\pi\)
\(198\) −7.53553 + 15.7782i −0.535527 + 1.12131i
\(199\) 4.98602 + 2.87868i 0.353450 + 0.204064i 0.666204 0.745770i \(-0.267918\pi\)
−0.312754 + 0.949834i \(0.601252\pi\)
\(200\) 4.64016 + 1.86250i 0.328109 + 0.131699i
\(201\) −1.65685 9.65685i −0.116865 0.681142i
\(202\) −3.75736 3.75736i −0.264367 0.264367i
\(203\) −25.5828 + 6.85490i −1.79556 + 0.481119i
\(204\) −8.31489 + 6.91189i −0.582159 + 0.483929i
\(205\) −4.45069 5.01910i −0.310850 0.350549i
\(206\) −2.59808 + 1.50000i −0.181017 + 0.104510i
\(207\) 8.97261 0.701625i 0.623639 0.0487663i
\(208\) 2.00000 2.00000i 0.138675 0.138675i
\(209\) −2.91421 25.2378i −0.201580 1.74574i
\(210\) 6.87868 + 9.36396i 0.474674 + 0.646175i
\(211\) 6.74264 + 11.6786i 0.464183 + 0.803988i 0.999164 0.0408759i \(-0.0130148\pi\)
−0.534982 + 0.844864i \(0.679682\pi\)
\(212\) −7.23023 1.93733i −0.496574 0.133057i
\(213\) 9.72188 + 21.1023i 0.666132 + 1.44591i
\(214\) −7.34847 + 4.24264i −0.502331 + 0.290021i
\(215\) 0.568406 9.46979i 0.0387650 0.645834i
\(216\) 4.53553 2.53553i 0.308604 0.172521i
\(217\) 4.75736 + 4.75736i 0.322951 + 0.322951i
\(218\) −6.02993 + 1.61571i −0.408398 + 0.109430i
\(219\) 4.65364 12.6045i 0.314464 0.851733i
\(220\) −12.3640 4.12132i −0.833578 0.277859i
\(221\) 17.6569i 1.18773i
\(222\) −4.71940 + 2.17423i −0.316745 + 0.145925i
\(223\) −0.497180 0.133219i −0.0332936 0.00892100i 0.242134 0.970243i \(-0.422153\pi\)
−0.275427 + 0.961322i \(0.588819\pi\)
\(224\) −1.50000 + 2.59808i −0.100223 + 0.173591i
\(225\) 14.6387 3.27249i 0.975912 0.218166i
\(226\) 10.0000 + 17.3205i 0.665190 + 1.15214i
\(227\) 7.75736 7.75736i 0.514874 0.514874i −0.401142 0.916016i \(-0.631387\pi\)
0.916016 + 0.401142i \(0.131387\pi\)
\(228\) −3.62302 + 6.62372i −0.239940 + 0.438667i
\(229\) 24.2426i 1.60200i −0.598665 0.800999i \(-0.704302\pi\)
0.598665 0.800999i \(-0.295698\pi\)
\(230\) 1.34486 + 6.57201i 0.0886777 + 0.433346i
\(231\) −19.3598 23.2895i −1.27378 1.53234i
\(232\) −8.52761 + 2.28497i −0.559865 + 0.150015i
\(233\) 1.67851 6.26430i 0.109963 0.410388i −0.888898 0.458106i \(-0.848528\pi\)
0.998861 + 0.0477177i \(0.0151948\pi\)
\(234\) 1.55051 8.34242i 0.101360 0.545361i
\(235\) −20.9706 + 10.4853i −1.36797 + 0.683984i
\(236\) 5.65685i 0.368230i
\(237\) 7.59915 + 16.4947i 0.493618 + 1.07145i
\(238\) −4.84714 18.0898i −0.314194 1.17259i
\(239\) −23.3137 −1.50804 −0.754019 0.656852i \(-0.771887\pi\)
−0.754019 + 0.656852i \(0.771887\pi\)
\(240\) 2.29289 + 3.12132i 0.148006 + 0.201480i
\(241\) −8.24264 + 14.2767i −0.530955 + 0.919641i 0.468392 + 0.883521i \(0.344833\pi\)
−0.999347 + 0.0361207i \(0.988500\pi\)
\(242\) 22.1879 + 5.94522i 1.42629 + 0.382173i
\(243\) 6.91215 13.9722i 0.443415 0.896317i
\(244\) 5.40629 3.12132i 0.346102 0.199822i
\(245\) −4.38134 + 0.896575i −0.279914 + 0.0572801i
\(246\) −0.878680 5.12132i −0.0560226 0.326523i
\(247\) 4.53590 + 11.4641i 0.288612 + 0.729443i
\(248\) 1.58579 + 1.58579i 0.100698 + 0.100698i
\(249\) −5.65099 + 4.69748i −0.358117 + 0.297691i
\(250\) 3.76795 + 10.5263i 0.238306 + 0.665740i
\(251\) 4.60181 + 2.65685i 0.290463 + 0.167699i 0.638151 0.769911i \(-0.279700\pi\)
−0.347687 + 0.937611i \(0.613033\pi\)
\(252\) 0.701625 + 8.97261i 0.0441982 + 0.565221i
\(253\) −4.52552 16.8895i −0.284517 1.06183i
\(254\) −8.65685 −0.543179
\(255\) −23.8995 3.65685i −1.49664 0.229001i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.0628000 + 0.234373i 0.00391736 + 0.0146198i 0.967857 0.251502i \(-0.0809244\pi\)
−0.963939 + 0.266122i \(0.914258\pi\)
\(258\) 4.24264 6.00000i 0.264135 0.373544i
\(259\) 9.00000i 0.559233i
\(260\) 6.31319 + 0.378937i 0.391528 + 0.0235007i
\(261\) −17.2109 + 20.1309i −1.06533 + 1.24607i
\(262\) −14.4889 + 3.88229i −0.895126 + 0.239848i
\(263\) −4.00789 + 14.9576i −0.247137 + 0.922327i 0.725161 + 0.688580i \(0.241766\pi\)
−0.972297 + 0.233747i \(0.924901\pi\)
\(264\) −6.45327 7.76318i −0.397171 0.477791i
\(265\) −7.48528 14.9706i −0.459817 0.919634i
\(266\) −7.79423 10.5000i −0.477895 0.643796i
\(267\) −8.72792 6.17157i −0.534140 0.377694i
\(268\) 5.46410 + 1.46410i 0.333773 + 0.0894342i
\(269\) 12.5355 + 21.7122i 0.764305 + 1.32382i 0.940613 + 0.339480i \(0.110251\pi\)
−0.176308 + 0.984335i \(0.556416\pi\)
\(270\) 10.9708 + 3.82647i 0.667661 + 0.232872i
\(271\) 1.00000 + 1.73205i 0.0607457 + 0.105215i 0.894799 0.446469i \(-0.147319\pi\)
−0.834053 + 0.551684i \(0.813985\pi\)
\(272\) −1.61571 6.02993i −0.0979671 0.365618i
\(273\) 12.0000 + 8.48528i 0.726273 + 0.513553i
\(274\) 3.51472i 0.212332i
\(275\) −11.4476 26.7996i −0.690318 1.61607i
\(276\) −1.79970 + 4.87453i −0.108329 + 0.293412i
\(277\) 3.51472 + 3.51472i 0.211179 + 0.211179i 0.804768 0.593589i \(-0.202290\pi\)
−0.593589 + 0.804768i \(0.702290\pi\)
\(278\) 9.89949 + 9.89949i 0.593732 + 0.593732i
\(279\) 6.61465 + 1.22939i 0.396008 + 0.0736016i
\(280\) −6.57201 + 1.34486i −0.392753 + 0.0803709i
\(281\) 10.2437 + 5.91421i 0.611089 + 0.352812i 0.773392 0.633929i \(-0.218559\pi\)
−0.162303 + 0.986741i \(0.551892\pi\)
\(282\) −18.0844 1.66631i −1.07691 0.0992271i
\(283\) −0.331453 0.0888127i −0.0197029 0.00527936i 0.248954 0.968515i \(-0.419913\pi\)
−0.268657 + 0.963236i \(0.586580\pi\)
\(284\) −13.4142 −0.795987
\(285\) −16.4567 + 3.76529i −0.974810 + 0.223036i
\(286\) −16.4853 −0.974795
\(287\) 8.69333 + 2.32937i 0.513151 + 0.137498i
\(288\) 0.233875 + 2.99087i 0.0137812 + 0.176239i
\(289\) 19.0271 + 10.9853i 1.11924 + 0.646193i
\(290\) −16.4741 10.8771i −0.967391 0.638724i
\(291\) −4.03820 1.49092i −0.236723 0.0873994i
\(292\) 5.48528 + 5.48528i 0.321002 + 0.321002i
\(293\) 5.63604 + 5.63604i 0.329261 + 0.329261i 0.852305 0.523044i \(-0.175204\pi\)
−0.523044 + 0.852305i \(0.675204\pi\)
\(294\) −3.24969 1.19980i −0.189526 0.0699738i
\(295\) −9.46410 + 8.39230i −0.551021 + 0.488619i
\(296\) 3.00000i 0.174371i
\(297\) −29.1421 8.24264i −1.69100 0.478287i
\(298\) 2.92820 + 10.9282i 0.169626 + 0.633054i
\(299\) 4.24264 + 7.34847i 0.245358 + 0.424973i
\(300\) −1.82042 + 8.46676i −0.105102 + 0.488829i
\(301\) 6.36396 + 11.0227i 0.366813 + 0.635338i
\(302\) −14.2261 3.81187i −0.818619 0.219348i
\(303\) 5.31371 7.51472i 0.305265 0.431709i
\(304\) −2.59808 3.50000i −0.149010 0.200739i
\(305\) 13.2426 + 4.41421i 0.758271 + 0.252757i
\(306\) −14.2347 12.1700i −0.813744 0.695711i
\(307\) −2.10734 + 7.86470i −0.120272 + 0.448862i −0.999627 0.0273048i \(-0.991308\pi\)
0.879355 + 0.476167i \(0.157974\pi\)
\(308\) 16.8895 4.52552i 0.962368 0.257866i
\(309\) −3.32162 3.99585i −0.188960 0.227316i
\(310\) −0.300457 + 5.00569i −0.0170648 + 0.284304i
\(311\) 8.48528i 0.481156i 0.970630 + 0.240578i \(0.0773370\pi\)
−0.970630 + 0.240578i \(0.922663\pi\)
\(312\) 4.00000 + 2.82843i 0.226455 + 0.160128i
\(313\) 2.47337 + 9.23072i 0.139803 + 0.521751i 0.999932 + 0.0116748i \(0.00371629\pi\)
−0.860129 + 0.510077i \(0.829617\pi\)
\(314\) 3.08579 5.34474i 0.174141 0.301621i
\(315\) −13.9706 + 14.4853i −0.787152 + 0.816153i
\(316\) −10.4853 −0.589843
\(317\) 5.81200 + 21.6907i 0.326434 + 1.21827i 0.912862 + 0.408268i \(0.133867\pi\)
−0.586428 + 0.810002i \(0.699466\pi\)
\(318\) 1.18955 12.9102i 0.0667067 0.723968i
\(319\) 44.5621 + 25.7279i 2.49500 + 1.44049i
\(320\) −2.19067 + 0.448288i −0.122462 + 0.0250600i
\(321\) −9.39496 11.3020i −0.524375 0.630815i
\(322\) −6.36396 6.36396i −0.354650 0.354650i
\(323\) 26.9182 + 3.98128i 1.49777 + 0.221525i
\(324\) 5.65685 + 7.00000i 0.314270 + 0.388889i
\(325\) 8.73205 + 11.1244i 0.484367 + 0.617068i
\(326\) 7.05130 4.07107i 0.390535 0.225476i
\(327\) −4.52432 9.82050i −0.250196 0.543075i
\(328\) 2.89778 + 0.776457i 0.160003 + 0.0428727i
\(329\) 15.7279 27.2416i 0.867108 1.50188i
\(330\) 3.41421 22.3137i 0.187946 1.22833i
\(331\) −29.4853 −1.62066 −0.810329 0.585975i \(-0.800712\pi\)
−0.810329 + 0.585975i \(0.800712\pi\)
\(332\) −1.09808 4.09808i −0.0602648 0.224911i
\(333\) −5.09393 7.41970i −0.279146 0.406597i
\(334\) 6.51472i 0.356470i
\(335\) 5.65685 + 11.3137i 0.309067 + 0.618134i
\(336\) −4.87453 1.79970i −0.265928 0.0981818i
\(337\) 3.74907 13.9917i 0.204225 0.762177i −0.785460 0.618913i \(-0.787573\pi\)
0.989684 0.143264i \(-0.0457599\pi\)
\(338\) −4.82963 + 1.29410i −0.262697 + 0.0703895i
\(339\) −26.6390 + 22.1441i −1.44683 + 1.20270i
\(340\) 7.69125 11.6489i 0.417117 0.631752i
\(341\) 13.0711i 0.707838i
\(342\) −12.3686 4.24484i −0.668815 0.229535i
\(343\) −10.6066 + 10.6066i −0.572703 + 0.572703i
\(344\) 2.12132 + 3.67423i 0.114374 + 0.198101i
\(345\) −10.8252 + 4.22072i −0.582811 + 0.227236i
\(346\) 6.98528 12.0989i 0.375531 0.650439i
\(347\) −22.1879 5.94522i −1.19111 0.319156i −0.391784 0.920057i \(-0.628142\pi\)
−0.799323 + 0.600901i \(0.794808\pi\)
\(348\) −6.39836 13.8883i −0.342988 0.744490i
\(349\) 13.7574i 0.736415i −0.929744 0.368207i \(-0.879972\pi\)
0.929744 0.368207i \(-0.120028\pi\)
\(350\) −12.0000 9.00000i −0.641427 0.481070i
\(351\) 14.6955 + 0.203449i 0.784389 + 0.0108593i
\(352\) 5.62983 1.50851i 0.300071 0.0804037i
\(353\) −20.4853 20.4853i −1.09032 1.09032i −0.995494 0.0948278i \(-0.969770\pi\)
−0.0948278 0.995494i \(-0.530230\pi\)
\(354\) −9.65685 + 1.65685i −0.513256 + 0.0880608i
\(355\) −19.9008 22.4424i −1.05623 1.19112i
\(356\) 5.34474 3.08579i 0.283271 0.163546i
\(357\) 29.4615 13.5730i 1.55927 0.718358i
\(358\) 19.9530 + 5.34639i 1.05455 + 0.282565i
\(359\) 16.6066 + 28.7635i 0.876463 + 1.51808i 0.855196 + 0.518304i \(0.173437\pi\)
0.0212668 + 0.999774i \(0.493230\pi\)
\(360\) −4.65685 + 4.82843i −0.245438 + 0.254480i
\(361\) 18.5000 4.33013i 0.973684 0.227901i
\(362\) −1.75736 + 1.75736i −0.0923648 + 0.0923648i
\(363\) −3.65045 + 39.6184i −0.191599 + 2.07942i
\(364\) −7.34847 + 4.24264i −0.385164 + 0.222375i
\(365\) −1.03929 + 17.3148i −0.0543989 + 0.906299i
\(366\) 6.91189 + 8.31489i 0.361290 + 0.434626i
\(367\) 5.79555 1.55291i 0.302526 0.0810615i −0.104363 0.994539i \(-0.533280\pi\)
0.406889 + 0.913478i \(0.366614\pi\)
\(368\) −2.12132 2.12132i −0.110581 0.110581i
\(369\) 8.48528 3.00000i 0.441726 0.156174i
\(370\) 5.01910 4.45069i 0.260930 0.231380i
\(371\) 19.4473 + 11.2279i 1.00966 + 0.582925i
\(372\) −2.24264 + 3.17157i −0.116276 + 0.164438i
\(373\) −0.363961 + 0.363961i −0.0188452 + 0.0188452i −0.716467 0.697621i \(-0.754242\pi\)
0.697621 + 0.716467i \(0.254242\pi\)
\(374\) −18.1924 + 31.5101i −0.940706 + 1.62935i
\(375\) −16.8659 + 9.51537i −0.870950 + 0.491371i
\(376\) 5.24264 9.08052i 0.270369 0.468292i
\(377\) −24.1197 6.46286i −1.24223 0.332854i
\(378\) −15.1117 + 3.82577i −0.777262 + 0.196776i
\(379\) 5.51472i 0.283272i 0.989919 + 0.141636i \(0.0452363\pi\)
−0.989919 + 0.141636i \(0.954764\pi\)
\(380\) 2.00120 9.53914i 0.102659 0.489348i
\(381\) −2.53553 14.7782i −0.129899 0.757109i
\(382\) −3.47185 + 12.9571i −0.177636 + 0.662945i
\(383\) −3.49787 + 13.0542i −0.178733 + 0.667039i 0.817153 + 0.576421i \(0.195551\pi\)
−0.995886 + 0.0906185i \(0.971116\pi\)
\(384\) −1.62484 0.599900i −0.0829175 0.0306135i
\(385\) 32.6280 + 21.5428i 1.66288 + 1.09792i
\(386\) 10.3923 + 6.00000i 0.528954 + 0.305392i
\(387\) 11.4853 + 5.48528i 0.583830 + 0.278833i
\(388\) 1.75736 1.75736i 0.0892164 0.0892164i
\(389\) −9.53553 + 16.5160i −0.483471 + 0.837396i −0.999820 0.0189823i \(-0.993957\pi\)
0.516349 + 0.856378i \(0.327291\pi\)
\(390\) 1.20220 + 10.8883i 0.0608760 + 0.551350i
\(391\) 18.7279 0.947112
\(392\) 1.41421 1.41421i 0.0714286 0.0714286i
\(393\) −10.8712 23.5970i −0.548378 1.19031i
\(394\) 22.0709 12.7426i 1.11192 0.641965i
\(395\) −15.5556 17.5422i −0.782686 0.882645i
\(396\) 11.3625 13.2902i 0.570985 0.667858i
\(397\) −6.72168 + 25.0856i −0.337351 + 1.25901i 0.563946 + 0.825811i \(0.309282\pi\)
−0.901298 + 0.433201i \(0.857384\pi\)
\(398\) −4.07107 4.07107i −0.204064 0.204064i
\(399\) 15.6417 16.3810i 0.783067 0.820074i
\(400\) −4.00000 3.00000i −0.200000 0.150000i
\(401\) 9.20361 5.31371i 0.459607 0.265354i −0.252272 0.967656i \(-0.581178\pi\)
0.711879 + 0.702302i \(0.247845\pi\)
\(402\) −0.898979 + 9.75663i −0.0448370 + 0.486616i
\(403\) 1.64173 + 6.12701i 0.0817802 + 0.305208i
\(404\) 2.65685 + 4.60181i 0.132183 + 0.228948i
\(405\) −3.31892 + 19.8490i −0.164919 + 0.986307i
\(406\) 26.4853 1.31444
\(407\) −12.3640 + 12.3640i −0.612859 + 0.612859i
\(408\) 9.82050 4.52432i 0.486187 0.223987i
\(409\) 22.9114 + 13.2279i 1.13290 + 0.654079i 0.944662 0.328045i \(-0.106390\pi\)
0.188235 + 0.982124i \(0.439723\pi\)
\(410\) 3.00000 + 6.00000i 0.148159 + 0.296319i
\(411\) −6.00000 + 1.02944i −0.295958 + 0.0507784i
\(412\) 2.89778 0.776457i 0.142763 0.0382533i
\(413\) 4.39230 16.3923i 0.216131 0.806613i
\(414\) −8.84847 1.64456i −0.434879 0.0808259i
\(415\) 5.22715 7.91688i 0.256591 0.388624i
\(416\) −2.44949 + 1.41421i −0.120096 + 0.0693375i
\(417\) −14.0000 + 19.7990i −0.685583 + 0.969561i
\(418\) −3.71712 + 25.1321i −0.181810 + 1.22925i
\(419\) 24.1716 1.18086 0.590429 0.807089i \(-0.298958\pi\)
0.590429 + 0.807089i \(0.298958\pi\)
\(420\) −4.22072 10.8252i −0.205950 0.528217i
\(421\) −6.48528 11.2328i −0.316073 0.547455i 0.663592 0.748095i \(-0.269031\pi\)
−0.979665 + 0.200640i \(0.935698\pi\)
\(422\) −3.49025 13.0258i −0.169903 0.634085i
\(423\) −2.45225 31.3601i −0.119232 1.52478i
\(424\) 6.48244 + 3.74264i 0.314815 + 0.181759i
\(425\) 30.8995 4.41421i 1.49885 0.214121i
\(426\) −3.92893 22.8995i −0.190357 1.10948i
\(427\) −18.0898 + 4.84714i −0.875426 + 0.234570i
\(428\) 8.19615 2.19615i 0.396176 0.106155i
\(429\) −4.82843 28.1421i −0.233119 1.35872i
\(430\) −3.00000 + 9.00000i −0.144673 + 0.434019i
\(431\) −9.79796 5.65685i −0.471951 0.272481i 0.245105 0.969497i \(-0.421178\pi\)
−0.717056 + 0.697015i \(0.754511\pi\)
\(432\) −5.03723 + 1.27526i −0.242354 + 0.0613557i
\(433\) −6.85490 25.5828i −0.329425 1.22943i −0.909788 0.415074i \(-0.863756\pi\)
0.580363 0.814358i \(-0.302911\pi\)
\(434\) −3.36396 5.82655i −0.161475 0.279683i
\(435\) 13.7432 31.3088i 0.658935 1.50114i
\(436\) 6.24264 0.298968
\(437\) 12.1595 4.81105i 0.581669 0.230144i
\(438\) −7.75736 + 10.9706i −0.370661 + 0.524194i
\(439\) −18.5813 + 10.7279i −0.886837 + 0.512016i −0.872907 0.487887i \(-0.837768\pi\)
−0.0139307 + 0.999903i \(0.504434\pi\)
\(440\) 10.8760 + 7.18092i 0.518493 + 0.342337i
\(441\) 1.09638 5.89898i 0.0522084 0.280904i
\(442\) 4.56993 17.0552i 0.217369 0.811234i
\(443\) −24.8797 + 6.66650i −1.18207 + 0.316735i −0.795747 0.605629i \(-0.792922\pi\)
−0.386323 + 0.922364i \(0.626255\pi\)
\(444\) 5.12132 0.878680i 0.243047 0.0417003i
\(445\) 13.0919 + 4.36396i 0.620615 + 0.206872i
\(446\) 0.445759 + 0.257359i 0.0211073 + 0.0121863i
\(447\) −17.7980 + 8.19955i −0.841815 + 0.387826i
\(448\) 2.12132 2.12132i 0.100223 0.100223i
\(449\) 12.1716 0.574412 0.287206 0.957869i \(-0.407274\pi\)
0.287206 + 0.957869i \(0.407274\pi\)
\(450\) −14.9869 0.627789i −0.706487 0.0295942i
\(451\) −8.74264 15.1427i −0.411675 0.713042i
\(452\) −5.17638 19.3185i −0.243476 0.908667i
\(453\) 2.34054 25.4019i 0.109968 1.19349i
\(454\) −9.50079 + 5.48528i −0.445894 + 0.257437i
\(455\) −18.0000 6.00000i −0.843853 0.281284i
\(456\) 5.21391 5.46032i 0.244164 0.255703i
\(457\) 8.97056 + 8.97056i 0.419625 + 0.419625i 0.885075 0.465449i \(-0.154107\pi\)
−0.465449 + 0.885075i \(0.654107\pi\)
\(458\) −6.27446 + 23.4166i −0.293186 + 1.09419i
\(459\) 16.6062 27.8647i 0.775110 1.30061i
\(460\) 0.401924 6.69615i 0.0187398 0.312210i
\(461\) −32.1405 + 18.5563i −1.49693 + 0.864255i −0.999994 0.00352933i \(-0.998877\pi\)
−0.496940 + 0.867785i \(0.665543\pi\)
\(462\) 12.6724 + 27.5067i 0.589572 + 1.27973i
\(463\) 17.3345 17.3345i 0.805604 0.805604i −0.178361 0.983965i \(-0.557080\pi\)
0.983965 + 0.178361i \(0.0570796\pi\)
\(464\) 8.82843 0.409849
\(465\) −8.63325 + 0.953220i −0.400357 + 0.0442045i
\(466\) −3.24264 + 5.61642i −0.150212 + 0.260176i
\(467\) −10.2426 + 10.2426i −0.473973 + 0.473973i −0.903198 0.429225i \(-0.858787\pi\)
0.429225 + 0.903198i \(0.358787\pi\)
\(468\) −3.65685 + 7.65685i −0.169038 + 0.353938i
\(469\) −14.6969 8.48528i −0.678642 0.391814i
\(470\) 22.9698 4.70042i 1.05952 0.216814i
\(471\) 10.0278 + 3.70233i 0.462059 + 0.170594i
\(472\) 1.46410 5.46410i 0.0673907 0.251506i
\(473\) 6.40006 23.8853i 0.294275 1.09825i
\(474\) −3.07107 17.8995i −0.141059 0.822151i
\(475\) 18.9282 10.8038i 0.868486 0.495715i
\(476\) 18.7279i 0.858393i
\(477\) 22.3875 1.75062i 1.02505 0.0801554i
\(478\) 22.5193 + 6.03403i 1.03001 + 0.275990i
\(479\) −3.19239 + 5.52938i −0.145864 + 0.252644i −0.929695 0.368330i \(-0.879930\pi\)
0.783831 + 0.620974i \(0.213263\pi\)
\(480\) −1.40691 3.60841i −0.0642163 0.164701i
\(481\) 4.24264 7.34847i 0.193448 0.335061i
\(482\) 11.6569 11.6569i 0.530955 0.530955i
\(483\) 9.00000 12.7279i 0.409514 0.579141i
\(484\) −19.8931 11.4853i −0.904231 0.522058i
\(485\) 5.54727 + 0.332965i 0.251889 + 0.0151191i
\(486\) −10.2929 + 11.7071i −0.466895 + 0.531045i
\(487\) 3.39340 + 3.39340i 0.153770 + 0.153770i 0.779799 0.626030i \(-0.215321\pi\)
−0.626030 + 0.779799i \(0.715321\pi\)
\(488\) −6.02993 + 1.61571i −0.272962 + 0.0731399i
\(489\) 9.01502 + 10.8449i 0.407673 + 0.490425i
\(490\) 4.46410 + 0.267949i 0.201668 + 0.0121047i
\(491\) 30.4340 17.5711i 1.37347 0.792971i 0.382104 0.924119i \(-0.375200\pi\)
0.991363 + 0.131148i \(0.0418664\pi\)
\(492\) −0.476756 + 5.17423i −0.0214938 + 0.233273i
\(493\) −38.9706 + 38.9706i −1.75515 + 1.75515i
\(494\) −1.41421 12.2474i −0.0636285 0.551039i
\(495\) 39.0919 0.707107i 1.75705 0.0317821i
\(496\) −1.12132 1.94218i −0.0503488 0.0872066i
\(497\) 38.8714 + 10.4156i 1.74362 + 0.467202i
\(498\) 6.67423 3.07483i 0.299080 0.137787i
\(499\) 3.48960 2.01472i 0.156216 0.0901912i −0.419854 0.907591i \(-0.637919\pi\)
0.576070 + 0.817400i \(0.304586\pi\)
\(500\) −0.915158 11.1428i −0.0409271 0.498322i
\(501\) −11.1213 + 1.90812i −0.496864 + 0.0852484i
\(502\) −3.75736 3.75736i −0.167699 0.167699i
\(503\) −15.4264 + 4.13349i −0.687828 + 0.184303i −0.585772 0.810476i \(-0.699209\pi\)
−0.102056 + 0.994779i \(0.532542\pi\)
\(504\) 1.64456 8.84847i 0.0732547 0.394142i
\(505\) −3.75736 + 11.2721i −0.167200 + 0.501601i
\(506\) 17.4853i 0.777316i
\(507\) −3.62372 7.86566i −0.160935 0.349326i
\(508\) 8.36188 + 2.24056i 0.370998 + 0.0994087i
\(509\) 6.36396 11.0227i 0.282078 0.488573i −0.689819 0.723982i \(-0.742310\pi\)
0.971896 + 0.235409i \(0.0756431\pi\)
\(510\) 22.1387 + 9.71789i 0.980317 + 0.430316i
\(511\) −11.6360 20.1542i −0.514748 0.891570i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 3.62372 22.3577i 0.159991 0.987118i
\(514\) 0.242641i 0.0107024i
\(515\) 5.59808 + 3.69615i 0.246681 + 0.162872i
\(516\) −5.65099 + 4.69748i −0.248771 + 0.206795i
\(517\) −59.0303 + 15.8171i −2.59615 + 0.695637i
\(518\) −2.32937 + 8.69333i −0.102347 + 0.381963i
\(519\) 22.7000 + 8.38095i 0.996419 + 0.367883i
\(520\) −6.00000 2.00000i −0.263117 0.0877058i
\(521\) 12.6863i 0.555797i −0.960611 0.277898i \(-0.910362\pi\)
0.960611 0.277898i \(-0.0896378\pi\)
\(522\) 21.8347 14.9905i 0.955681 0.656115i
\(523\) 3.19464 + 11.9226i 0.139692 + 0.521337i 0.999934 + 0.0114522i \(0.00364543\pi\)
−0.860243 + 0.509885i \(0.829688\pi\)
\(524\) 15.0000 0.655278
\(525\) 11.8492 23.1213i 0.517143 1.00910i
\(526\) 7.74264 13.4106i 0.337595 0.584732i
\(527\) 13.5230 + 3.62347i 0.589069 + 0.157841i
\(528\) 4.22412 + 9.16889i 0.183831 + 0.399025i
\(529\) −12.1244 + 7.00000i −0.527146 + 0.304348i
\(530\) 3.35556 + 16.3978i 0.145756 + 0.712274i
\(531\) −5.65685 16.0000i −0.245487 0.694341i
\(532\) 4.81105 + 12.1595i 0.208585 + 0.527182i
\(533\) 6.00000 + 6.00000i 0.259889 + 0.259889i
\(534\) 6.83320 + 8.22023i 0.295702 + 0.355724i
\(535\) 15.8338 + 10.4543i 0.684553 + 0.451979i
\(536\) −4.89898 2.82843i −0.211604 0.122169i
\(537\) −3.28276 + 35.6278i −0.141661 + 1.53745i
\(538\) −6.48887 24.2168i −0.279755 1.04406i
\(539\) −11.6569 −0.502096
\(540\) −9.60660 6.53553i −0.413402 0.281245i
\(541\) −13.3640 + 23.1471i −0.574562 + 0.995170i 0.421528 + 0.906816i \(0.361494\pi\)
−0.996089 + 0.0883542i \(0.971839\pi\)
\(542\) −0.517638 1.93185i −0.0222345 0.0829801i
\(543\) −3.51472 2.48528i −0.150831 0.106654i
\(544\) 6.24264i 0.267651i
\(545\) 9.26136 + 10.4441i 0.396713 + 0.447378i
\(546\) −9.39496 11.3020i −0.402067 0.483680i
\(547\) −30.3840 + 8.14137i −1.29913 + 0.348100i −0.841120 0.540849i \(-0.818103\pi\)
−0.458007 + 0.888949i \(0.651436\pi\)
\(548\) 0.909676 3.39496i 0.0388594 0.145025i
\(549\) −12.1700 + 14.2347i −0.519401 + 0.607523i
\(550\) 4.12132 + 28.8492i 0.175734 + 1.23014i
\(551\) −15.2913 + 35.3137i −0.651431 + 1.50441i
\(552\) 3.00000 4.24264i 0.127688 0.180579i
\(553\) 30.3840 + 8.14137i 1.29206 + 0.346206i
\(554\) −2.48528 4.30463i −0.105589 0.182886i
\(555\) 9.06787 + 7.26456i 0.384909 + 0.308363i
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) −5.16876 19.2901i −0.219007 0.817347i −0.984717 0.174161i \(-0.944279\pi\)
0.765710 0.643186i \(-0.222388\pi\)
\(558\) −6.07107 2.89949i −0.257009 0.122745i
\(559\) 12.0000i 0.507546i
\(560\) 6.69615 + 0.401924i 0.282964 + 0.0169844i
\(561\) −59.1196 21.8272i −2.49603 0.921547i
\(562\) −8.36396 8.36396i −0.352812 0.352812i
\(563\) −32.8284 32.8284i −1.38355 1.38355i −0.838218 0.545335i \(-0.816402\pi\)
−0.545335 0.838218i \(-0.683598\pi\)
\(564\) 17.0370 + 6.29012i 0.717385 + 0.264862i
\(565\) 24.6410 37.3205i 1.03666 1.57009i
\(566\) 0.297173 + 0.171573i 0.0124911 + 0.00721175i
\(567\) −10.9571 24.6767i −0.460155 1.03633i
\(568\) 12.9571 + 3.47185i 0.543669 + 0.145676i
\(569\) −28.7990 −1.20732 −0.603658 0.797243i \(-0.706291\pi\)
−0.603658 + 0.797243i \(0.706291\pi\)
\(570\) 16.8705 + 0.622316i 0.706626 + 0.0260660i
\(571\) 6.48528 0.271401 0.135700 0.990750i \(-0.456672\pi\)
0.135700 + 0.990750i \(0.456672\pi\)
\(572\) 15.9236 + 4.26670i 0.665797 + 0.178400i
\(573\) −23.1361 2.13177i −0.966524 0.0890559i
\(574\) −7.79423 4.50000i −0.325325 0.187826i
\(575\) 11.7992 9.26174i 0.492059 0.386241i
\(576\) 0.548188 2.94949i 0.0228412 0.122895i
\(577\) 14.4853 + 14.4853i 0.603030 + 0.603030i 0.941115 0.338085i \(-0.109779\pi\)
−0.338085 + 0.941115i \(0.609779\pi\)
\(578\) −15.5355 15.5355i −0.646193 0.646193i
\(579\) −7.19881 + 19.4981i −0.299172 + 0.810315i
\(580\) 13.0975 + 14.7702i 0.543846 + 0.613301i
\(581\) 12.7279i 0.528043i
\(582\) 3.51472 + 2.48528i 0.145690 + 0.103018i
\(583\) −11.2916 42.1408i −0.467651 1.74530i
\(584\) −3.87868 6.71807i −0.160501 0.277996i
\(585\) −18.2353 + 5.24140i −0.753939 + 0.216705i
\(586\) −3.98528 6.90271i −0.164630 0.285148i
\(587\) 6.78991 + 1.81935i 0.280250 + 0.0750927i 0.396206 0.918162i \(-0.370327\pi\)
−0.115956 + 0.993254i \(0.536993\pi\)
\(588\) 2.82843 + 2.00000i 0.116642 + 0.0824786i
\(589\) 9.71092 1.12132i 0.400131 0.0462032i
\(590\) 11.3137 5.65685i 0.465778 0.232889i
\(591\) 28.2175 + 33.9452i 1.16071 + 1.39632i
\(592\) −0.776457 + 2.89778i −0.0319122 + 0.119098i
\(593\) 20.7816 5.56842i 0.853399 0.228668i 0.194503 0.980902i \(-0.437691\pi\)
0.658896 + 0.752234i \(0.271024\pi\)
\(594\) 26.0158 + 15.5043i 1.06744 + 0.636150i
\(595\) −31.3324 + 27.7841i −1.28450 + 1.13904i
\(596\) 11.3137i 0.463428i
\(597\) 5.75736 8.14214i 0.235633 0.333235i
\(598\) −2.19615 8.19615i −0.0898074 0.335166i
\(599\) 17.8492 30.9158i 0.729300 1.26319i −0.227879 0.973689i \(-0.573179\pi\)
0.957179 0.289496i \(-0.0934876\pi\)
\(600\) 3.94975 7.70711i 0.161248 0.314641i
\(601\) 23.0000 0.938190 0.469095 0.883148i \(-0.344580\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(602\) −3.29423 12.2942i −0.134263 0.501075i
\(603\) −16.9189 + 1.32300i −0.688991 + 0.0538766i
\(604\) 12.7548 + 7.36396i 0.518984 + 0.299635i
\(605\) −10.2974 50.3209i −0.418650 2.04584i
\(606\) −7.07760 + 5.88337i −0.287508 + 0.238996i
\(607\) 8.36396 + 8.36396i 0.339483 + 0.339483i 0.856173 0.516690i \(-0.172836\pi\)
−0.516690 + 0.856173i \(0.672836\pi\)
\(608\) 1.60368 + 4.05317i 0.0650379 + 0.164378i
\(609\) 7.75736 + 45.2132i 0.314344 + 1.83213i
\(610\) −11.6489 7.69125i −0.471651 0.311410i
\(611\) 25.6836 14.8284i 1.03905 0.599894i
\(612\) 10.5999 + 15.4395i 0.428474 + 0.624105i
\(613\) −27.8177 7.45373i −1.12355 0.301053i −0.351228 0.936290i \(-0.614236\pi\)
−0.772318 + 0.635237i \(0.780903\pi\)
\(614\) 4.07107 7.05130i 0.164295 0.284567i
\(615\) −9.36396 + 6.87868i −0.377591 + 0.277375i
\(616\) −17.4853 −0.704502
\(617\) −11.4356 42.6782i −0.460380 1.71816i −0.671770 0.740760i \(-0.734466\pi\)
0.211390 0.977402i \(-0.432201\pi\)
\(618\) 2.17423 + 4.71940i 0.0874605 + 0.189842i
\(619\) 42.9411i 1.72595i −0.505247 0.862975i \(-0.668599\pi\)
0.505247 0.862975i \(-0.331401\pi\)
\(620\) 1.58579 4.75736i 0.0636867 0.191060i
\(621\) 0.215791 15.5870i 0.00865938 0.625483i
\(622\) 2.19615 8.19615i 0.0880577 0.328636i
\(623\) −17.8838 + 4.79196i −0.716501 + 0.191986i
\(624\) −3.13165 3.76733i −0.125366 0.150814i
\(625\) 17.2846 18.0622i 0.691384 0.722487i
\(626\) 9.55635i 0.381949i
\(627\) −43.9919 + 1.01551i −1.75687 + 0.0405557i
\(628\) −4.36396 + 4.36396i −0.174141 + 0.174141i
\(629\) −9.36396 16.2189i −0.373366 0.646688i
\(630\) 17.2436 10.3759i 0.687001 0.413384i
\(631\) −4.12132 + 7.13834i −0.164067 + 0.284173i −0.936324 0.351138i \(-0.885795\pi\)
0.772256 + 0.635311i \(0.219128\pi\)
\(632\) 10.1280 + 2.71379i 0.402870 + 0.107949i
\(633\) 21.2141 9.77339i 0.843186 0.388457i
\(634\) 22.4558i 0.891836i
\(635\) 8.65685 + 17.3137i 0.343537 + 0.687074i
\(636\) −4.49042 + 12.1624i −0.178057 + 0.482271i
\(637\) 5.46410 1.46410i 0.216496 0.0580098i
\(638\) −36.3848 36.3848i −1.44049 1.44049i
\(639\) 37.9411 13.4142i 1.50093 0.530658i
\(640\) 2.23205 + 0.133975i 0.0882296 + 0.00529581i
\(641\) −5.49333 + 3.17157i −0.216973 + 0.125270i −0.604548 0.796569i \(-0.706646\pi\)
0.387575 + 0.921838i \(0.373313\pi\)
\(642\) 6.14966 + 13.3485i 0.242708 + 0.526822i
\(643\) −18.7527 5.02477i −0.739534 0.198158i −0.130663 0.991427i \(-0.541711\pi\)
−0.608871 + 0.793269i \(0.708377\pi\)
\(644\) 4.50000 + 7.79423i 0.177325 + 0.307136i
\(645\) −16.2426 2.48528i −0.639553 0.0978579i
\(646\) −24.9706 10.8126i −0.982454 0.425415i
\(647\) −11.2929 + 11.2929i −0.443969 + 0.443969i −0.893344 0.449374i \(-0.851647\pi\)
0.449374 + 0.893344i \(0.351647\pi\)
\(648\) −3.65237 8.22558i −0.143479 0.323131i
\(649\) −28.5533 + 16.4853i −1.12082 + 0.647104i
\(650\) −5.55532 13.0053i −0.217898 0.510111i
\(651\) 8.96126 7.44920i 0.351220 0.291957i
\(652\) −7.86470 + 2.10734i −0.308005 + 0.0825298i
\(653\) 14.8492 + 14.8492i 0.581096 + 0.581096i 0.935204 0.354109i \(-0.115216\pi\)
−0.354109 + 0.935204i \(0.615216\pi\)
\(654\) 1.82843 + 10.6569i 0.0714972 + 0.416716i
\(655\) 22.2535 + 25.0955i 0.869515 + 0.980562i
\(656\) −2.59808 1.50000i −0.101438 0.0585652i
\(657\) −21.0000 10.0294i −0.819288 0.391286i
\(658\) −22.2426 + 22.2426i −0.867108 + 0.867108i
\(659\) −22.7132 + 39.3404i −0.884781 + 1.53249i −0.0388161 + 0.999246i \(0.512359\pi\)
−0.845965 + 0.533239i \(0.820975\pi\)
\(660\) −9.07309 + 20.6697i −0.353170 + 0.804568i
\(661\) −7.12132 + 12.3345i −0.276987 + 0.479756i −0.970635 0.240559i \(-0.922669\pi\)
0.693647 + 0.720315i \(0.256003\pi\)
\(662\) 28.4806 + 7.63135i 1.10693 + 0.296601i
\(663\) 30.4536 + 2.80600i 1.18272 + 0.108976i
\(664\) 4.24264i 0.164646i
\(665\) −13.2058 + 26.0885i −0.512098 + 1.01167i
\(666\) 3.00000 + 8.48528i 0.116248 + 0.328798i
\(667\) −6.85490 + 25.5828i −0.265423 + 0.990571i
\(668\) 1.68613 6.29273i 0.0652385 0.243473i
\(669\) −0.308780 + 0.836338i −0.0119381 + 0.0323347i
\(670\) −2.53590 12.3923i −0.0979703 0.478757i
\(671\) 31.5101 + 18.1924i 1.21644 + 0.702309i
\(672\) 4.24264 + 3.00000i 0.163663 + 0.115728i
\(673\) 4.97056 4.97056i 0.191601 0.191601i −0.604787 0.796388i \(-0.706742\pi\)
0.796388 + 0.604787i \(0.206742\pi\)
\(674\) −7.24264 + 12.5446i −0.278976 + 0.483201i
\(675\) −3.31785 25.7680i −0.127704 0.991812i
\(676\) 5.00000 0.192308
\(677\) 13.3934 13.3934i 0.514750 0.514750i −0.401228 0.915978i \(-0.631417\pi\)
0.915978 + 0.401228i \(0.131417\pi\)
\(678\) 31.4626 14.4949i 1.20832 0.556673i
\(679\) −6.45695 + 3.72792i −0.247795 + 0.143065i
\(680\) −10.4441 + 9.26136i −0.400515 + 0.355157i
\(681\) −12.1467 14.6123i −0.465462 0.559943i
\(682\) −3.38304 + 12.6257i −0.129543 + 0.483462i
\(683\) 18.8995 + 18.8995i 0.723169 + 0.723169i 0.969249 0.246080i \(-0.0791427\pi\)
−0.246080 + 0.969249i \(0.579143\pi\)
\(684\) 10.8485 + 7.30142i 0.414802 + 0.279177i
\(685\) 7.02944 3.51472i 0.268581 0.134290i
\(686\) 12.9904 7.50000i 0.495975 0.286351i
\(687\) −41.8124 3.85261i −1.59524 0.146986i
\(688\) −1.09808 4.09808i −0.0418638 0.156238i
\(689\) 10.5858 + 18.3351i 0.403286 + 0.698512i
\(690\) 11.5488 1.27513i 0.439654 0.0485434i
\(691\) 5.97056 0.227131 0.113565 0.993531i \(-0.463773\pi\)
0.113565 + 0.993531i \(0.463773\pi\)
\(692\) −9.87868 + 9.87868i −0.375531 + 0.375531i
\(693\) −43.2452 + 29.6896i −1.64275 + 1.12781i
\(694\) 19.8931 + 11.4853i 0.755131 + 0.435975i
\(695\) 9.89949 29.6985i 0.375509 1.12653i
\(696\) 2.58579 + 15.0711i 0.0980140 + 0.571267i
\(697\) 18.0898 4.84714i 0.685199 0.183599i
\(698\) −3.56067 + 13.2886i −0.134773 + 0.502980i
\(699\) −10.5376 3.89052i −0.398568 0.147153i
\(700\) 9.26174 + 11.7992i 0.350061 + 0.445966i
\(701\) −7.97887 + 4.60660i −0.301358 + 0.173989i −0.643053 0.765822i \(-0.722332\pi\)
0.341695 + 0.939811i \(0.388999\pi\)
\(702\) −14.1421 4.00000i −0.533761 0.150970i
\(703\) −10.2462 8.12493i −0.386445 0.306437i
\(704\) −5.82843 −0.219667
\(705\) 14.7518 + 37.8352i 0.555586 + 1.42496i
\(706\) 14.4853 + 25.0892i 0.545161 + 0.944246i
\(707\) −4.12587 15.3979i −0.155169 0.579099i
\(708\) 9.75663 + 0.898979i 0.366677 + 0.0337857i
\(709\) 13.5953 + 7.84924i 0.510582 + 0.294784i 0.733073 0.680150i \(-0.238085\pi\)
−0.222491 + 0.974935i \(0.571419\pi\)
\(710\) 13.4142 + 26.8284i 0.503426 + 1.00685i
\(711\) 29.6569 10.4853i 1.11222 0.393229i
\(712\) −5.96128 + 1.59732i −0.223408 + 0.0598621i
\(713\) 6.49867 1.74131i 0.243377 0.0652127i
\(714\) −31.9706 + 5.48528i −1.19647 + 0.205281i
\(715\) 16.4853 + 32.9706i 0.616515 + 1.23303i
\(716\) −17.8894 10.3284i −0.668557 0.385991i
\(717\) −3.70498 + 40.2102i −0.138365 + 1.50168i
\(718\) −8.59621 32.0815i −0.320808 1.19727i
\(719\) 2.29289 + 3.97141i 0.0855105 + 0.148109i 0.905609 0.424114i \(-0.139415\pi\)
−0.820098 + 0.572223i \(0.806081\pi\)
\(720\) 5.74786 3.45862i 0.214210 0.128895i
\(721\) −9.00000 −0.335178
\(722\) −18.9903 0.605571i −0.706748 0.0225370i
\(723\) 23.3137 + 16.4853i 0.867046 + 0.613094i
\(724\) 2.15232 1.24264i 0.0799902 0.0461824i
\(725\) −5.28007 + 43.8252i −0.196097 + 1.62763i
\(726\) 13.7801 37.3236i 0.511426 1.38521i
\(727\) 5.39079 20.1187i 0.199933 0.746162i −0.791001 0.611815i \(-0.790440\pi\)
0.990934 0.134347i \(-0.0428936\pi\)
\(728\) 8.19615 2.19615i 0.303770 0.0813948i
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 5.48528 16.4558i 0.203019 0.609058i
\(731\) 22.9369 + 13.2426i 0.848353 + 0.489797i
\(732\) −4.52432 9.82050i −0.167224 0.362976i
\(733\) −3.87868 + 3.87868i −0.143262 + 0.143262i −0.775100 0.631838i \(-0.782301\pi\)
0.631838 + 0.775100i \(0.282301\pi\)
\(734\) −6.00000 −0.221464
\(735\) 0.850087 + 7.69918i 0.0313559 + 0.283988i
\(736\) 1.50000 + 2.59808i 0.0552907 + 0.0957664i
\(737\) 8.53341 + 31.8471i 0.314332 + 1.17310i
\(738\) −8.97261 + 0.701625i −0.330286 + 0.0258272i
\(739\) −0.0254934 + 0.0147186i −0.000937790 + 0.000541433i −0.500469 0.865755i \(-0.666839\pi\)
0.499531 + 0.866296i \(0.333506\pi\)
\(740\) −6.00000 + 3.00000i −0.220564 + 0.110282i
\(741\) 20.4935 6.00141i 0.752847 0.220467i
\(742\) −15.8787 15.8787i −0.582925 0.582925i
\(743\) −2.06293 + 7.69897i −0.0756817 + 0.282448i −0.993387 0.114814i \(-0.963373\pi\)
0.917705 + 0.397262i \(0.130040\pi\)
\(744\) 2.98709 2.48307i 0.109512 0.0910336i
\(745\) 18.9282 16.7846i 0.693476 0.614941i
\(746\) 0.445759 0.257359i 0.0163204 0.00942259i
\(747\) 7.20390 + 10.4930i 0.263577 + 0.383920i
\(748\) 25.7279 25.7279i 0.940706 0.940706i
\(749\) −25.4558 −0.930136
\(750\) 18.7539 4.82593i 0.684797 0.176218i
\(751\) 0.393398 0.681386i 0.0143553 0.0248641i −0.858759 0.512381i \(-0.828764\pi\)
0.873114 + 0.487516i \(0.162097\pi\)
\(752\) −7.41421 + 7.41421i −0.270369 + 0.270369i
\(753\) 5.31371 7.51472i 0.193642 0.273852i
\(754\) 21.6251 + 12.4853i 0.787541 + 0.454687i
\(755\) 6.60235 + 32.2640i 0.240284 + 1.17421i
\(756\) 15.5870 + 0.215791i 0.566892 + 0.00784823i
\(757\) −7.18729 + 26.8233i −0.261226 + 0.974910i 0.703293 + 0.710900i \(0.251712\pi\)
−0.964520 + 0.264011i \(0.914955\pi\)
\(758\) 1.42731 5.32681i 0.0518424 0.193478i
\(759\) −29.8492 + 5.12132i −1.08346 + 0.185892i
\(760\) −4.40192 + 8.69615i −0.159675 + 0.315443i
\(761\) 23.4853i 0.851341i 0.904878 + 0.425670i \(0.139962\pi\)
−0.904878 + 0.425670i \(0.860038\pi\)
\(762\) −1.37574 + 14.9309i −0.0498376 + 0.540888i
\(763\) −18.0898 4.84714i −0.654894 0.175478i
\(764\) 6.70711 11.6170i 0.242655 0.420290i
\(765\) −10.1052 + 40.6394i −0.365355 + 1.46932i
\(766\) 6.75736 11.7041i 0.244153 0.422886i
\(767\) 11.3137 11.3137i 0.408514 0.408514i
\(768\) 1.41421 + 1.00000i 0.0510310 + 0.0360844i
\(769\) −4.35562 2.51472i −0.157068 0.0906831i 0.419406 0.907799i \(-0.362238\pi\)
−0.576474 + 0.817116i \(0.695572\pi\)
\(770\) −25.9405 29.2534i −0.934832 1.05422i
\(771\) 0.414214 0.0710678i 0.0149175 0.00255944i
\(772\) −8.48528 8.48528i −0.305392 0.305392i
\(773\) 41.0092 10.9884i 1.47500 0.395225i 0.570356 0.821397i \(-0.306805\pi\)
0.904642 + 0.426173i \(0.140138\pi\)
\(774\) −9.67423 8.27098i −0.347733 0.297294i
\(775\) 10.3118 4.40477i 0.370412 0.158224i
\(776\) −2.15232 + 1.24264i −0.0772637 + 0.0446082i
\(777\) −15.5227 1.43027i −0.556874 0.0513106i
\(778\) 13.4853 13.4853i 0.483471 0.483471i
\(779\) 10.5000 7.79423i 0.376202 0.279257i
\(780\) 1.65685 10.8284i 0.0593249 0.387720i
\(781\) −39.0919 67.7091i −1.39882 2.42282i
\(782\) −18.0898 4.84714i −0.646889 0.173333i
\(783\) 31.9856 + 32.8836i 1.14307 + 1.17517i
\(784\) −1.73205 + 1.00000i −0.0618590 + 0.0357143i
\(785\) −13.7753 0.826834i −0.491660 0.0295110i
\(786\) 4.39340 + 25.6066i 0.156707 + 0.913357i
\(787\) −22.7279 22.7279i −0.810163 0.810163i 0.174495 0.984658i \(-0.444171\pi\)
−0.984658 + 0.174495i \(0.944171\pi\)
\(788\) −24.6169 + 6.59608i −0.876940 + 0.234975i
\(789\) 25.1612 + 9.28963i 0.895761 + 0.330719i
\(790\) 10.4853 + 20.9706i 0.373050 + 0.746099i
\(791\) 60.0000i 2.13335i
\(792\) −14.4151 + 9.89653i −0.512217 + 0.351658i
\(793\) −17.0552 4.56993i −0.605648 0.162283i
\(794\) 12.9853 22.4912i 0.460830 0.798182i
\(795\) −27.0100 + 10.5311i −0.957944 + 0.373500i
\(796\) 2.87868 + 4.98602i 0.102032 + 0.176725i
\(797\) 13.7782 13.7782i 0.488048 0.488048i −0.419642 0.907690i \(-0.637844\pi\)
0.907690 + 0.419642i \(0.137844\pi\)
\(798\) −19.3485 + 11.7744i −0.684928 + 0.416810i
\(799\) 65.4558i 2.31566i
\(800\) 3.08725 + 3.93305i 0.109151 + 0.139054i
\(801\) −12.0314 + 14.0727i −0.425109 + 0.497233i
\(802\) −10.2653 + 2.75058i −0.362480 + 0.0971263i
\(803\) −11.7020 + 43.6726i −0.412956 + 1.54117i
\(804\) 3.39355 9.19151i 0.119681 0.324160i
\(805\) −6.36396 + 19.0919i −0.224300 + 0.672900i
\(806\) 6.34315i 0.223428i
\(807\) 39.4401 18.1701i 1.38836 0.639619i
\(808\) −1.37529 5.13265i −0.0483825 0.180566i
\(809\) −47.3137 −1.66346 −0.831731 0.555179i \(-0.812650\pi\)
−0.831731 + 0.555179i \(0.812650\pi\)
\(810\) 8.34315 18.3137i 0.293148 0.643478i
\(811\) 15.2279 26.3755i 0.534725 0.926170i −0.464452 0.885598i \(-0.653749\pi\)
0.999177 0.0405720i \(-0.0129180\pi\)
\(812\) −25.5828 6.85490i −0.897781 0.240560i
\(813\) 3.14626 1.44949i 0.110344 0.0508358i
\(814\) 15.1427 8.74264i 0.530751 0.306429i
\(815\) −15.1934 10.0315i −0.532203 0.351389i
\(816\) −10.6569 + 1.82843i −0.373065 + 0.0640078i
\(817\) 18.2942 + 2.70577i 0.640034 + 0.0946630i
\(818\) −18.7071 18.7071i −0.654079 0.654079i
\(819\) 16.5420 19.3485i 0.578023 0.676090i
\(820\) −1.34486 6.57201i −0.0469647 0.229505i
\(821\) −25.3864 14.6569i −0.885992 0.511528i −0.0133626 0.999911i \(-0.504254\pi\)
−0.872629 + 0.488383i \(0.837587\pi\)
\(822\) 6.06199 + 0.558554i 0.211436 + 0.0194818i
\(823\) 13.1110 + 48.9308i 0.457019 + 1.70562i 0.682083 + 0.731275i \(0.261074\pi\)
−0.225063 + 0.974344i \(0.572259\pi\)
\(824\) −3.00000 −0.104510
\(825\) −48.0416 + 15.4853i −1.67259 + 0.539128i
\(826\) −8.48528 + 14.6969i −0.295241 + 0.511372i
\(827\) −6.98050 26.0516i −0.242736 0.905902i −0.974508 0.224353i \(-0.927973\pi\)
0.731772 0.681549i \(-0.238693\pi\)
\(828\) 8.12132 + 3.87868i 0.282235 + 0.134793i
\(829\) 4.97056i 0.172635i −0.996268 0.0863174i \(-0.972490\pi\)
0.996268 0.0863174i \(-0.0275099\pi\)
\(830\) −7.09808 + 6.29423i −0.246378 + 0.218476i
\(831\) 6.62055 5.50344i 0.229664 0.190912i
\(832\) 2.73205 0.732051i 0.0947168 0.0253793i
\(833\) 3.23143 12.0599i 0.111962 0.417849i
\(834\) 18.6473 15.5009i 0.645704 0.536752i
\(835\) 13.0294 6.51472i 0.450902 0.225451i
\(836\) 10.0951 23.3137i 0.349147 0.806321i
\(837\) 3.17157 11.2132i 0.109626 0.387585i
\(838\) −23.3479 6.25606i −0.806541 0.216112i
\(839\) −9.87868 17.1104i −0.341050 0.590716i 0.643578 0.765380i \(-0.277449\pi\)
−0.984628 + 0.174665i \(0.944116\pi\)
\(840\) 1.27513 + 11.5488i 0.0439962 + 0.398470i
\(841\) −24.4706 42.3843i −0.843813 1.46153i
\(842\) 3.35703 + 12.5286i 0.115691 + 0.431764i
\(843\) 11.8284 16.7279i 0.407393 0.576140i
\(844\) 13.4853i 0.464183i
\(845\) 7.41782 + 8.36516i 0.255181 + 0.287770i
\(846\) −5.74791 + 30.9262i −0.197617 + 1.06327i
\(847\) 48.7279 + 48.7279i 1.67431 + 1.67431i
\(848\) −5.29289 5.29289i −0.181759 0.181759i
\(849\) −0.205853 + 0.557558i −0.00706487 + 0.0191354i
\(850\) −30.9891 3.73357i −1.06292 0.128061i
\(851\) −7.79423 4.50000i −0.267183 0.154258i
\(852\) −2.13177 + 23.1361i −0.0730332 + 0.792630i
\(853\) 25.9143 + 6.94371i 0.887288 + 0.237748i 0.673549 0.739143i \(-0.264769\pi\)
0.213739 + 0.976891i \(0.431436\pi\)
\(854\) 18.7279 0.640856
\(855\) 3.87889 + 28.9820i 0.132655 + 0.991162i
\(856\) −8.48528 −0.290021
\(857\) 8.19615 + 2.19615i 0.279975 + 0.0750191i 0.396074 0.918219i \(-0.370372\pi\)
−0.116099 + 0.993238i \(0.537039\pi\)
\(858\) −2.61982 + 28.4329i −0.0894391 + 0.970683i
\(859\) −31.5717 18.2279i −1.07721 0.621929i −0.147069 0.989126i \(-0.546984\pi\)
−0.930143 + 0.367198i \(0.880317\pi\)
\(860\) 5.22715 7.91688i 0.178244 0.269963i
\(861\) 5.39910 14.6236i 0.184001 0.498371i
\(862\) 8.00000 + 8.00000i 0.272481 + 0.272481i
\(863\) −27.2340 27.2340i −0.927057 0.927057i 0.0704580 0.997515i \(-0.477554\pi\)
−0.997515 + 0.0704580i \(0.977554\pi\)
\(864\) 5.19565 + 0.0719302i 0.176760 + 0.00244711i
\(865\) −31.1830 1.87170i −1.06025 0.0636397i
\(866\) 26.4853i 0.900006i
\(867\) 21.9706 31.0711i 0.746159 1.05523i
\(868\) 1.74131 + 6.49867i 0.0591041 + 0.220579i
\(869\) −30.5563 52.9251i −1.03655 1.79536i
\(870\) −21.3782 + 26.6850i −0.724789 + 0.904706i
\(871\) −8.00000 13.8564i −0.271070 0.469506i
\(872\) −6.02993 1.61571i −0.204199 0.0547150i
\(873\) −3.21320 + 6.72792i −0.108750 + 0.227706i
\(874\) −12.9904 + 1.50000i −0.439406 + 0.0507383i
\(875\) −6.00000 + 33.0000i −0.202837 + 1.11560i
\(876\) 10.3324 8.58900i 0.349100 0.290195i
\(877\) 5.81200 21.6907i 0.196257 0.732442i −0.795681 0.605717i \(-0.792887\pi\)
0.991938 0.126726i \(-0.0404468\pi\)
\(878\) 20.7248 5.55318i 0.699427 0.187411i
\(879\) 10.6164 8.82506i 0.358082 0.297662i
\(880\) −8.64684 9.75115i −0.291485 0.328711i
\(881\) 7.28427i 0.245413i 0.992443 + 0.122707i \(0.0391574\pi\)
−0.992443 + 0.122707i \(0.960843\pi\)
\(882\) −2.58579 + 5.41421i −0.0870680 + 0.182306i
\(883\) −5.30198 19.7873i −0.178426 0.665894i −0.995943 0.0899897i \(-0.971317\pi\)
0.817517 0.575905i \(-0.195350\pi\)
\(884\) −8.82843 + 15.2913i −0.296932 + 0.514302i
\(885\) 12.9706 + 17.6569i 0.436001 + 0.593529i
\(886\) 25.7574 0.865335
\(887\) 8.14137 + 30.3840i 0.273361 + 1.02020i 0.956932 + 0.290312i \(0.0937590\pi\)
−0.683572 + 0.729883i \(0.739574\pi\)
\(888\) −5.17423 0.476756i −0.173636 0.0159989i
\(889\) −22.4912 12.9853i −0.754330 0.435512i
\(890\) −11.5163 7.60369i −0.386028 0.254876i
\(891\) −18.8477 + 48.9528i −0.631421 + 1.63998i
\(892\) −0.363961 0.363961i −0.0121863 0.0121863i
\(893\) −16.8151 42.4986i −0.562695 1.42216i
\(894\) 19.3137 3.31371i 0.645947 0.110827i
\(895\) −9.26021 45.2524i −0.309535 1.51262i
\(896\) −2.59808 + 1.50000i −0.0867956 + 0.0501115i
\(897\) 13.3485 6.14966i 0.445692 0.205331i
\(898\) −11.7568 3.15023i −0.392331 0.105125i
\(899\) −9.89949 + 17.1464i −0.330167 + 0.571865i
\(900\) 14.3137 + 4.48528i 0.477124 + 0.149509i
\(901\) 46.7279 1.55673
\(902\) 4.52552 + 16.8895i 0.150683 + 0.562358i
\(903\) 20.0227 9.22450i 0.666314 0.306972i
\(904\) 20.0000i 0.665190i
\(905\) 5.27208 + 1.75736i 0.175250 + 0.0584166i
\(906\) −8.83529 + 23.9306i −0.293533 + 0.795040i
\(907\) −10.4156 + 38.8714i −0.345843 + 1.29070i 0.545781 + 0.837928i \(0.316233\pi\)
−0.891624 + 0.452776i \(0.850434\pi\)
\(908\) 10.5967 2.83939i 0.351665 0.0942285i
\(909\) −12.1165 10.3590i −0.401880 0.343587i
\(910\) 15.8338 + 10.4543i 0.524884 + 0.346557i
\(911\) 6.68629i 0.221527i −0.993847 0.110763i \(-0.964670\pi\)
0.993847 0.110763i \(-0.0353296\pi\)
\(912\) −6.44949 + 3.92480i −0.213564 + 0.129963i
\(913\) 17.4853 17.4853i 0.578678 0.578678i
\(914\) −6.34315 10.9867i −0.209813 0.363406i
\(915\) 9.71789 22.1387i 0.321264 0.731882i
\(916\) 12.1213 20.9947i 0.400500 0.693686i
\(917\) −43.4667 11.6469i −1.43540 0.384613i
\(918\) −23.2522 + 22.6172i −0.767438 + 0.746479i
\(919\) 48.7279i 1.60739i 0.595044 + 0.803693i \(0.297135\pi\)
−0.595044 + 0.803693i \(0.702865\pi\)
\(920\) −2.12132 + 6.36396i −0.0699379 + 0.209814i
\(921\) 13.2297 + 4.88447i 0.435934 + 0.160949i
\(922\) 35.8481 9.60547i 1.18059 0.316339i
\(923\) 26.8284 + 26.8284i 0.883068 + 0.883068i
\(924\) −5.12132 29.8492i −0.168479 0.981968i
\(925\) −13.9205 5.58750i −0.457703 0.183716i
\(926\) −21.2304 + 12.2574i −0.697673 + 0.402802i
\(927\) −7.41970 + 5.09393i −0.243695 + 0.167307i
\(928\) −8.52761 2.28497i −0.279932 0.0750077i
\(929\) 15.2990 + 26.4986i 0.501944 + 0.869392i 0.999997 + 0.00224570i \(0.000714830\pi\)
−0.498054 + 0.867146i \(0.665952\pi\)
\(930\) 8.58579 + 1.31371i 0.281539 + 0.0430782i
\(931\) −1.00000 8.66025i −0.0327737 0.283828i
\(932\) 4.58579 4.58579i 0.150212 0.150212i
\(933\) 14.6349 + 1.34847i 0.479127 + 0.0441469i
\(934\) 12.5446 7.24264i 0.410473 0.236986i
\(935\) 81.2127 + 4.87464i 2.65594 + 0.159418i
\(936\) 5.51399 6.44949i 0.180230 0.210808i
\(937\) −40.9406 + 10.9700i −1.33747 + 0.358374i −0.855495 0.517811i \(-0.826747\pi\)
−0.481975 + 0.876185i \(0.660080\pi\)
\(938\) 12.0000 + 12.0000i 0.391814 + 0.391814i
\(939\) 16.3137 2.79899i 0.532378 0.0913416i
\(940\) −23.4037 1.40476i −0.763344 0.0458183i
\(941\) 11.9503 + 6.89949i 0.389568 + 0.224917i 0.681973 0.731377i \(-0.261122\pi\)
−0.292405 + 0.956295i \(0.594456\pi\)
\(942\) −8.72792 6.17157i −0.284371 0.201081i
\(943\) 6.36396 6.36396i 0.207239 0.207239i
\(944\) −2.82843 + 4.89898i −0.0920575 + 0.159448i
\(945\) 22.7632 + 26.3976i 0.740488 + 0.858715i
\(946\) −12.3640 + 21.4150i −0.401987 + 0.696262i
\(947\) −12.3511 3.30947i −0.401357 0.107543i 0.0524933 0.998621i \(-0.483283\pi\)
−0.453850 + 0.891078i \(0.649950\pi\)
\(948\) −1.66631 + 18.0844i −0.0541191 + 0.587355i
\(949\) 21.9411i 0.712239i
\(950\) −21.0795 + 5.53674i −0.683909 + 0.179635i
\(951\) 38.3345 6.57716i 1.24308 0.213279i
\(952\) 4.84714 18.0898i 0.157097 0.586293i
\(953\) 7.49813 27.9834i 0.242888 0.906472i −0.731545 0.681794i \(-0.761200\pi\)
0.974433 0.224678i \(-0.0721331\pi\)
\(954\) −22.0778 4.10334i −0.714794 0.132851i
\(955\) 29.3861 6.01343i 0.950913 0.194590i
\(956\) −20.1903 11.6569i −0.653000 0.377010i
\(957\) 51.4558 72.7696i 1.66333 2.35231i
\(958\) 4.51472 4.51472i 0.145864 0.145864i
\(959\) −5.27208 + 9.13151i −0.170244 + 0.294872i
\(960\) 0.425044 + 3.84959i 0.0137182 + 0.124245i
\(961\) −25.9706 −0.837760
\(962\) −6.00000 + 6.00000i −0.193448 + 0.193448i
\(963\) −20.9861 + 14.4078i −0.676267 + 0.464285i
\(964\) −14.2767 + 8.24264i −0.459821 + 0.265478i
\(965\) 1.60770 26.7846i 0.0517535 0.862227i
\(966\) −11.9876 + 9.96486i −0.385693 + 0.320614i
\(967\) −1.92971 + 7.20179i −0.0620554 + 0.231594i −0.989987 0.141155i \(-0.954918\pi\)
0.927932 + 0.372749i \(0.121585\pi\)
\(968\) 16.2426 + 16.2426i 0.522058 + 0.522058i
\(969\) 11.1445 45.7943i 0.358013 1.47113i
\(970\) −5.27208 1.75736i −0.169276 0.0564254i
\(971\) −27.2416 + 15.7279i −0.874223 + 0.504733i −0.868749 0.495252i \(-0.835076\pi\)
−0.00547389 + 0.999985i \(0.501742\pi\)
\(972\) 12.9722 8.64420i 0.416083 0.277263i
\(973\) 10.8704 + 40.5689i 0.348489 + 1.30058i
\(974\) −2.39949 4.15605i −0.0768848 0.133168i
\(975\) 20.5744 13.2927i 0.658907 0.425707i
\(976\) 6.24264 0.199822
\(977\) −16.2426 + 16.2426i −0.519648 + 0.519648i −0.917465 0.397817i \(-0.869768\pi\)
0.397817 + 0.917465i \(0.369768\pi\)
\(978\) −5.90097 12.8087i −0.188692 0.409576i
\(979\) 31.1514 + 17.9853i 0.995604 + 0.574812i
\(980\) −4.24264 1.41421i −0.135526 0.0451754i
\(981\) −17.6569 + 6.24264i −0.563740 + 0.199312i
\(982\) −33.9447 + 9.09545i −1.08322 + 0.290248i
\(983\) −8.91783 + 33.2818i −0.284435 + 1.06152i 0.664817 + 0.747006i \(0.268510\pi\)
−0.949252 + 0.314518i \(0.898157\pi\)
\(984\) 1.79970 4.87453i 0.0573724 0.155394i
\(985\) −47.5562 31.3992i −1.51527 1.00046i
\(986\) 47.7290 27.5563i 1.52000 0.877573i
\(987\) −44.4853 31.4558i −1.41598 1.00125i
\(988\) −1.80385 + 12.1962i −0.0573880 + 0.388011i
\(989\) 12.7279 0.404724
\(990\) −37.9429 9.43471i −1.20590 0.299855i
\(991\) −3.00000 5.19615i −0.0952981 0.165061i 0.814435 0.580255i \(-0.197047\pi\)
−0.909733 + 0.415194i \(0.863714\pi\)
\(992\) 0.580438 + 2.16622i 0.0184289 + 0.0687777i
\(993\) −4.68576 + 50.8546i −0.148698 + 1.61382i
\(994\) −34.8511 20.1213i −1.10541 0.638210i
\(995\) −4.07107 + 12.2132i −0.129062 + 0.387185i
\(996\) −7.24264 + 1.24264i −0.229492 + 0.0393746i
\(997\) −37.0082 + 9.91632i −1.17206 + 0.314053i −0.791773 0.610815i \(-0.790842\pi\)
−0.380288 + 0.924868i \(0.624175\pi\)
\(998\) −3.89214 + 1.04290i −0.123203 + 0.0330123i
\(999\) −13.6066 + 7.60660i −0.430494 + 0.240662i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 570.2.v.a.197.1 yes 8
3.2 odd 2 570.2.v.b.197.2 yes 8
5.3 odd 4 570.2.v.b.83.1 yes 8
15.8 even 4 inner 570.2.v.a.83.2 8
19.11 even 3 inner 570.2.v.a.467.2 yes 8
57.11 odd 6 570.2.v.b.467.1 yes 8
95.68 odd 12 570.2.v.b.353.2 yes 8
285.68 even 12 inner 570.2.v.a.353.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.v.a.83.2 8 15.8 even 4 inner
570.2.v.a.197.1 yes 8 1.1 even 1 trivial
570.2.v.a.353.1 yes 8 285.68 even 12 inner
570.2.v.a.467.2 yes 8 19.11 even 3 inner
570.2.v.b.83.1 yes 8 5.3 odd 4
570.2.v.b.197.2 yes 8 3.2 odd 2
570.2.v.b.353.2 yes 8 95.68 odd 12
570.2.v.b.467.1 yes 8 57.11 odd 6