Properties

Label 429.2.n.c.157.3
Level $429$
Weight $2$
Character 429.157
Analytic conductor $3.426$
Analytic rank $0$
Dimension $28$
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] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 157.3
Character \(\chi\) \(=\) 429.157
Dual form 429.2.n.c.235.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35790 + 0.986569i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.252528 - 0.777201i) q^{4} +(0.627776 + 0.456106i) q^{5} +(1.35790 + 0.986569i) q^{6} +(0.0948896 - 0.292040i) q^{7} +(-0.613484 - 1.88811i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.35790 + 0.986569i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.252528 - 0.777201i) q^{4} +(0.627776 + 0.456106i) q^{5} +(1.35790 + 0.986569i) q^{6} +(0.0948896 - 0.292040i) q^{7} +(-0.613484 - 1.88811i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.30243 q^{10} +(-1.11510 - 3.12355i) q^{11} -0.817197 q^{12} +(-0.809017 + 0.587785i) q^{13} +(0.159267 + 0.490175i) q^{14} +(0.239789 - 0.737995i) q^{15} +(4.01805 + 2.91928i) q^{16} +(-2.88671 - 2.09732i) q^{17} +(0.518670 - 1.59630i) q^{18} +(0.616165 + 1.89636i) q^{19} +(0.513017 - 0.372729i) q^{20} -0.307069 q^{21} +(4.59578 + 3.14133i) q^{22} -4.18140 q^{23} +(-1.60612 + 1.16692i) q^{24} +(-1.35901 - 4.18262i) q^{25} +(0.518670 - 1.59630i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.203012 - 0.147497i) q^{28} +(2.46290 - 7.58001i) q^{29} +(0.402474 + 1.23869i) q^{30} +(2.78484 - 2.02330i) q^{31} -4.36561 q^{32} +(-2.62609 + 2.02575i) q^{33} +5.98900 q^{34} +(0.192771 - 0.140056i) q^{35} +(0.252528 + 0.777201i) q^{36} +(3.20487 - 9.86359i) q^{37} +(-2.70758 - 1.96717i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.476048 - 1.46512i) q^{40} +(-3.95358 - 12.1679i) q^{41} +(0.416968 - 0.302945i) q^{42} -0.426420 q^{43} +(-2.70922 + 0.0778729i) q^{44} -0.775974 q^{45} +(5.67790 - 4.12524i) q^{46} +(2.23136 + 6.86741i) q^{47} +(1.53476 - 4.72350i) q^{48} +(5.58684 + 4.05907i) q^{49} +(5.97184 + 4.33880i) q^{50} +(-1.10263 + 3.39353i) q^{51} +(0.252528 + 0.777201i) q^{52} +(-4.35227 + 3.16211i) q^{53} -1.67845 q^{54} +(0.724637 - 2.46949i) q^{55} -0.609617 q^{56} +(1.61314 - 1.17201i) q^{57} +(4.13385 + 12.7227i) q^{58} +(1.35726 - 4.17722i) q^{59} +(-0.513017 - 0.372729i) q^{60} +(-3.23644 - 2.35141i) q^{61} +(-1.78539 + 5.49486i) q^{62} +(0.0948896 + 0.292040i) q^{63} +(-2.10805 + 1.53159i) q^{64} -0.775974 q^{65} +(1.56741 - 5.34157i) q^{66} +0.00770561 q^{67} +(-2.35901 + 1.71392i) q^{68} +(1.29212 + 3.97675i) q^{69} +(-0.123587 + 0.380363i) q^{70} +(9.42803 + 6.84986i) q^{71} +(1.60612 + 1.16692i) q^{72} +(2.33300 - 7.18023i) q^{73} +(5.37922 + 16.5556i) q^{74} +(-3.55795 + 2.58500i) q^{75} +1.62945 q^{76} +(-1.01801 + 0.0292614i) q^{77} -1.67845 q^{78} +(-9.13869 + 6.63965i) q^{79} +(1.19093 + 3.66531i) q^{80} +(0.309017 - 0.951057i) q^{81} +(17.3730 + 12.6222i) q^{82} +(-13.9770 - 10.1549i) q^{83} +(-0.0775435 + 0.238654i) q^{84} +(-0.855609 - 2.63329i) q^{85} +(0.579033 - 0.420692i) q^{86} -7.97010 q^{87} +(-5.21351 + 4.02168i) q^{88} +5.89819 q^{89} +(1.05369 - 0.765552i) q^{90} +(0.0948896 + 0.292040i) q^{91} +(-1.05592 + 3.24979i) q^{92} +(-2.78484 - 2.02330i) q^{93} +(-9.80512 - 7.12384i) q^{94} +(-0.478128 + 1.47153i) q^{95} +(1.34905 + 4.15195i) q^{96} +(-6.91981 + 5.02754i) q^{97} -11.5909 q^{98} +(2.73811 + 1.87156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35790 + 0.986569i −0.960177 + 0.697609i −0.953192 0.302366i \(-0.902223\pi\)
−0.00698512 + 0.999976i \(0.502223\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i
\(4\) 0.252528 0.777201i 0.126264 0.388600i
\(5\) 0.627776 + 0.456106i 0.280750 + 0.203977i 0.719244 0.694757i \(-0.244488\pi\)
−0.438494 + 0.898734i \(0.644488\pi\)
\(6\) 1.35790 + 0.986569i 0.554358 + 0.402765i
\(7\) 0.0948896 0.292040i 0.0358649 0.110381i −0.931521 0.363687i \(-0.881518\pi\)
0.967386 + 0.253306i \(0.0815179\pi\)
\(8\) −0.613484 1.88811i −0.216899 0.667548i
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) −1.30243 −0.411866
\(11\) −1.11510 3.12355i −0.336215 0.941785i
\(12\) −0.817197 −0.235905
\(13\) −0.809017 + 0.587785i −0.224381 + 0.163022i
\(14\) 0.159267 + 0.490175i 0.0425660 + 0.131005i
\(15\) 0.239789 0.737995i 0.0619133 0.190550i
\(16\) 4.01805 + 2.91928i 1.00451 + 0.729821i
\(17\) −2.88671 2.09732i −0.700130 0.508674i 0.179844 0.983695i \(-0.442441\pi\)
−0.879975 + 0.475021i \(0.842441\pi\)
\(18\) 0.518670 1.59630i 0.122252 0.376252i
\(19\) 0.616165 + 1.89636i 0.141358 + 0.435055i 0.996525 0.0832981i \(-0.0265454\pi\)
−0.855167 + 0.518353i \(0.826545\pi\)
\(20\) 0.513017 0.372729i 0.114714 0.0833447i
\(21\) −0.307069 −0.0670080
\(22\) 4.59578 + 3.14133i 0.979824 + 0.669734i
\(23\) −4.18140 −0.871882 −0.435941 0.899975i \(-0.643584\pi\)
−0.435941 + 0.899975i \(0.643584\pi\)
\(24\) −1.60612 + 1.16692i −0.327848 + 0.238196i
\(25\) −1.35901 4.18262i −0.271803 0.836524i
\(26\) 0.518670 1.59630i 0.101720 0.313061i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) −0.203012 0.147497i −0.0383656 0.0278742i
\(29\) 2.46290 7.58001i 0.457348 1.40757i −0.411008 0.911632i \(-0.634823\pi\)
0.868356 0.495941i \(-0.165177\pi\)
\(30\) 0.402474 + 1.23869i 0.0734814 + 0.226153i
\(31\) 2.78484 2.02330i 0.500171 0.363396i −0.308911 0.951091i \(-0.599965\pi\)
0.809082 + 0.587695i \(0.199965\pi\)
\(32\) −4.36561 −0.771739
\(33\) −2.62609 + 2.02575i −0.457143 + 0.352638i
\(34\) 5.98900 1.02711
\(35\) 0.192771 0.140056i 0.0325842 0.0236738i
\(36\) 0.252528 + 0.777201i 0.0420880 + 0.129533i
\(37\) 3.20487 9.86359i 0.526878 1.62156i −0.233694 0.972310i \(-0.575081\pi\)
0.760572 0.649254i \(-0.224919\pi\)
\(38\) −2.70758 1.96717i −0.439227 0.319117i
\(39\) 0.809017 + 0.587785i 0.129546 + 0.0941210i
\(40\) 0.476048 1.46512i 0.0752698 0.231656i
\(41\) −3.95358 12.1679i −0.617446 1.90030i −0.350193 0.936678i \(-0.613884\pi\)
−0.267254 0.963626i \(-0.586116\pi\)
\(42\) 0.416968 0.302945i 0.0643395 0.0467454i
\(43\) −0.426420 −0.0650284 −0.0325142 0.999471i \(-0.510351\pi\)
−0.0325142 + 0.999471i \(0.510351\pi\)
\(44\) −2.70922 + 0.0778729i −0.408430 + 0.0117398i
\(45\) −0.775974 −0.115675
\(46\) 5.67790 4.12524i 0.837161 0.608233i
\(47\) 2.23136 + 6.86741i 0.325477 + 1.00171i 0.971225 + 0.238164i \(0.0765456\pi\)
−0.645748 + 0.763550i \(0.723454\pi\)
\(48\) 1.53476 4.72350i 0.221523 0.681779i
\(49\) 5.58684 + 4.05907i 0.798119 + 0.579868i
\(50\) 5.97184 + 4.33880i 0.844546 + 0.613598i
\(51\) −1.10263 + 3.39353i −0.154398 + 0.475190i
\(52\) 0.252528 + 0.777201i 0.0350193 + 0.107778i
\(53\) −4.35227 + 3.16211i −0.597831 + 0.434349i −0.845108 0.534595i \(-0.820464\pi\)
0.247278 + 0.968945i \(0.420464\pi\)
\(54\) −1.67845 −0.228408
\(55\) 0.724637 2.46949i 0.0977100 0.332986i
\(56\) −0.609617 −0.0814635
\(57\) 1.61314 1.17201i 0.213666 0.155237i
\(58\) 4.13385 + 12.7227i 0.542801 + 1.67057i
\(59\) 1.35726 4.17722i 0.176700 0.543827i −0.823007 0.568031i \(-0.807705\pi\)
0.999707 + 0.0242042i \(0.00770517\pi\)
\(60\) −0.513017 0.372729i −0.0662302 0.0481191i
\(61\) −3.23644 2.35141i −0.414384 0.301067i 0.360990 0.932569i \(-0.382439\pi\)
−0.775374 + 0.631502i \(0.782439\pi\)
\(62\) −1.78539 + 5.49486i −0.226745 + 0.697848i
\(63\) 0.0948896 + 0.292040i 0.0119550 + 0.0367936i
\(64\) −2.10805 + 1.53159i −0.263507 + 0.191449i
\(65\) −0.775974 −0.0962477
\(66\) 1.56741 5.34157i 0.192935 0.657502i
\(67\) 0.00770561 0.000941390 0.000470695 1.00000i \(-0.499850\pi\)
0.000470695 1.00000i \(0.499850\pi\)
\(68\) −2.35901 + 1.71392i −0.286072 + 0.207844i
\(69\) 1.29212 + 3.97675i 0.155553 + 0.478744i
\(70\) −0.123587 + 0.380363i −0.0147715 + 0.0454621i
\(71\) 9.42803 + 6.84986i 1.11890 + 0.812929i 0.984042 0.177936i \(-0.0569419\pi\)
0.134859 + 0.990865i \(0.456942\pi\)
\(72\) 1.60612 + 1.16692i 0.189283 + 0.137522i
\(73\) 2.33300 7.18023i 0.273057 0.840383i −0.716670 0.697412i \(-0.754335\pi\)
0.989727 0.142970i \(-0.0456653\pi\)
\(74\) 5.37922 + 16.5556i 0.625322 + 1.92454i
\(75\) −3.55795 + 2.58500i −0.410836 + 0.298490i
\(76\) 1.62945 0.186911
\(77\) −1.01801 + 0.0292614i −0.116013 + 0.00333465i
\(78\) −1.67845 −0.190047
\(79\) −9.13869 + 6.63965i −1.02818 + 0.747018i −0.967944 0.251166i \(-0.919186\pi\)
−0.0602386 + 0.998184i \(0.519186\pi\)
\(80\) 1.19093 + 3.66531i 0.133150 + 0.409795i
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 17.3730 + 12.6222i 1.91853 + 1.39389i
\(83\) −13.9770 10.1549i −1.53418 1.11465i −0.953858 0.300257i \(-0.902928\pi\)
−0.580320 0.814389i \(-0.697072\pi\)
\(84\) −0.0775435 + 0.238654i −0.00846069 + 0.0260393i
\(85\) −0.855609 2.63329i −0.0928038 0.285621i
\(86\) 0.579033 0.420692i 0.0624388 0.0453644i
\(87\) −7.97010 −0.854484
\(88\) −5.21351 + 4.02168i −0.555762 + 0.428712i
\(89\) 5.89819 0.625207 0.312604 0.949884i \(-0.398799\pi\)
0.312604 + 0.949884i \(0.398799\pi\)
\(90\) 1.05369 0.765552i 0.111069 0.0806962i
\(91\) 0.0948896 + 0.292040i 0.00994713 + 0.0306141i
\(92\) −1.05592 + 3.24979i −0.110087 + 0.338814i
\(93\) −2.78484 2.02330i −0.288774 0.209807i
\(94\) −9.80512 7.12384i −1.01132 0.734767i
\(95\) −0.478128 + 1.47153i −0.0490549 + 0.150975i
\(96\) 1.34905 + 4.15195i 0.137687 + 0.423756i
\(97\) −6.91981 + 5.02754i −0.702601 + 0.510469i −0.880778 0.473529i \(-0.842980\pi\)
0.178178 + 0.983998i \(0.442980\pi\)
\(98\) −11.5909 −1.17086
\(99\) 2.73811 + 1.87156i 0.275190 + 0.188099i
\(100\) −3.59392 −0.359392
\(101\) −10.0738 + 7.31905i −1.00238 + 0.728273i −0.962598 0.270935i \(-0.912667\pi\)
−0.0397843 + 0.999208i \(0.512667\pi\)
\(102\) −1.85070 5.69588i −0.183247 0.563976i
\(103\) −1.41848 + 4.36565i −0.139767 + 0.430160i −0.996301 0.0859313i \(-0.972613\pi\)
0.856534 + 0.516091i \(0.172613\pi\)
\(104\) 1.60612 + 1.16692i 0.157493 + 0.114426i
\(105\) −0.192771 0.140056i −0.0188125 0.0136681i
\(106\) 2.79029 8.58763i 0.271017 0.834104i
\(107\) 1.39246 + 4.28555i 0.134614 + 0.414300i 0.995530 0.0944477i \(-0.0301085\pi\)
−0.860916 + 0.508748i \(0.830109\pi\)
\(108\) 0.661127 0.480337i 0.0636169 0.0462204i
\(109\) 14.1424 1.35460 0.677299 0.735708i \(-0.263150\pi\)
0.677299 + 0.735708i \(0.263150\pi\)
\(110\) 1.45234 + 4.06822i 0.138475 + 0.387889i
\(111\) −10.3712 −0.984390
\(112\) 1.23382 0.896422i 0.116585 0.0847039i
\(113\) 3.50841 + 10.7978i 0.330043 + 1.01577i 0.969112 + 0.246620i \(0.0793198\pi\)
−0.639069 + 0.769149i \(0.720680\pi\)
\(114\) −1.03420 + 3.18295i −0.0968619 + 0.298110i
\(115\) −2.62498 1.90716i −0.244781 0.177844i
\(116\) −5.26924 3.82833i −0.489237 0.355451i
\(117\) 0.309017 0.951057i 0.0285686 0.0879252i
\(118\) 2.27809 + 7.01125i 0.209716 + 0.645438i
\(119\) −0.886420 + 0.644022i −0.0812580 + 0.0590374i
\(120\) −1.54052 −0.140630
\(121\) −8.51311 + 6.96613i −0.773919 + 0.633285i
\(122\) 6.71457 0.607909
\(123\) −10.3506 + 7.52016i −0.933284 + 0.678070i
\(124\) −0.869263 2.67532i −0.0780621 0.240250i
\(125\) 2.25351 6.93558i 0.201560 0.620337i
\(126\) −0.416968 0.302945i −0.0371464 0.0269885i
\(127\) −9.59180 6.96885i −0.851134 0.618385i 0.0743243 0.997234i \(-0.476320\pi\)
−0.925459 + 0.378849i \(0.876320\pi\)
\(128\) 4.04959 12.4634i 0.357937 1.10162i
\(129\) 0.131771 + 0.405549i 0.0116018 + 0.0357066i
\(130\) 1.05369 0.765552i 0.0924149 0.0671433i
\(131\) −2.68464 −0.234558 −0.117279 0.993099i \(-0.537417\pi\)
−0.117279 + 0.993099i \(0.537417\pi\)
\(132\) 0.911256 + 2.55256i 0.0793146 + 0.222171i
\(133\) 0.612281 0.0530915
\(134\) −0.0104634 + 0.00760211i −0.000903901 + 0.000656723i
\(135\) 0.239789 + 0.737995i 0.0206378 + 0.0635165i
\(136\) −2.18902 + 6.73710i −0.187707 + 0.577702i
\(137\) −1.67185 1.21467i −0.142836 0.103776i 0.514073 0.857747i \(-0.328136\pi\)
−0.656908 + 0.753970i \(0.728136\pi\)
\(138\) −5.67790 4.12524i −0.483335 0.351164i
\(139\) −4.69117 + 14.4380i −0.397900 + 1.22461i 0.528780 + 0.848759i \(0.322650\pi\)
−0.926680 + 0.375852i \(0.877350\pi\)
\(140\) −0.0601717 0.185190i −0.00508544 0.0156514i
\(141\) 5.84177 4.24429i 0.491965 0.357434i
\(142\) −19.5601 −1.64145
\(143\) 2.73811 + 1.87156i 0.228972 + 0.156508i
\(144\) −4.96658 −0.413882
\(145\) 5.00344 3.63521i 0.415513 0.301888i
\(146\) 3.91582 + 12.0517i 0.324076 + 0.997403i
\(147\) 2.13398 6.56772i 0.176008 0.541696i
\(148\) −6.85667 4.98166i −0.563615 0.409490i
\(149\) 14.7373 + 10.7073i 1.20732 + 0.877172i 0.994985 0.100024i \(-0.0318918\pi\)
0.212339 + 0.977196i \(0.431892\pi\)
\(150\) 2.28104 7.02032i 0.186246 0.573207i
\(151\) −0.704145 2.16714i −0.0573025 0.176359i 0.918309 0.395865i \(-0.129555\pi\)
−0.975611 + 0.219506i \(0.929555\pi\)
\(152\) 3.20253 2.32677i 0.259759 0.188726i
\(153\) 3.56817 0.288470
\(154\) 1.35349 1.04407i 0.109067 0.0841338i
\(155\) 2.67109 0.214547
\(156\) 0.661127 0.480337i 0.0529325 0.0384577i
\(157\) −3.99344 12.2905i −0.318711 0.980892i −0.974200 0.225687i \(-0.927537\pi\)
0.655489 0.755205i \(-0.272463\pi\)
\(158\) 5.85892 18.0319i 0.466110 1.43454i
\(159\) 4.35227 + 3.16211i 0.345158 + 0.250772i
\(160\) −2.74063 1.99118i −0.216666 0.157417i
\(161\) −0.396771 + 1.22114i −0.0312699 + 0.0962390i
\(162\) 0.518670 + 1.59630i 0.0407506 + 0.125417i
\(163\) 1.14958 0.835219i 0.0900421 0.0654194i −0.541853 0.840473i \(-0.682277\pi\)
0.631895 + 0.775054i \(0.282277\pi\)
\(164\) −10.4553 −0.816420
\(165\) −2.57255 + 0.0739446i −0.200273 + 0.00575658i
\(166\) 28.9979 2.25067
\(167\) 2.63525 1.91462i 0.203922 0.148158i −0.481138 0.876645i \(-0.659776\pi\)
0.685059 + 0.728487i \(0.259776\pi\)
\(168\) 0.188382 + 0.579780i 0.0145340 + 0.0447310i
\(169\) 0.309017 0.951057i 0.0237705 0.0731582i
\(170\) 3.75975 + 2.73162i 0.288360 + 0.209506i
\(171\) −1.61314 1.17201i −0.123360 0.0896262i
\(172\) −0.107683 + 0.331414i −0.00821074 + 0.0252701i
\(173\) 3.79288 + 11.6733i 0.288368 + 0.887504i 0.985369 + 0.170434i \(0.0545171\pi\)
−0.697002 + 0.717070i \(0.745483\pi\)
\(174\) 10.8226 7.86305i 0.820456 0.596096i
\(175\) −1.35045 −0.102084
\(176\) 4.63800 15.8059i 0.349603 1.19141i
\(177\) −4.39219 −0.330137
\(178\) −8.00913 + 5.81897i −0.600310 + 0.436150i
\(179\) 5.37319 + 16.5370i 0.401611 + 1.23603i 0.923692 + 0.383136i \(0.125156\pi\)
−0.522081 + 0.852896i \(0.674844\pi\)
\(180\) −0.195955 + 0.603088i −0.0146056 + 0.0449515i
\(181\) 5.93533 + 4.31227i 0.441170 + 0.320529i 0.786100 0.618100i \(-0.212097\pi\)
−0.344930 + 0.938628i \(0.612097\pi\)
\(182\) −0.416968 0.302945i −0.0309077 0.0224558i
\(183\) −1.23621 + 3.80466i −0.0913833 + 0.281249i
\(184\) 2.56522 + 7.89494i 0.189111 + 0.582023i
\(185\) 6.51079 4.73036i 0.478683 0.347783i
\(186\) 5.77764 0.423637
\(187\) −3.33211 + 11.3555i −0.243668 + 0.830396i
\(188\) 5.90083 0.430363
\(189\) 0.248424 0.180491i 0.0180702 0.0131288i
\(190\) −0.802514 2.46988i −0.0582205 0.179184i
\(191\) 7.18952 22.1271i 0.520216 1.60106i −0.253371 0.967369i \(-0.581539\pi\)
0.773587 0.633690i \(-0.218461\pi\)
\(192\) 2.10805 + 1.53159i 0.152136 + 0.110533i
\(193\) −19.8691 14.4357i −1.43021 1.03911i −0.989978 0.141221i \(-0.954897\pi\)
−0.440230 0.897885i \(-0.645103\pi\)
\(194\) 4.43637 13.6537i 0.318513 0.980281i
\(195\) 0.239789 + 0.737995i 0.0171717 + 0.0528489i
\(196\) 4.56555 3.31706i 0.326111 0.236933i
\(197\) 17.0488 1.21468 0.607338 0.794444i \(-0.292238\pi\)
0.607338 + 0.794444i \(0.292238\pi\)
\(198\) −5.56449 + 0.159944i −0.395451 + 0.0113667i
\(199\) 13.4899 0.956274 0.478137 0.878285i \(-0.341312\pi\)
0.478137 + 0.878285i \(0.341312\pi\)
\(200\) −7.06351 + 5.13194i −0.499465 + 0.362883i
\(201\) −0.00238116 0.00732847i −0.000167954 0.000516910i
\(202\) 6.45843 19.8770i 0.454414 1.39854i
\(203\) −1.97996 1.43853i −0.138966 0.100965i
\(204\) 2.35901 + 1.71392i 0.165164 + 0.119999i
\(205\) 3.06788 9.44196i 0.214270 0.659455i
\(206\) −2.38086 7.32752i −0.165882 0.510533i
\(207\) 3.38282 2.45776i 0.235122 0.170826i
\(208\) −4.96658 −0.344371
\(209\) 5.23629 4.03925i 0.362202 0.279401i
\(210\) 0.399937 0.0275983
\(211\) 18.5782 13.4978i 1.27897 0.929229i 0.279453 0.960159i \(-0.409847\pi\)
0.999522 + 0.0309299i \(0.00984686\pi\)
\(212\) 1.35853 + 4.18111i 0.0933039 + 0.287160i
\(213\) 3.60119 11.0833i 0.246749 0.759416i
\(214\) −6.11881 4.44558i −0.418273 0.303893i
\(215\) −0.267696 0.194493i −0.0182567 0.0132643i
\(216\) 0.613484 1.88811i 0.0417423 0.128470i
\(217\) −0.326633 1.00527i −0.0221733 0.0682424i
\(218\) −19.2039 + 13.9525i −1.30065 + 0.944981i
\(219\) −7.54974 −0.510164
\(220\) −1.73630 1.18680i −0.117061 0.0800143i
\(221\) 3.56817 0.240021
\(222\) 14.0830 10.2319i 0.945189 0.686720i
\(223\) −3.10519 9.55678i −0.207939 0.639969i −0.999580 0.0289832i \(-0.990773\pi\)
0.791641 0.610986i \(-0.209227\pi\)
\(224\) −0.414251 + 1.27493i −0.0276783 + 0.0851851i
\(225\) 3.55795 + 2.58500i 0.237196 + 0.172333i
\(226\) −15.4168 11.2010i −1.02551 0.745077i
\(227\) −6.10872 + 18.8007i −0.405450 + 1.24785i 0.515069 + 0.857149i \(0.327766\pi\)
−0.920519 + 0.390698i \(0.872234\pi\)
\(228\) −0.503528 1.54970i −0.0333470 0.102631i
\(229\) 4.00661 2.91097i 0.264764 0.192363i −0.447480 0.894294i \(-0.647679\pi\)
0.712245 + 0.701931i \(0.247679\pi\)
\(230\) 5.44600 0.359098
\(231\) 0.342412 + 0.959145i 0.0225291 + 0.0631071i
\(232\) −15.8228 −1.03882
\(233\) 10.4559 7.59667i 0.684990 0.497674i −0.190019 0.981780i \(-0.560855\pi\)
0.875009 + 0.484106i \(0.160855\pi\)
\(234\) 0.518670 + 1.59630i 0.0339065 + 0.104354i
\(235\) −1.73147 + 5.32893i −0.112949 + 0.347621i
\(236\) −2.90379 2.10973i −0.189021 0.137332i
\(237\) 9.13869 + 6.63965i 0.593622 + 0.431291i
\(238\) 0.568294 1.74903i 0.0368370 0.113373i
\(239\) −2.67482 8.23224i −0.173020 0.532499i 0.826518 0.562910i \(-0.190318\pi\)
−0.999537 + 0.0304111i \(0.990318\pi\)
\(240\) 3.11790 2.26529i 0.201260 0.146224i
\(241\) −8.92483 −0.574899 −0.287449 0.957796i \(-0.592807\pi\)
−0.287449 + 0.957796i \(0.592807\pi\)
\(242\) 4.68734 17.8580i 0.301314 1.14796i
\(243\) −1.00000 −0.0641500
\(244\) −2.64481 + 1.92157i −0.169317 + 0.123016i
\(245\) 1.65591 + 5.09638i 0.105792 + 0.325596i
\(246\) 6.63590 20.4232i 0.423089 1.30214i
\(247\) −1.61314 1.17201i −0.102642 0.0745735i
\(248\) −5.52867 4.01681i −0.351071 0.255068i
\(249\) −5.33875 + 16.4310i −0.338330 + 1.04127i
\(250\) 3.78240 + 11.6410i 0.239220 + 0.736243i
\(251\) −9.12966 + 6.63309i −0.576259 + 0.418677i −0.837373 0.546631i \(-0.815910\pi\)
0.261115 + 0.965308i \(0.415910\pi\)
\(252\) 0.250936 0.0158075
\(253\) 4.66267 + 13.0608i 0.293140 + 0.821126i
\(254\) 19.8999 1.24863
\(255\) −2.24001 + 1.62746i −0.140275 + 0.101916i
\(256\) 5.18664 + 15.9628i 0.324165 + 0.997676i
\(257\) 3.10711 9.56271i 0.193816 0.596506i −0.806172 0.591681i \(-0.798464\pi\)
0.999988 0.00482422i \(-0.00153560\pi\)
\(258\) −0.579033 0.420692i −0.0360490 0.0261912i
\(259\) −2.57645 1.87190i −0.160093 0.116314i
\(260\) −0.195955 + 0.603088i −0.0121526 + 0.0374019i
\(261\) 2.46290 + 7.58001i 0.152449 + 0.469191i
\(262\) 3.64546 2.64858i 0.225217 0.163630i
\(263\) −7.99294 −0.492866 −0.246433 0.969160i \(-0.579258\pi\)
−0.246433 + 0.969160i \(0.579258\pi\)
\(264\) 5.43590 + 3.71557i 0.334557 + 0.228678i
\(265\) −4.17451 −0.256438
\(266\) −0.831413 + 0.604057i −0.0509772 + 0.0370371i
\(267\) −1.82264 5.60952i −0.111544 0.343297i
\(268\) 0.00194588 0.00598881i 0.000118864 0.000365825i
\(269\) −5.95850 4.32911i −0.363296 0.263950i 0.391129 0.920336i \(-0.372085\pi\)
−0.754426 + 0.656385i \(0.772085\pi\)
\(270\) −1.05369 0.765552i −0.0641256 0.0465900i
\(271\) 1.99183 6.13021i 0.120995 0.372384i −0.872155 0.489229i \(-0.837278\pi\)
0.993150 + 0.116845i \(0.0372782\pi\)
\(272\) −5.47628 16.8543i −0.332048 1.02194i
\(273\) 0.248424 0.180491i 0.0150353 0.0109238i
\(274\) 3.46855 0.209543
\(275\) −11.5492 + 8.90898i −0.696441 + 0.537232i
\(276\) 3.41703 0.205681
\(277\) 7.28194 5.29064i 0.437530 0.317884i −0.347123 0.937820i \(-0.612841\pi\)
0.784653 + 0.619936i \(0.212841\pi\)
\(278\) −7.87391 24.2334i −0.472246 1.45342i
\(279\) −1.06371 + 3.27377i −0.0636828 + 0.195995i
\(280\) −0.382703 0.278050i −0.0228709 0.0166167i
\(281\) 9.44855 + 6.86477i 0.563653 + 0.409518i 0.832794 0.553583i \(-0.186740\pi\)
−0.269141 + 0.963101i \(0.586740\pi\)
\(282\) −3.74522 + 11.5266i −0.223025 + 0.686399i
\(283\) 3.55419 + 10.9387i 0.211275 + 0.650237i 0.999397 + 0.0347181i \(0.0110533\pi\)
−0.788122 + 0.615518i \(0.788947\pi\)
\(284\) 7.70456 5.59769i 0.457181 0.332162i
\(285\) 1.54725 0.0916514
\(286\) −5.56449 + 0.159944i −0.329035 + 0.00945769i
\(287\) −3.92866 −0.231902
\(288\) 3.53186 2.56604i 0.208117 0.151206i
\(289\) −1.31893 4.05925i −0.0775842 0.238780i
\(290\) −3.20776 + 9.87247i −0.188366 + 0.579731i
\(291\) 6.91981 + 5.02754i 0.405647 + 0.294720i
\(292\) −4.99133 3.62642i −0.292096 0.212220i
\(293\) 2.16500 6.66318i 0.126481 0.389267i −0.867687 0.497110i \(-0.834394\pi\)
0.994168 + 0.107843i \(0.0343944\pi\)
\(294\) 3.58178 + 11.0236i 0.208894 + 0.642909i
\(295\) 2.75731 2.00330i 0.160537 0.116637i
\(296\) −20.5897 −1.19675
\(297\) 0.933842 3.18244i 0.0541870 0.184664i
\(298\) −30.5751 −1.77117
\(299\) 3.38282 2.45776i 0.195634 0.142136i
\(300\) 1.11058 + 3.41802i 0.0641196 + 0.197340i
\(301\) −0.0404628 + 0.124532i −0.00233224 + 0.00717789i
\(302\) 3.09418 + 2.24806i 0.178050 + 0.129361i
\(303\) 10.0738 + 7.31905i 0.578725 + 0.420469i
\(304\) −3.06023 + 9.41843i −0.175516 + 0.540184i
\(305\) −0.959267 2.95232i −0.0549275 0.169049i
\(306\) −4.84520 + 3.52025i −0.276982 + 0.201239i
\(307\) 27.3102 1.55868 0.779339 0.626603i \(-0.215555\pi\)
0.779339 + 0.626603i \(0.215555\pi\)
\(308\) −0.234335 + 0.798590i −0.0133524 + 0.0455039i
\(309\) 4.59031 0.261134
\(310\) −3.62706 + 2.63522i −0.206003 + 0.149670i
\(311\) 4.09766 + 12.6113i 0.232357 + 0.715121i 0.997461 + 0.0712144i \(0.0226874\pi\)
−0.765104 + 0.643907i \(0.777313\pi\)
\(312\) 0.613484 1.88811i 0.0347317 0.106893i
\(313\) −11.0861 8.05450i −0.626622 0.455267i 0.228607 0.973519i \(-0.426583\pi\)
−0.855228 + 0.518252i \(0.826583\pi\)
\(314\) 17.5481 + 12.7495i 0.990298 + 0.719494i
\(315\) −0.0736318 + 0.226616i −0.00414868 + 0.0127683i
\(316\) 2.85256 + 8.77929i 0.160469 + 0.493874i
\(317\) −21.2833 + 15.4632i −1.19539 + 0.868501i −0.993823 0.110973i \(-0.964603\pi\)
−0.201566 + 0.979475i \(0.564603\pi\)
\(318\) −9.02957 −0.506353
\(319\) −26.4229 + 0.759492i −1.47940 + 0.0425234i
\(320\) −2.02195 −0.113031
\(321\) 3.64551 2.64862i 0.203473 0.147831i
\(322\) −0.665961 2.04962i −0.0371125 0.114221i
\(323\) 2.19858 6.76654i 0.122332 0.376500i
\(324\) −0.661127 0.480337i −0.0367293 0.0266854i
\(325\) 3.55795 + 2.58500i 0.197359 + 0.143390i
\(326\) −0.737009 + 2.26828i −0.0408191 + 0.125628i
\(327\) −4.37025 13.4502i −0.241675 0.743800i
\(328\) −20.5488 + 14.9296i −1.13462 + 0.824349i
\(329\) 2.21729 0.122243
\(330\) 3.42031 2.63841i 0.188282 0.145240i
\(331\) −11.7249 −0.644461 −0.322231 0.946661i \(-0.604433\pi\)
−0.322231 + 0.946661i \(0.604433\pi\)
\(332\) −11.4220 + 8.29856i −0.626863 + 0.455443i
\(333\) 3.20487 + 9.86359i 0.175626 + 0.540521i
\(334\) −1.68949 + 5.19971i −0.0924447 + 0.284515i
\(335\) 0.00483740 + 0.00351458i 0.000264295 + 0.000192022i
\(336\) −1.23382 0.896422i −0.0673104 0.0489038i
\(337\) −0.188128 + 0.578999i −0.0102480 + 0.0315401i −0.956050 0.293204i \(-0.905278\pi\)
0.945802 + 0.324745i \(0.105278\pi\)
\(338\) 0.518670 + 1.59630i 0.0282119 + 0.0868274i
\(339\) 9.18513 6.67339i 0.498868 0.362449i
\(340\) −2.26266 −0.122710
\(341\) −9.42525 6.44239i −0.510406 0.348875i
\(342\) 3.34675 0.180971
\(343\) 3.45451 2.50985i 0.186526 0.135519i
\(344\) 0.261602 + 0.805127i 0.0141046 + 0.0434096i
\(345\) −1.00265 + 3.08585i −0.0539811 + 0.166137i
\(346\) −16.6668 12.1092i −0.896015 0.650993i
\(347\) 6.34083 + 4.60688i 0.340394 + 0.247310i 0.744828 0.667257i \(-0.232532\pi\)
−0.404434 + 0.914567i \(0.632532\pi\)
\(348\) −2.01267 + 6.19437i −0.107891 + 0.332053i
\(349\) −3.52953 10.8628i −0.188931 0.581471i 0.811063 0.584959i \(-0.198890\pi\)
−0.999994 + 0.00348870i \(0.998890\pi\)
\(350\) 1.83377 1.33231i 0.0980190 0.0712150i
\(351\) −1.00000 −0.0533761
\(352\) 4.86809 + 13.6362i 0.259470 + 0.726812i
\(353\) −16.0778 −0.855732 −0.427866 0.903842i \(-0.640735\pi\)
−0.427866 + 0.903842i \(0.640735\pi\)
\(354\) 5.96413 4.33319i 0.316990 0.230307i
\(355\) 2.79443 + 8.60036i 0.148313 + 0.456460i
\(356\) 1.48946 4.58408i 0.0789411 0.242956i
\(357\) 0.886420 + 0.644022i 0.0469143 + 0.0340852i
\(358\) −23.6111 17.1545i −1.24788 0.906641i
\(359\) −9.30077 + 28.6248i −0.490876 + 1.51076i 0.332411 + 0.943135i \(0.392138\pi\)
−0.823287 + 0.567625i \(0.807862\pi\)
\(360\) 0.476048 + 1.46512i 0.0250899 + 0.0772188i
\(361\) 12.1548 8.83098i 0.639726 0.464788i
\(362\) −12.3139 −0.647205
\(363\) 9.25588 + 5.94379i 0.485808 + 0.311968i
\(364\) 0.250936 0.0131526
\(365\) 4.73955 3.44348i 0.248079 0.180240i
\(366\) −2.07492 6.38594i −0.108458 0.333798i
\(367\) −9.12405 + 28.0809i −0.476271 + 1.46581i 0.367964 + 0.929840i \(0.380055\pi\)
−0.844235 + 0.535973i \(0.819945\pi\)
\(368\) −16.8011 12.2067i −0.875816 0.636318i
\(369\) 10.3506 + 7.52016i 0.538832 + 0.391484i
\(370\) −4.17414 + 12.8467i −0.217003 + 0.667867i
\(371\) 0.510478 + 1.57109i 0.0265027 + 0.0815669i
\(372\) −2.27576 + 1.65344i −0.117993 + 0.0857267i
\(373\) −15.2700 −0.790650 −0.395325 0.918541i \(-0.629368\pi\)
−0.395325 + 0.918541i \(0.629368\pi\)
\(374\) −6.67833 18.7069i −0.345328 0.967312i
\(375\) −7.29250 −0.376583
\(376\) 11.5975 8.42609i 0.598096 0.434542i
\(377\) 2.46290 + 7.58001i 0.126846 + 0.390391i
\(378\) −0.159267 + 0.490175i −0.00819184 + 0.0252119i
\(379\) 4.70246 + 3.41654i 0.241549 + 0.175496i 0.701973 0.712203i \(-0.252303\pi\)
−0.460424 + 0.887699i \(0.652303\pi\)
\(380\) 1.02293 + 0.743203i 0.0524752 + 0.0381255i
\(381\) −3.66374 + 11.2758i −0.187699 + 0.577678i
\(382\) 12.0673 + 37.1392i 0.617415 + 1.90021i
\(383\) 16.7336 12.1576i 0.855045 0.621227i −0.0714874 0.997442i \(-0.522775\pi\)
0.926532 + 0.376215i \(0.122775\pi\)
\(384\) −13.1048 −0.668750
\(385\) −0.652430 0.445952i −0.0332509 0.0227278i
\(386\) 41.2220 2.09814
\(387\) 0.344981 0.250643i 0.0175364 0.0127409i
\(388\) 2.15996 + 6.64768i 0.109655 + 0.337485i
\(389\) 9.01746 27.7529i 0.457204 1.40713i −0.411325 0.911489i \(-0.634934\pi\)
0.868529 0.495639i \(-0.165066\pi\)
\(390\) −1.05369 0.765552i −0.0533557 0.0387652i
\(391\) 12.0705 + 8.76973i 0.610431 + 0.443504i
\(392\) 4.23654 13.0387i 0.213978 0.658556i
\(393\) 0.829599 + 2.55324i 0.0418477 + 0.128794i
\(394\) −23.1505 + 16.8198i −1.16630 + 0.847369i
\(395\) −8.76543 −0.441037
\(396\) 2.14603 1.65544i 0.107842 0.0831889i
\(397\) 38.0612 1.91024 0.955118 0.296226i \(-0.0957281\pi\)
0.955118 + 0.296226i \(0.0957281\pi\)
\(398\) −18.3179 + 13.3087i −0.918192 + 0.667106i
\(399\) −0.189205 0.582314i −0.00947210 0.0291521i
\(400\) 6.74966 20.7733i 0.337483 1.03867i
\(401\) 1.38434 + 1.00578i 0.0691308 + 0.0502264i 0.621814 0.783165i \(-0.286396\pi\)
−0.552683 + 0.833391i \(0.686396\pi\)
\(402\) 0.0104634 + 0.00760211i 0.000521867 + 0.000379159i
\(403\) −1.06371 + 3.27377i −0.0529873 + 0.163078i
\(404\) 3.14446 + 9.67764i 0.156443 + 0.481481i
\(405\) 0.627776 0.456106i 0.0311944 0.0226641i
\(406\) 4.10779 0.203866
\(407\) −34.3832 + 0.988298i −1.70431 + 0.0489881i
\(408\) 7.08381 0.350701
\(409\) 19.3054 14.0262i 0.954589 0.693550i 0.00270130 0.999996i \(-0.499140\pi\)
0.951888 + 0.306447i \(0.0991401\pi\)
\(410\) 5.14928 + 15.8479i 0.254305 + 0.782670i
\(411\) −0.638589 + 1.96537i −0.0314993 + 0.0969448i
\(412\) 3.03478 + 2.20489i 0.149513 + 0.108627i
\(413\) −1.09112 0.792749i −0.0536907 0.0390086i
\(414\) −2.16877 + 6.67477i −0.106589 + 0.328047i
\(415\) −4.14273 12.7500i −0.203359 0.625874i
\(416\) 3.53186 2.56604i 0.173163 0.125811i
\(417\) 15.1810 0.743415
\(418\) −3.12533 + 10.6508i −0.152865 + 0.520949i
\(419\) 15.7851 0.771154 0.385577 0.922676i \(-0.374002\pi\)
0.385577 + 0.922676i \(0.374002\pi\)
\(420\) −0.157532 + 0.114453i −0.00768676 + 0.00558476i
\(421\) 0.227790 + 0.701065i 0.0111018 + 0.0341678i 0.956454 0.291883i \(-0.0942819\pi\)
−0.945352 + 0.326051i \(0.894282\pi\)
\(422\) −11.9107 + 36.6573i −0.579803 + 1.78445i
\(423\) −5.84177 4.24429i −0.284036 0.206365i
\(424\) 8.64046 + 6.27766i 0.419618 + 0.304870i
\(425\) −4.84920 + 14.9243i −0.235221 + 0.723935i
\(426\) 6.04441 + 18.6028i 0.292853 + 0.901308i
\(427\) −0.993811 + 0.722046i −0.0480939 + 0.0349422i
\(428\) 3.68237 0.177994
\(429\) 0.933842 3.18244i 0.0450863 0.153650i
\(430\) 0.555384 0.0267830
\(431\) −23.4928 + 17.0685i −1.13161 + 0.822163i −0.985928 0.167168i \(-0.946538\pi\)
−0.145682 + 0.989331i \(0.546538\pi\)
\(432\) 1.53476 + 4.72350i 0.0738411 + 0.227260i
\(433\) 1.78898 5.50592i 0.0859730 0.264598i −0.898823 0.438311i \(-0.855577\pi\)
0.984796 + 0.173714i \(0.0555767\pi\)
\(434\) 1.43531 + 1.04281i 0.0688969 + 0.0500565i
\(435\) −5.00344 3.63521i −0.239896 0.174295i
\(436\) 3.57136 10.9915i 0.171037 0.526398i
\(437\) −2.57643 7.92944i −0.123247 0.379316i
\(438\) 10.2518 7.44834i 0.489848 0.355895i
\(439\) 24.3031 1.15992 0.579961 0.814644i \(-0.303068\pi\)
0.579961 + 0.814644i \(0.303068\pi\)
\(440\) −5.10723 + 0.146800i −0.243477 + 0.00699844i
\(441\) −6.90571 −0.328843
\(442\) −4.84520 + 3.52025i −0.230463 + 0.167441i
\(443\) −9.82575 30.2405i −0.466835 1.43677i −0.856660 0.515882i \(-0.827464\pi\)
0.389824 0.920889i \(-0.372536\pi\)
\(444\) −2.61901 + 8.06050i −0.124293 + 0.382534i
\(445\) 3.70275 + 2.69020i 0.175527 + 0.127528i
\(446\) 13.6449 + 9.91363i 0.646107 + 0.469424i
\(447\) 5.62914 17.3247i 0.266249 0.819430i
\(448\) 0.247254 + 0.760968i 0.0116816 + 0.0359524i
\(449\) 9.11348 6.62133i 0.430092 0.312480i −0.351594 0.936153i \(-0.614360\pi\)
0.781686 + 0.623673i \(0.214360\pi\)
\(450\) −7.38160 −0.347972
\(451\) −33.5983 + 25.9176i −1.58208 + 1.22041i
\(452\) 9.27801 0.436401
\(453\) −1.84348 + 1.33936i −0.0866141 + 0.0629288i
\(454\) −10.2532 31.5561i −0.481206 1.48100i
\(455\) −0.0736318 + 0.226616i −0.00345191 + 0.0106239i
\(456\) −3.20253 2.32677i −0.149972 0.108961i
\(457\) 6.86402 + 4.98700i 0.321085 + 0.233282i 0.736638 0.676287i \(-0.236412\pi\)
−0.415553 + 0.909569i \(0.636412\pi\)
\(458\) −2.56868 + 7.90560i −0.120027 + 0.369404i
\(459\) −1.10263 3.39353i −0.0514662 0.158397i
\(460\) −2.14513 + 1.55853i −0.100017 + 0.0726667i
\(461\) 29.5182 1.37480 0.687399 0.726280i \(-0.258752\pi\)
0.687399 + 0.726280i \(0.258752\pi\)
\(462\) −1.41122 0.964605i −0.0656560 0.0448775i
\(463\) 15.2387 0.708201 0.354100 0.935207i \(-0.384787\pi\)
0.354100 + 0.935207i \(0.384787\pi\)
\(464\) 32.0243 23.2670i 1.48669 1.08014i
\(465\) −0.825413 2.54036i −0.0382776 0.117806i
\(466\) −6.70341 + 20.6310i −0.310529 + 0.955711i
\(467\) 10.7222 + 7.79013i 0.496164 + 0.360484i 0.807550 0.589799i \(-0.200793\pi\)
−0.311386 + 0.950284i \(0.600793\pi\)
\(468\) −0.661127 0.480337i −0.0305606 0.0222036i
\(469\) 0.000731182 0.00225035i 3.37628e−5 0.000103911i
\(470\) −2.90619 8.94435i −0.134053 0.412572i
\(471\) −10.4550 + 7.59597i −0.481739 + 0.350004i
\(472\) −8.71970 −0.401357
\(473\) 0.475500 + 1.33194i 0.0218635 + 0.0612428i
\(474\) −18.9598 −0.870855
\(475\) 7.09437 5.15436i 0.325512 0.236498i
\(476\) 0.276689 + 0.851560i 0.0126820 + 0.0390312i
\(477\) 1.66242 5.11640i 0.0761170 0.234264i
\(478\) 11.7538 + 8.53963i 0.537606 + 0.390594i
\(479\) 1.94025 + 1.40967i 0.0886521 + 0.0644096i 0.631228 0.775597i \(-0.282551\pi\)
−0.542576 + 0.840007i \(0.682551\pi\)
\(480\) −1.04683 + 3.22180i −0.0477809 + 0.147054i
\(481\) 3.20487 + 9.86359i 0.146130 + 0.449741i
\(482\) 12.1190 8.80496i 0.552005 0.401055i
\(483\) 1.28398 0.0584230
\(484\) 3.26429 + 8.37554i 0.148377 + 0.380706i
\(485\) −6.63718 −0.301379
\(486\) 1.35790 0.986569i 0.0615954 0.0447517i
\(487\) −12.0231 37.0033i −0.544819 1.67678i −0.721421 0.692497i \(-0.756511\pi\)
0.176602 0.984282i \(-0.443489\pi\)
\(488\) −2.45422 + 7.55331i −0.111097 + 0.341922i
\(489\) −1.14958 0.835219i −0.0519858 0.0377699i
\(490\) −7.27649 5.28668i −0.328718 0.238828i
\(491\) 1.13313 3.48742i 0.0511376 0.157385i −0.922227 0.386650i \(-0.873632\pi\)
0.973364 + 0.229265i \(0.0736322\pi\)
\(492\) 3.23086 + 9.94356i 0.145658 + 0.448290i
\(493\) −23.0074 + 16.7158i −1.03620 + 0.752843i
\(494\) 3.34675 0.150577
\(495\) 0.865288 + 2.42379i 0.0388918 + 0.108941i
\(496\) 17.0962 0.767642
\(497\) 2.89506 2.10338i 0.129861 0.0943495i
\(498\) −8.96083 27.5786i −0.401544 1.23583i
\(499\) 5.66147 17.4242i 0.253442 0.780014i −0.740691 0.671846i \(-0.765502\pi\)
0.994133 0.108168i \(-0.0344984\pi\)
\(500\) −4.82126 3.50285i −0.215613 0.156652i
\(501\) −2.63525 1.91462i −0.117734 0.0855389i
\(502\) 5.85313 18.0141i 0.261238 0.804007i
\(503\) −8.98571 27.6552i −0.400653 1.23308i −0.924471 0.381253i \(-0.875493\pi\)
0.523818 0.851830i \(-0.324507\pi\)
\(504\) 0.493191 0.358324i 0.0219685 0.0159610i
\(505\) −9.66236 −0.429970
\(506\) −19.2168 13.1352i −0.854291 0.583929i
\(507\) −1.00000 −0.0444116
\(508\) −7.83839 + 5.69492i −0.347772 + 0.252671i
\(509\) 7.09219 + 21.8275i 0.314356 + 0.967488i 0.976019 + 0.217686i \(0.0698510\pi\)
−0.661663 + 0.749801i \(0.730149\pi\)
\(510\) 1.43610 4.41985i 0.0635915 0.195714i
\(511\) −1.87554 1.36266i −0.0829689 0.0602804i
\(512\) −1.58738 1.15330i −0.0701527 0.0509690i
\(513\) −0.616165 + 1.89636i −0.0272043 + 0.0837263i
\(514\) 5.21514 + 16.0505i 0.230030 + 0.707959i
\(515\) −2.88169 + 2.09367i −0.126982 + 0.0922581i
\(516\) 0.348469 0.0153405
\(517\) 18.9625 14.6276i 0.833970 0.643321i
\(518\) 5.34532 0.234860
\(519\) 9.92990 7.21449i 0.435874 0.316681i
\(520\) 0.476048 + 1.46512i 0.0208761 + 0.0642499i
\(521\) −9.00598 + 27.7176i −0.394559 + 1.21433i 0.534745 + 0.845013i \(0.320408\pi\)
−0.929304 + 0.369315i \(0.879592\pi\)
\(522\) −10.8226 7.86305i −0.473691 0.344156i
\(523\) 14.8720 + 10.8052i 0.650309 + 0.472477i 0.863376 0.504561i \(-0.168345\pi\)
−0.213068 + 0.977037i \(0.568345\pi\)
\(524\) −0.677946 + 2.08650i −0.0296162 + 0.0911493i
\(525\) 0.417311 + 1.28435i 0.0182130 + 0.0560537i
\(526\) 10.8536 7.88558i 0.473238 0.343828i
\(527\) −12.2825 −0.535035
\(528\) −16.4655 + 0.473279i −0.716569 + 0.0205968i
\(529\) −5.51590 −0.239822
\(530\) 5.66855 4.11844i 0.246226 0.178894i
\(531\) 1.35726 + 4.17722i 0.0589001 + 0.181276i
\(532\) 0.154618 0.475865i 0.00670354 0.0206314i
\(533\) 10.3506 + 7.52016i 0.448335 + 0.325734i
\(534\) 8.00913 + 5.81897i 0.346589 + 0.251812i
\(535\) −1.08051 + 3.32548i −0.0467147 + 0.143773i
\(536\) −0.00472727 0.0145490i −0.000204187 0.000628423i
\(537\) 14.0672 10.2204i 0.607044 0.441043i
\(538\) 12.3620 0.532963
\(539\) 6.44884 21.9770i 0.277771 0.946617i
\(540\) 0.634124 0.0272883
\(541\) 5.83059 4.23617i 0.250677 0.182127i −0.455350 0.890313i \(-0.650486\pi\)
0.706027 + 0.708185i \(0.250486\pi\)
\(542\) 3.34318 + 10.2893i 0.143602 + 0.441961i
\(543\) 2.26710 6.97740i 0.0972904 0.299429i
\(544\) 12.6023 + 9.15608i 0.540318 + 0.392564i
\(545\) 8.87828 + 6.45045i 0.380304 + 0.276307i
\(546\) −0.159267 + 0.490175i −0.00681602 + 0.0209776i
\(547\) −3.81000 11.7260i −0.162904 0.501366i 0.835972 0.548772i \(-0.184905\pi\)
−0.998876 + 0.0474058i \(0.984905\pi\)
\(548\) −1.36623 + 0.992624i −0.0583624 + 0.0424028i
\(549\) 4.00046 0.170735
\(550\) 6.89324 23.4915i 0.293929 1.00168i
\(551\) 15.8920 0.677021
\(552\) 6.71584 4.87934i 0.285845 0.207679i
\(553\) 1.07188 + 3.29890i 0.0455808 + 0.140283i
\(554\) −4.66854 + 14.3683i −0.198347 + 0.610450i
\(555\) −6.51079 4.73036i −0.276368 0.200793i
\(556\) 10.0365 + 7.29197i 0.425644 + 0.309248i
\(557\) 1.13082 3.48032i 0.0479145 0.147466i −0.924237 0.381820i \(-0.875298\pi\)
0.972151 + 0.234354i \(0.0752975\pi\)
\(558\) −1.78539 5.49486i −0.0755815 0.232616i
\(559\) 0.344981 0.250643i 0.0145911 0.0106011i
\(560\) 1.18343 0.0500089
\(561\) 11.8294 0.340020i 0.499438 0.0143557i
\(562\) −19.6027 −0.826890
\(563\) −10.6729 + 7.75435i −0.449811 + 0.326807i −0.789521 0.613723i \(-0.789671\pi\)
0.339710 + 0.940530i \(0.389671\pi\)
\(564\) −1.82346 5.61203i −0.0767814 0.236309i
\(565\) −2.72243 + 8.37879i −0.114534 + 0.352498i
\(566\) −15.6180 11.3471i −0.656472 0.476955i
\(567\) −0.248424 0.180491i −0.0104328 0.00757990i
\(568\) 7.14935 22.0034i 0.299980 0.923243i
\(569\) −3.15811 9.71966i −0.132395 0.407469i 0.862781 0.505578i \(-0.168721\pi\)
−0.995176 + 0.0981088i \(0.968721\pi\)
\(570\) −2.10101 + 1.52647i −0.0880016 + 0.0639369i
\(571\) 15.2983 0.640215 0.320107 0.947381i \(-0.396281\pi\)
0.320107 + 0.947381i \(0.396281\pi\)
\(572\) 2.14603 1.65544i 0.0897301 0.0692174i
\(573\) −23.2658 −0.971942
\(574\) 5.33471 3.87590i 0.222667 0.161777i
\(575\) 5.68258 + 17.4892i 0.236980 + 0.729350i
\(576\) 0.805205 2.47817i 0.0335502 0.103257i
\(577\) −30.6847 22.2937i −1.27742 0.928101i −0.277949 0.960596i \(-0.589655\pi\)
−0.999472 + 0.0324953i \(0.989655\pi\)
\(578\) 5.79570 + 4.21083i 0.241070 + 0.175147i
\(579\) −7.58931 + 23.3575i −0.315401 + 0.970705i
\(580\) −1.56178 4.80667i −0.0648494 0.199586i
\(581\) −4.29191 + 3.11826i −0.178059 + 0.129367i
\(582\) −14.3564 −0.595092
\(583\) 14.7302 + 10.0685i 0.610063 + 0.416993i
\(584\) −14.9883 −0.620221
\(585\) 0.627776 0.456106i 0.0259554 0.0188577i
\(586\) 3.63384 + 11.1838i 0.150113 + 0.461999i
\(587\) −11.8736 + 36.5432i −0.490076 + 1.50830i 0.334416 + 0.942426i \(0.391461\pi\)
−0.824492 + 0.565874i \(0.808539\pi\)
\(588\) −4.56555 3.31706i −0.188280 0.136793i
\(589\) 5.55282 + 4.03436i 0.228800 + 0.166233i
\(590\) −1.76774 + 5.44055i −0.0727768 + 0.223984i
\(591\) −5.26836 16.2144i −0.216711 0.666969i
\(592\) 41.6720 30.2765i 1.71271 1.24435i
\(593\) −11.7601 −0.482927 −0.241464 0.970410i \(-0.577627\pi\)
−0.241464 + 0.970410i \(0.577627\pi\)
\(594\) 1.87164 + 5.24272i 0.0767943 + 0.215112i
\(595\) −0.850216 −0.0348554
\(596\) 12.0433 8.74994i 0.493311 0.358412i
\(597\) −4.16861 12.8297i −0.170610 0.525083i
\(598\) −2.16877 + 6.67477i −0.0886874 + 0.272952i
\(599\) −36.5496 26.5548i −1.49338 1.08500i −0.972928 0.231108i \(-0.925765\pi\)
−0.520448 0.853893i \(-0.674235\pi\)
\(600\) 7.06351 + 5.13194i 0.288366 + 0.209511i
\(601\) −4.94125 + 15.2076i −0.201558 + 0.620331i 0.798280 + 0.602287i \(0.205744\pi\)
−0.999837 + 0.0180435i \(0.994256\pi\)
\(602\) −0.0679148 0.209020i −0.00276800 0.00851903i
\(603\) −0.00623397 + 0.00452924i −0.000253867 + 0.000184445i
\(604\) −1.86212 −0.0757684
\(605\) −8.52162 + 0.490290i −0.346453 + 0.0199331i
\(606\) −20.8999 −0.849002
\(607\) 3.47157 2.52224i 0.140907 0.102375i −0.515099 0.857131i \(-0.672245\pi\)
0.656005 + 0.754756i \(0.272245\pi\)
\(608\) −2.68994 8.27877i −0.109091 0.335749i
\(609\) −0.756279 + 2.32759i −0.0306460 + 0.0943186i
\(610\) 4.21525 + 3.06256i 0.170670 + 0.123999i
\(611\) −5.84177 4.24429i −0.236333 0.171706i
\(612\) 0.901063 2.77319i 0.0364233 0.112099i
\(613\) −13.6062 41.8757i −0.549551 1.69134i −0.709916 0.704286i \(-0.751267\pi\)
0.160365 0.987058i \(-0.448733\pi\)
\(614\) −37.0844 + 26.9434i −1.49661 + 1.08735i
\(615\) −9.92786 −0.400330
\(616\) 0.679783 + 1.90417i 0.0273892 + 0.0767211i
\(617\) 45.4122 1.82823 0.914113 0.405460i \(-0.132889\pi\)
0.914113 + 0.405460i \(0.132889\pi\)
\(618\) −6.23316 + 4.52866i −0.250735 + 0.182169i
\(619\) 2.43194 + 7.48473i 0.0977478 + 0.300837i 0.987960 0.154709i \(-0.0494440\pi\)
−0.890212 + 0.455546i \(0.849444\pi\)
\(620\) 0.674525 2.07598i 0.0270896 0.0833732i
\(621\) −3.38282 2.45776i −0.135748 0.0986267i
\(622\) −18.0061 13.0822i −0.721979 0.524548i
\(623\) 0.559677 1.72251i 0.0224230 0.0690109i
\(624\) 1.53476 + 4.72350i 0.0614395 + 0.189091i
\(625\) −13.2117 + 9.59885i −0.528467 + 0.383954i
\(626\) 23.0000 0.919266
\(627\) −5.45966 3.73181i −0.218038 0.149034i
\(628\) −10.5607 −0.421417
\(629\) −29.9386 + 21.7517i −1.19373 + 0.867297i
\(630\) −0.123587 0.380363i −0.00492384 0.0151540i
\(631\) 1.95698 6.02296i 0.0779061 0.239770i −0.904517 0.426437i \(-0.859769\pi\)
0.982423 + 0.186667i \(0.0597685\pi\)
\(632\) 18.1428 + 13.1815i 0.721683 + 0.524333i
\(633\) −18.5782 13.4978i −0.738416 0.536491i
\(634\) 13.6450 41.9949i 0.541911 1.66783i
\(635\) −2.84297 8.74975i −0.112820 0.347223i
\(636\) 3.55667 2.58407i 0.141031 0.102465i
\(637\) −6.90571 −0.273614
\(638\) 35.1303 27.0993i 1.39082 1.07287i
\(639\) −11.6537 −0.461013
\(640\) 8.22686 5.97716i 0.325195 0.236268i
\(641\) −2.06303 6.34935i −0.0814848 0.250784i 0.902012 0.431712i \(-0.142090\pi\)
−0.983496 + 0.180927i \(0.942090\pi\)
\(642\) −2.33718 + 7.19309i −0.0922410 + 0.283889i
\(643\) 0.298516 + 0.216884i 0.0117723 + 0.00855308i 0.593656 0.804719i \(-0.297684\pi\)
−0.581884 + 0.813272i \(0.697684\pi\)
\(644\) 0.848872 + 0.616742i 0.0334503 + 0.0243030i
\(645\) −0.102251 + 0.314696i −0.00402612 + 0.0123911i
\(646\) 3.69021 + 11.3573i 0.145189 + 0.446847i
\(647\) −16.9325 + 12.3022i −0.665684 + 0.483648i −0.868578 0.495553i \(-0.834965\pi\)
0.202894 + 0.979201i \(0.434965\pi\)
\(648\) −1.98528 −0.0779890
\(649\) −14.5612 + 0.418543i −0.571578 + 0.0164292i
\(650\) −7.38160 −0.289530
\(651\) −0.855137 + 0.621293i −0.0335155 + 0.0243504i
\(652\) −0.358832 1.10437i −0.0140529 0.0432505i
\(653\) 1.50895 4.64406i 0.0590496 0.181736i −0.917181 0.398471i \(-0.869541\pi\)
0.976230 + 0.216735i \(0.0695409\pi\)
\(654\) 19.2039 + 13.9525i 0.750933 + 0.545585i
\(655\) −1.68535 1.22448i −0.0658521 0.0478444i
\(656\) 19.6358 60.4328i 0.766649 2.35950i
\(657\) 2.33300 + 7.18023i 0.0910189 + 0.280128i
\(658\) −3.01085 + 2.18751i −0.117375 + 0.0852780i
\(659\) −23.2054 −0.903956 −0.451978 0.892029i \(-0.649281\pi\)
−0.451978 + 0.892029i \(0.649281\pi\)
\(660\) −0.592171 + 2.01806i −0.0230502 + 0.0785530i
\(661\) 4.13915 0.160994 0.0804971 0.996755i \(-0.474349\pi\)
0.0804971 + 0.996755i \(0.474349\pi\)
\(662\) 15.9213 11.5675i 0.618797 0.449582i
\(663\) −1.10263 3.39353i −0.0428224 0.131794i
\(664\) −10.5989 + 32.6200i −0.411317 + 1.26590i
\(665\) 0.384375 + 0.279265i 0.0149054 + 0.0108294i
\(666\) −14.0830 10.2319i −0.545705 0.396478i
\(667\) −10.2983 + 31.6951i −0.398754 + 1.22724i
\(668\) −0.822571 2.53161i −0.0318262 0.0979510i
\(669\) −8.12948 + 5.90642i −0.314304 + 0.228355i
\(670\) −0.0100360 −0.000387726
\(671\) −3.73580 + 12.7312i −0.144219 + 0.491484i
\(672\) 1.34055 0.0517126
\(673\) 25.9585 18.8600i 1.00063 0.726999i 0.0384050 0.999262i \(-0.487772\pi\)
0.962223 + 0.272264i \(0.0877723\pi\)
\(674\) −0.315764 0.971822i −0.0121628 0.0374332i
\(675\) 1.35901 4.18262i 0.0523085 0.160989i
\(676\) −0.661127 0.480337i −0.0254279 0.0184745i
\(677\) 31.5825 + 22.9461i 1.21382 + 0.881889i 0.995572 0.0940058i \(-0.0299672\pi\)
0.218244 + 0.975894i \(0.429967\pi\)
\(678\) −5.88869 + 18.1235i −0.226154 + 0.696030i
\(679\) 0.811625 + 2.49792i 0.0311473 + 0.0958615i
\(680\) −4.44704 + 3.23097i −0.170536 + 0.123902i
\(681\) 19.7682 0.757521
\(682\) 19.1544 0.550566i 0.733458 0.0210823i
\(683\) 32.1749 1.23114 0.615570 0.788082i \(-0.288926\pi\)
0.615570 + 0.788082i \(0.288926\pi\)
\(684\) −1.31825 + 0.957767i −0.0504047 + 0.0366211i
\(685\) −0.495528 1.52508i −0.0189332 0.0582703i
\(686\) −2.21473 + 6.81623i −0.0845587 + 0.260245i
\(687\) −4.00661 2.91097i −0.152862 0.111061i
\(688\) −1.71338 1.24484i −0.0653218 0.0474591i
\(689\) 1.66242 5.11640i 0.0633332 0.194919i
\(690\) −1.68291 5.17945i −0.0640671 0.197178i
\(691\) −15.1197 + 10.9851i −0.575182 + 0.417894i −0.836984 0.547227i \(-0.815683\pi\)
0.261802 + 0.965122i \(0.415683\pi\)
\(692\) 10.0303 0.381295
\(693\) 0.806390 0.622046i 0.0306322 0.0236296i
\(694\) −13.1552 −0.499364
\(695\) −9.53025 + 6.92413i −0.361503 + 0.262647i
\(696\) 4.88953 + 15.0484i 0.185337 + 0.570409i
\(697\) −14.1071 + 43.4171i −0.534343 + 1.64454i
\(698\) 15.5096 + 11.2684i 0.587047 + 0.426514i
\(699\) −10.4559 7.59667i −0.395479 0.287332i
\(700\) −0.341026 + 1.04957i −0.0128896 + 0.0396700i
\(701\) 5.47164 + 16.8400i 0.206661 + 0.636037i 0.999641 + 0.0267897i \(0.00852845\pi\)
−0.792980 + 0.609248i \(0.791472\pi\)
\(702\) 1.35790 0.986569i 0.0512505 0.0372356i
\(703\) 20.6796 0.779948
\(704\) 7.13469 + 4.87673i 0.268899 + 0.183799i
\(705\) 5.60317 0.211028
\(706\) 21.8319 15.8618i 0.821654 0.596967i
\(707\) 1.18156 + 3.63646i 0.0444370 + 0.136763i
\(708\) −1.10915 + 3.41361i −0.0416844 + 0.128291i
\(709\) −32.5437 23.6443i −1.22220 0.887982i −0.225921 0.974146i \(-0.572539\pi\)
−0.996281 + 0.0861635i \(0.972539\pi\)
\(710\) −12.2794 8.92149i −0.460837 0.334818i
\(711\) 3.49067 10.7432i 0.130910 0.402900i
\(712\) −3.61845 11.1364i −0.135607 0.417356i
\(713\) −11.6445 + 8.46023i −0.436090 + 0.316838i
\(714\) −1.83904 −0.0688242
\(715\) 0.865288 + 2.42379i 0.0323599 + 0.0906447i
\(716\) 14.2094 0.531031
\(717\) −7.00276 + 5.08780i −0.261523 + 0.190008i
\(718\) −15.6109 48.0453i −0.582593 1.79304i
\(719\) 14.6708 45.1520i 0.547127 1.68388i −0.168751 0.985659i \(-0.553973\pi\)
0.715878 0.698225i \(-0.246027\pi\)
\(720\) −3.11790 2.26529i −0.116197 0.0844223i
\(721\) 1.14034 + 0.828509i 0.0424686 + 0.0308553i
\(722\) −7.79258 + 23.9831i −0.290010 + 0.892558i
\(723\) 2.75792 + 8.48802i 0.102568 + 0.315673i
\(724\) 4.85034 3.52398i 0.180261 0.130968i
\(725\) −35.0514 −1.30178
\(726\) −18.4325 + 1.06051i −0.684093 + 0.0393592i
\(727\) 34.2838 1.27152 0.635758 0.771889i \(-0.280688\pi\)
0.635758 + 0.771889i \(0.280688\pi\)
\(728\) 0.493191 0.358324i 0.0182789 0.0132804i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −3.03858 + 9.35178i −0.112463 + 0.346125i
\(731\) 1.23095 + 0.894338i 0.0455284 + 0.0330783i
\(732\) 2.64481 + 1.92157i 0.0977550 + 0.0710232i
\(733\) −4.62571 + 14.2365i −0.170855 + 0.525837i −0.999420 0.0340559i \(-0.989158\pi\)
0.828565 + 0.559893i \(0.189158\pi\)
\(734\) −15.3143 47.1325i −0.565260 1.73969i
\(735\) 4.33524 3.14974i 0.159908 0.116180i
\(736\) 18.2544 0.672865
\(737\) −0.00859252 0.0240688i −0.000316509 0.000886587i
\(738\) −21.4742 −0.790477
\(739\) 12.2801 8.92201i 0.451731 0.328201i −0.338548 0.940949i \(-0.609936\pi\)
0.790279 + 0.612748i \(0.209936\pi\)
\(740\) −2.03229 6.25474i −0.0747084 0.229929i
\(741\) −0.616165 + 1.89636i −0.0226354 + 0.0696645i
\(742\) −2.24316 1.62975i −0.0823491 0.0598301i
\(743\) −0.382040 0.277569i −0.0140157 0.0101830i 0.580755 0.814078i \(-0.302757\pi\)
−0.594771 + 0.803895i \(0.702757\pi\)
\(744\) −2.11176 + 6.49934i −0.0774210 + 0.238277i
\(745\) 4.36806 + 13.4435i 0.160033 + 0.492532i
\(746\) 20.7350 15.0649i 0.759164 0.551565i
\(747\) 17.2766 0.632116
\(748\) 7.98405 + 5.45730i 0.291926 + 0.199539i
\(749\) 1.38368 0.0505587
\(750\) 9.90245 7.19455i 0.361586 0.262708i
\(751\) −8.46110 26.0406i −0.308750 0.950234i −0.978251 0.207424i \(-0.933492\pi\)
0.669501 0.742811i \(-0.266508\pi\)
\(752\) −11.0822 + 34.1076i −0.404127 + 1.24377i
\(753\) 9.12966 + 6.63309i 0.332703 + 0.241723i
\(754\) −10.8226 7.86305i −0.394134 0.286355i
\(755\) 0.546398 1.68164i 0.0198855 0.0612012i
\(756\) −0.0775435 0.238654i −0.00282023 0.00867978i
\(757\) 32.6314 23.7081i 1.18601 0.861685i 0.193171 0.981165i \(-0.438123\pi\)
0.992837 + 0.119480i \(0.0381228\pi\)
\(758\) −9.75610 −0.354358
\(759\) 10.9807 8.47048i 0.398575 0.307459i
\(760\) 3.07173 0.111423
\(761\) 27.5431 20.0112i 0.998436 0.725406i 0.0366837 0.999327i \(-0.488321\pi\)
0.961752 + 0.273921i \(0.0883206\pi\)
\(762\) −6.14941 18.9259i −0.222770 0.685614i
\(763\) 1.34197 4.13016i 0.0485825 0.149522i
\(764\) −15.3816 11.1754i −0.556488 0.404312i
\(765\) 2.24001 + 1.62746i 0.0809878 + 0.0588411i
\(766\) −10.7281 + 33.0176i −0.387621 + 1.19297i
\(767\) 1.35726 + 4.17722i 0.0490078 + 0.150831i
\(768\) 13.5788 9.86557i 0.489982 0.355993i
\(769\) 5.84163 0.210654 0.105327 0.994438i \(-0.466411\pi\)
0.105327 + 0.994438i \(0.466411\pi\)
\(770\) 1.32589 0.0381111i 0.0477819 0.00137343i
\(771\) −10.0548 −0.362116
\(772\) −16.2370 + 11.7968i −0.584381 + 0.424578i
\(773\) −3.21738 9.90207i −0.115721 0.356153i 0.876376 0.481628i \(-0.159954\pi\)
−0.992097 + 0.125475i \(0.959954\pi\)
\(774\) −0.221171 + 0.680695i −0.00794983 + 0.0244671i
\(775\) −12.2473 8.89820i −0.439937 0.319633i
\(776\) 13.7377 + 9.98105i 0.493156 + 0.358299i
\(777\) −0.984118 + 3.02880i −0.0353050 + 0.108658i
\(778\) 15.1354 + 46.5819i 0.542629 + 1.67004i
\(779\) 20.6386 14.9948i 0.739455 0.537246i
\(780\) 0.634124 0.0227053
\(781\) 10.8827 37.0872i 0.389413 1.32708i
\(782\) −25.0424 −0.895514
\(783\) 6.44795 4.68471i 0.230431 0.167418i
\(784\) 10.5986 + 32.6191i 0.378521 + 1.16497i
\(785\) 3.09880 9.53714i 0.110601 0.340395i
\(786\) −3.64546 2.64858i −0.130029 0.0944717i
\(787\) 31.9300 + 23.1985i 1.13818 + 0.826936i 0.986865 0.161549i \(-0.0516491\pi\)
0.151315 + 0.988486i \(0.451649\pi\)
\(788\) 4.30529 13.2503i 0.153370 0.472023i
\(789\) 2.46995 + 7.60174i 0.0879327 + 0.270629i
\(790\) 11.9025 8.64770i 0.423473 0.307671i
\(791\) 3.48629 0.123958
\(792\) 1.85393 6.31803i 0.0658767 0.224501i
\(793\) 4.00046 0.142060
\(794\) −51.6831 + 37.5500i −1.83416 + 1.33260i
\(795\) 1.28999 + 3.97020i 0.0457514 + 0.140808i
\(796\) 3.40658 10.4844i 0.120743 0.371608i
\(797\) 20.5407 + 14.9237i 0.727589 + 0.528624i 0.888800 0.458296i \(-0.151540\pi\)
−0.161211 + 0.986920i \(0.551540\pi\)
\(798\) 0.831413 + 0.604057i 0.0294317 + 0.0213834i
\(799\) 7.96186 24.5041i 0.281670 0.866892i
\(800\) 5.93293 + 18.2597i 0.209761 + 0.645578i
\(801\) −4.77174 + 3.46687i −0.168601 + 0.122496i
\(802\) −2.87207 −0.101416
\(803\) −25.0293 + 0.719435i −0.883266 + 0.0253883i
\(804\) −0.00629700 −0.000222078
\(805\) −0.806051 + 0.585630i −0.0284096 + 0.0206408i
\(806\) −1.78539 5.49486i −0.0628876 0.193548i
\(807\) −2.27595 + 7.00464i −0.0801171 + 0.246575i
\(808\) 19.9993 + 14.5303i 0.703573 + 0.511176i
\(809\) 9.97535 + 7.24751i 0.350715 + 0.254809i 0.749169 0.662379i \(-0.230453\pi\)
−0.398454 + 0.917188i \(0.630453\pi\)
\(810\) −0.402474 + 1.23869i −0.0141415 + 0.0435231i
\(811\) 15.4332 + 47.4984i 0.541932 + 1.66789i 0.728176 + 0.685390i \(0.240368\pi\)
−0.186244 + 0.982503i \(0.559632\pi\)
\(812\) −1.61802 + 1.17556i −0.0567814 + 0.0412541i
\(813\) −6.44568 −0.226060
\(814\) 45.7137 35.2633i 1.60226 1.23598i
\(815\) 1.10263 0.0386234
\(816\) −14.3371 + 10.4165i −0.501899 + 0.364651i
\(817\) −0.262745 0.808645i −0.00919228 0.0282909i
\(818\) −12.3769 + 38.0921i −0.432748 + 1.33186i
\(819\) −0.248424 0.180491i −0.00868064 0.00630686i
\(820\) −6.56357 4.76872i −0.229210 0.166531i
\(821\) 2.95508 9.09479i 0.103133 0.317410i −0.886155 0.463389i \(-0.846633\pi\)
0.989288 + 0.145979i \(0.0466332\pi\)
\(822\) −1.07184 3.29878i −0.0373847 0.115058i
\(823\) 6.30685 4.58220i 0.219843 0.159725i −0.472413 0.881377i \(-0.656617\pi\)
0.692256 + 0.721652i \(0.256617\pi\)
\(824\) 9.11304 0.317468
\(825\) 12.0418 + 8.23089i 0.419243 + 0.286563i
\(826\) 2.26373 0.0787654
\(827\) −29.1094 + 21.1492i −1.01223 + 0.735430i −0.964676 0.263438i \(-0.915143\pi\)
−0.0475565 + 0.998869i \(0.515143\pi\)
\(828\) −1.05592 3.24979i −0.0366957 0.112938i
\(829\) 7.95549 24.4845i 0.276306 0.850381i −0.712565 0.701606i \(-0.752467\pi\)
0.988871 0.148776i \(-0.0475332\pi\)
\(830\) 18.2042 + 13.2261i 0.631876 + 0.459085i
\(831\) −7.28194 5.29064i −0.252608 0.183530i
\(832\) 0.805205 2.47817i 0.0279155 0.0859150i
\(833\) −7.61441 23.4347i −0.263824 0.811966i
\(834\) −20.6142 + 14.9771i −0.713810 + 0.518613i
\(835\) 2.52762 0.0874718
\(836\) −1.81700 5.08967i −0.0628422 0.176030i
\(837\) 3.44225 0.118981
\(838\) −21.4345 + 15.5731i −0.740444 + 0.537964i
\(839\) −4.49487 13.8338i −0.155180 0.477595i 0.842999 0.537915i \(-0.180788\pi\)
−0.998179 + 0.0603199i \(0.980788\pi\)
\(840\) −0.146180 + 0.449894i −0.00504367 + 0.0155228i
\(841\) −27.9293 20.2918i −0.963078 0.699717i
\(842\) −1.00096 0.727243i −0.0344955 0.0250624i
\(843\) 3.60902 11.1074i 0.124301 0.382560i
\(844\) −5.79902 17.8476i −0.199611 0.614338i
\(845\) 0.627776 0.456106i 0.0215962 0.0156905i
\(846\) 12.1198 0.416687
\(847\) 1.22658 + 3.14718i 0.0421459 + 0.108138i
\(848\) −26.7188 −0.917526
\(849\) 9.30499 6.76047i 0.319346 0.232019i
\(850\) −8.13914 25.0497i −0.279170 0.859198i
\(851\) −13.4009 + 41.2436i −0.459376 + 1.41381i
\(852\) −7.70456 5.59769i −0.263954 0.191774i
\(853\) 3.17471 + 2.30656i 0.108700 + 0.0789751i 0.640807 0.767702i \(-0.278600\pi\)
−0.532107 + 0.846677i \(0.678600\pi\)
\(854\) 0.637143 1.96092i 0.0218026 0.0671015i
\(855\) −0.478128 1.47153i −0.0163516 0.0503251i
\(856\) 7.23735 5.25824i 0.247367 0.179723i
\(857\) 22.1704 0.757327 0.378663 0.925534i \(-0.376384\pi\)
0.378663 + 0.925534i \(0.376384\pi\)
\(858\) 1.87164 + 5.24272i 0.0638967 + 0.178984i
\(859\) −41.2926 −1.40888 −0.704442 0.709762i \(-0.748803\pi\)
−0.704442 + 0.709762i \(0.748803\pi\)
\(860\) −0.218761 + 0.158939i −0.00745967 + 0.00541977i
\(861\) 1.21402 + 3.73638i 0.0413738 + 0.127336i
\(862\) 15.0615 46.3546i 0.512998 1.57884i
\(863\) −3.09399 2.24791i −0.105321 0.0765199i 0.533878 0.845561i \(-0.320734\pi\)
−0.639199 + 0.769041i \(0.720734\pi\)
\(864\) −3.53186 2.56604i −0.120156 0.0872986i
\(865\) −2.94318 + 9.05817i −0.100071 + 0.307987i
\(866\) 3.00272 + 9.24142i 0.102037 + 0.314036i
\(867\) −3.45301 + 2.50876i −0.117270 + 0.0852019i
\(868\) −0.863784 −0.0293187
\(869\) 30.9298 + 21.1413i 1.04922 + 0.717169i
\(870\) 10.3805 0.351933
\(871\) −0.00623397 + 0.00452924i −0.000211230 + 0.000153468i
\(872\) −8.67615 26.7025i −0.293812 0.904259i
\(873\) 2.64313 8.13473i 0.0894565 0.275319i
\(874\) 11.3215 + 8.22552i 0.382954 + 0.278232i
\(875\) −1.81163 1.31623i −0.0612444 0.0444966i
\(876\) −1.90652 + 5.86767i −0.0644153 + 0.198250i
\(877\) −9.37478 28.8526i −0.316564 0.974284i −0.975106 0.221740i \(-0.928827\pi\)
0.658542 0.752544i \(-0.271173\pi\)
\(878\) −33.0010 + 23.9766i −1.11373 + 0.809173i
\(879\) −7.00608 −0.236309
\(880\) 10.1208 7.80712i 0.341171 0.263178i
\(881\) −0.995648 −0.0335442 −0.0167721 0.999859i \(-0.505339\pi\)
−0.0167721 + 0.999859i \(0.505339\pi\)
\(882\) 9.37723 6.81296i 0.315748 0.229404i
\(883\) 13.8362 + 42.5833i 0.465624 + 1.43304i 0.858196 + 0.513322i \(0.171585\pi\)
−0.392572 + 0.919721i \(0.628415\pi\)
\(884\) 0.901063 2.77319i 0.0303060 0.0932723i
\(885\) −2.75731 2.00330i −0.0926859 0.0673403i
\(886\) 43.1767 + 31.3697i 1.45055 + 1.05389i
\(887\) 12.3998 38.1626i 0.416343 1.28137i −0.494700 0.869064i \(-0.664722\pi\)
0.911044 0.412310i \(-0.135278\pi\)
\(888\) 6.36256 + 19.5819i 0.213514 + 0.657127i
\(889\) −2.94534 + 2.13992i −0.0987837 + 0.0717705i
\(890\) −7.68201 −0.257502
\(891\) −3.31526 + 0.0952926i −0.111065 + 0.00319242i
\(892\) −8.21169 −0.274948
\(893\) −11.6482 + 8.46291i −0.389792 + 0.283200i
\(894\) 9.44823 + 29.0787i 0.315996 + 0.972536i
\(895\) −4.16946 + 12.8323i −0.139370 + 0.428935i
\(896\) −3.25554 2.36529i −0.108760 0.0790187i
\(897\) −3.38282 2.45776i −0.112949 0.0820624i
\(898\) −5.84275 + 17.9821i −0.194975 + 0.600072i
\(899\) −8.47789 26.0923i −0.282754 0.870226i
\(900\) 2.90754 2.11245i 0.0969182 0.0704152i
\(901\) 19.1957 0.639502
\(902\) 20.0535 68.3405i 0.667709 2.27549i
\(903\) 0.130940 0.00435742
\(904\) 18.2350 13.2485i 0.606488 0.440639i
\(905\) 1.75921 + 5.41428i 0.0584780 + 0.179977i
\(906\) 1.18187 3.63743i 0.0392651 0.120846i
\(907\) 46.2080 + 33.5721i 1.53431 + 1.11474i 0.953780 + 0.300505i \(0.0971553\pi\)
0.580532 + 0.814238i \(0.302845\pi\)
\(908\) 13.0693 + 9.49541i 0.433720 + 0.315116i
\(909\) 3.84785 11.8425i 0.127625 0.392790i
\(910\) −0.123587 0.380363i −0.00409688 0.0126089i
\(911\) 17.3726 12.6220i 0.575582 0.418184i −0.261547 0.965191i \(-0.584233\pi\)
0.837128 + 0.547006i \(0.184233\pi\)
\(912\) 9.90312 0.327925
\(913\) −16.1336 + 54.9816i −0.533943 + 1.81963i
\(914\) −14.2406 −0.471038
\(915\) −2.51139 + 1.82463i −0.0830241 + 0.0603205i
\(916\) −1.25063 3.84904i −0.0413220 0.127176i
\(917\) −0.254744 + 0.784022i −0.00841239 + 0.0258907i
\(918\) 4.84520 + 3.52025i 0.159916 + 0.116185i
\(919\) −31.0248 22.5408i −1.02341 0.743553i −0.0564332 0.998406i \(-0.517973\pi\)
−0.966980 + 0.254853i \(0.917973\pi\)
\(920\) −1.99055 + 6.12627i −0.0656263 + 0.201977i
\(921\) −8.43933 25.9736i −0.278085 0.855859i
\(922\) −40.0826 + 29.1217i −1.32005 + 0.959072i
\(923\) −11.6537 −0.383586
\(924\) 0.831917 0.0239124i 0.0273681 0.000786659i
\(925\) −45.6111 −1.49968
\(926\) −20.6925 + 15.0340i −0.679998 + 0.494047i
\(927\) −1.41848 4.36565i −0.0465891 0.143387i
\(928\) −10.7521 + 33.0914i −0.352953 + 1.08628i
\(929\) −47.9260 34.8203i −1.57240 1.14242i −0.924809 0.380431i \(-0.875776\pi\)
−0.647593 0.761986i \(-0.724224\pi\)
\(930\) 3.62706 + 2.63522i 0.118936 + 0.0864122i
\(931\) −4.25505 + 13.0957i −0.139454 + 0.429194i
\(932\) −3.26373 10.0447i −0.106907 0.329026i
\(933\) 10.7278 7.79421i 0.351213 0.255171i
\(934\) −22.2451 −0.727882
\(935\) −7.27113 + 5.60892i −0.237791 + 0.183431i
\(936\) −1.98528 −0.0648908
\(937\) −32.3622 + 23.5125i −1.05723 + 0.768121i −0.973573 0.228374i \(-0.926659\pi\)
−0.0836539 + 0.996495i \(0.526659\pi\)
\(938\) 0.00122725 + 0.00377710i 4.00712e−5 + 0.000123327i
\(939\) −4.23450 + 13.0325i −0.138188 + 0.425298i
\(940\) 3.70440 + 2.69141i 0.120824 + 0.0877840i
\(941\) 1.11870 + 0.812785i 0.0364687 + 0.0264960i 0.605870 0.795563i \(-0.292825\pi\)
−0.569402 + 0.822059i \(0.692825\pi\)
\(942\) 6.70279 20.6291i 0.218389 0.672131i
\(943\) 16.5315 + 50.8788i 0.538340 + 1.65684i
\(944\) 17.6480 12.8220i 0.574394 0.417322i
\(945\) 0.238278 0.00775117
\(946\) −1.95973 1.33953i −0.0637164 0.0435517i
\(947\) −7.84116 −0.254803 −0.127402 0.991851i \(-0.540664\pi\)
−0.127402 + 0.991851i \(0.540664\pi\)
\(948\) 7.46811 5.42590i 0.242553 0.176225i
\(949\) 2.33300 + 7.18023i 0.0757323 + 0.233080i
\(950\) −4.54828 + 13.9982i −0.147566 + 0.454161i
\(951\) 21.2833 + 15.4632i 0.690159 + 0.501430i
\(952\) 1.75979 + 1.27856i 0.0570351 + 0.0414384i
\(953\) 2.93875 9.04455i 0.0951955 0.292982i −0.892109 0.451820i \(-0.850775\pi\)
0.987305 + 0.158838i \(0.0507749\pi\)
\(954\) 2.79029 + 8.58763i 0.0903390 + 0.278035i
\(955\) 14.6057 10.6117i 0.472630 0.343386i
\(956\) −7.07357 −0.228776
\(957\) 8.88745 + 24.8950i 0.287290 + 0.804741i
\(958\) −4.02539 −0.130054
\(959\) −0.513373 + 0.372987i −0.0165777 + 0.0120444i
\(960\) 0.624818 + 1.92299i 0.0201659 + 0.0620643i
\(961\) −5.91797 + 18.2136i −0.190902 + 0.587536i
\(962\) −14.0830 10.2319i −0.454054 0.329889i
\(963\) −3.64551 2.64862i −0.117475 0.0853505i
\(964\) −2.25377 + 6.93639i −0.0725890 + 0.223406i
\(965\) −5.88911 18.1248i −0.189577 0.583458i
\(966\) −1.74351 + 1.26673i −0.0560965 + 0.0407565i
\(967\) −29.1462 −0.937277 −0.468639 0.883390i \(-0.655255\pi\)
−0.468639 + 0.883390i \(0.655255\pi\)
\(968\) 18.3755 + 11.8001i 0.590610 + 0.379269i
\(969\) −7.11476 −0.228559
\(970\) 9.01260 6.54804i 0.289377 0.210245i
\(971\) 5.81365 + 17.8926i 0.186569 + 0.574200i 0.999972 0.00750047i \(-0.00238750\pi\)
−0.813403 + 0.581701i \(0.802387\pi\)
\(972\) −0.252528 + 0.777201i −0.00809983 + 0.0249287i
\(973\) 3.77132 + 2.74002i 0.120903 + 0.0878411i
\(974\) 52.8324 + 38.3850i 1.69286 + 1.22993i
\(975\) 1.35901 4.18262i 0.0435233 0.133951i
\(976\) −6.13974 18.8962i −0.196528 0.604852i
\(977\) −31.8476 + 23.1387i −1.01890 + 0.740271i −0.966056 0.258332i \(-0.916827\pi\)
−0.0528396 + 0.998603i \(0.516827\pi\)
\(978\) 2.38501 0.0762642
\(979\) −6.57707 18.4233i −0.210204 0.588811i
\(980\) 4.37907 0.139884
\(981\) −11.4415 + 8.31271i −0.365298 + 0.265404i
\(982\) 1.90191 + 5.85347i 0.0606923 + 0.186792i
\(983\) −1.02851 + 3.16542i −0.0328043 + 0.100961i −0.966118 0.258101i \(-0.916903\pi\)
0.933314 + 0.359062i \(0.116903\pi\)
\(984\) 20.5488 + 14.9296i 0.655073 + 0.475938i
\(985\) 10.7028 + 7.77605i 0.341020 + 0.247766i
\(986\) 14.7503 45.3967i 0.469745 1.44573i
\(987\) −0.685181 2.10877i −0.0218095 0.0671229i
\(988\) −1.31825 + 0.957767i −0.0419392 + 0.0304706i
\(989\) 1.78303 0.0566971
\(990\) −3.56621 2.43759i −0.113342 0.0774717i
\(991\) −15.7573 −0.500546 −0.250273 0.968175i \(-0.580520\pi\)
−0.250273 + 0.968175i \(0.580520\pi\)
\(992\) −12.1575 + 8.83295i −0.386001 + 0.280446i
\(993\) 3.62321 + 11.1511i 0.114979 + 0.353869i
\(994\) −1.85605 + 5.71234i −0.0588704 + 0.181184i
\(995\) 8.46864 + 6.15283i 0.268474 + 0.195058i
\(996\) 11.4220 + 8.29856i 0.361920 + 0.262950i
\(997\) −2.94253 + 9.05617i −0.0931908 + 0.286812i −0.986778 0.162078i \(-0.948180\pi\)
0.893587 + 0.448890i \(0.148180\pi\)
\(998\) 9.50249 + 29.2457i 0.300796 + 0.925755i
\(999\) 8.39047 6.09603i 0.265463 0.192870i
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 429.2.n.c.157.3 28
11.2 odd 10 4719.2.a.bo.1.5 14
11.4 even 5 inner 429.2.n.c.235.3 yes 28
11.9 even 5 4719.2.a.bp.1.10 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.c.157.3 28 1.1 even 1 trivial
429.2.n.c.235.3 yes 28 11.4 even 5 inner
4719.2.a.bo.1.5 14 11.2 odd 10
4719.2.a.bp.1.10 14 11.9 even 5