Properties

Label 130.2.m.a.69.4
Level $130$
Weight $2$
Character 130.69
Analytic conductor $1.038$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [130,2,Mod(49,130)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(130, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("130.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 130.m (of order \(6\), degree \(2\), 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: \(1.03805522628\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.50027374224.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 69.4
Root \(-2.40987i\) of defining polynomial
Character \(\chi\) \(=\) 130.69
Dual form 130.2.m.a.49.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(2.08700 + 1.20493i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.10653 - 0.750022i) q^{5} +(-2.08700 + 1.20493i) q^{6} +(-0.702803 - 1.21729i) q^{7} +1.00000 q^{8} +(1.40373 + 2.43133i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(2.08700 + 1.20493i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.10653 - 0.750022i) q^{5} +(-2.08700 + 1.20493i) q^{6} +(-0.702803 - 1.21729i) q^{7} +1.00000 q^{8} +(1.40373 + 2.43133i) q^{9} +(-0.403726 + 2.19932i) q^{10} +(-4.59726 - 2.65423i) q^{11} -2.40987i q^{12} +(-1.58700 + 3.23750i) q^{13} +1.40561 q^{14} +(5.30006 + 0.972927i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.09726 + 3.52026i) q^{17} -2.80745 q^{18} +(2.28793 - 1.32094i) q^{19} +(-1.70280 - 1.44930i) q^{20} -3.38732i q^{21} +(4.59726 - 2.65423i) q^{22} +(2.30933 + 1.33329i) q^{23} +(2.08700 + 1.20493i) q^{24} +(3.87493 - 3.15989i) q^{25} +(-2.01026 - 2.99314i) q^{26} -0.464013i q^{27} +(-0.702803 + 1.21729i) q^{28} +(-2.10653 + 3.64862i) q^{29} +(-3.49261 + 4.10353i) q^{30} -5.07645i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-6.39634 - 11.0788i) q^{33} -7.04051i q^{34} +(-2.39347 - 2.03714i) q^{35} +(1.40373 - 2.43133i) q^{36} +(0.412995 - 0.715328i) q^{37} +2.64187i q^{38} +(-7.21306 + 4.84445i) q^{39} +(2.10653 - 0.750022i) q^{40} +(2.43440 + 1.40550i) q^{41} +(2.93351 + 1.69366i) q^{42} +(4.57586 - 2.64187i) q^{43} +5.30846i q^{44} +(4.78054 + 4.06883i) q^{45} +(-2.30933 + 1.33329i) q^{46} +1.79070 q^{47} +(-2.08700 + 1.20493i) q^{48} +(2.51214 - 4.35115i) q^{49} +(0.799077 + 4.93573i) q^{50} -16.9667 q^{51} +(3.59726 - 0.244364i) q^{52} +7.93952i q^{53} +(0.401847 + 0.232006i) q^{54} +(-11.6750 - 2.14317i) q^{55} +(-0.702803 - 1.21729i) q^{56} +6.36656 q^{57} +(-2.10653 - 3.64862i) q^{58} +(5.59815 - 3.23210i) q^{59} +(-1.80745 - 5.07645i) q^{60} +(7.36754 + 12.7610i) q^{61} +(4.39634 + 2.53823i) q^{62} +(1.97309 - 3.41749i) q^{63} +1.00000 q^{64} +(-0.914875 + 8.01018i) q^{65} +12.7927 q^{66} +(-2.00000 + 3.46410i) q^{67} +(6.09726 + 3.52026i) q^{68} +(3.21306 + 5.56518i) q^{69} +(2.96095 - 1.05424i) q^{70} +(-8.34802 + 4.81973i) q^{71} +(1.40373 + 2.43133i) q^{72} +7.04281 q^{73} +(0.412995 + 0.715328i) q^{74} +(11.8945 - 1.92567i) q^{75} +(-2.28793 - 1.32094i) q^{76} +7.46160i q^{77} +(-0.588885 - 8.66892i) q^{78} +4.05956 q^{79} +(-0.403726 + 2.19932i) q^{80} +(4.77028 - 8.26237i) q^{81} +(-2.43440 + 1.40550i) q^{82} -8.55910 q^{83} +(-2.93351 + 1.69366i) q^{84} +(-10.2038 + 11.9886i) q^{85} +5.28374i q^{86} +(-8.79268 + 5.07645i) q^{87} +(-4.59726 - 2.65423i) q^{88} +(-13.1289 - 7.57999i) q^{89} +(-5.91398 + 2.10565i) q^{90} +(5.05633 - 0.343480i) q^{91} -2.66659i q^{92} +(6.11679 - 10.5946i) q^{93} +(-0.895350 + 1.55079i) q^{94} +(3.82886 - 4.49859i) q^{95} -2.40987i q^{96} +(-2.18328 - 3.78155i) q^{97} +(2.51214 + 4.35115i) q^{98} -14.9033i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9} - 3 q^{11} + 4 q^{13} - 10 q^{14} - 2 q^{15} - 4 q^{16} - 15 q^{17} - 16 q^{18} + 9 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} + 5 q^{28} - 3 q^{29} + 10 q^{30} - 4 q^{32} - 10 q^{33} - 33 q^{35} + 8 q^{36} + 20 q^{37} - 30 q^{39} + 3 q^{40} + 21 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{45} + 6 q^{46} + 6 q^{47} - 15 q^{49} - q^{50} - 20 q^{51} - 5 q^{52} + 18 q^{54} - 23 q^{55} + 5 q^{56} + 24 q^{57} - 3 q^{58} + 30 q^{59} - 8 q^{60} - 5 q^{61} - 6 q^{62} - 25 q^{63} + 8 q^{64} - 6 q^{65} + 20 q^{66} - 16 q^{67} + 15 q^{68} - 2 q^{69} + 18 q^{70} + 8 q^{72} + 26 q^{73} + 20 q^{74} + 72 q^{75} - 9 q^{76} + 30 q^{78} + 4 q^{79} + 8 q^{81} - 21 q^{82} - 48 q^{83} - 6 q^{84} - 34 q^{85} + 12 q^{87} - 3 q^{88} - 39 q^{89} - 27 q^{90} + 19 q^{91} + 18 q^{93} - 3 q^{94} + 9 q^{95} - 4 q^{97} - 15 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 2.08700 + 1.20493i 1.20493 + 0.695668i 0.961648 0.274287i \(-0.0884417\pi\)
0.243285 + 0.969955i \(0.421775\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.10653 0.750022i 0.942069 0.335420i
\(6\) −2.08700 + 1.20493i −0.852016 + 0.491912i
\(7\) −0.702803 1.21729i −0.265635 0.460093i 0.702095 0.712083i \(-0.252248\pi\)
−0.967730 + 0.251991i \(0.918915\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.40373 + 2.43133i 0.467909 + 0.810442i
\(10\) −0.403726 + 2.19932i −0.127670 + 0.695486i
\(11\) −4.59726 2.65423i −1.38613 0.800280i −0.393250 0.919432i \(-0.628649\pi\)
−0.992876 + 0.119151i \(0.961983\pi\)
\(12\) 2.40987i 0.695668i
\(13\) −1.58700 + 3.23750i −0.440156 + 0.897921i
\(14\) 1.40561 0.375664
\(15\) 5.30006 + 0.972927i 1.36847 + 0.251209i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.09726 + 3.52026i −1.47880 + 0.853787i −0.999712 0.0239782i \(-0.992367\pi\)
−0.479091 + 0.877766i \(0.659033\pi\)
\(18\) −2.80745 −0.661723
\(19\) 2.28793 1.32094i 0.524887 0.303044i −0.214045 0.976824i \(-0.568664\pi\)
0.738932 + 0.673780i \(0.235331\pi\)
\(20\) −1.70280 1.44930i −0.380758 0.324073i
\(21\) 3.38732i 0.739174i
\(22\) 4.59726 2.65423i 0.980139 0.565884i
\(23\) 2.30933 + 1.33329i 0.481529 + 0.278011i 0.721054 0.692879i \(-0.243658\pi\)
−0.239524 + 0.970890i \(0.576992\pi\)
\(24\) 2.08700 + 1.20493i 0.426008 + 0.245956i
\(25\) 3.87493 3.15989i 0.774987 0.631978i
\(26\) −2.01026 2.99314i −0.394244 0.587003i
\(27\) 0.464013i 0.0892993i
\(28\) −0.702803 + 1.21729i −0.132817 + 0.230046i
\(29\) −2.10653 + 3.64862i −0.391173 + 0.677531i −0.992605 0.121393i \(-0.961264\pi\)
0.601432 + 0.798924i \(0.294597\pi\)
\(30\) −3.49261 + 4.10353i −0.637661 + 0.749198i
\(31\) 5.07645i 0.911758i −0.890042 0.455879i \(-0.849325\pi\)
0.890042 0.455879i \(-0.150675\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −6.39634 11.0788i −1.11346 1.92857i
\(34\) 7.04051i 1.20744i
\(35\) −2.39347 2.03714i −0.404570 0.344340i
\(36\) 1.40373 2.43133i 0.233954 0.405221i
\(37\) 0.412995 0.715328i 0.0678960 0.117599i −0.830079 0.557646i \(-0.811705\pi\)
0.897975 + 0.440047i \(0.145038\pi\)
\(38\) 2.64187i 0.428568i
\(39\) −7.21306 + 4.84445i −1.15501 + 0.775732i
\(40\) 2.10653 0.750022i 0.333072 0.118589i
\(41\) 2.43440 + 1.40550i 0.380189 + 0.219502i 0.677901 0.735154i \(-0.262890\pi\)
−0.297711 + 0.954656i \(0.596223\pi\)
\(42\) 2.93351 + 1.69366i 0.452650 + 0.261338i
\(43\) 4.57586 2.64187i 0.697812 0.402882i −0.108720 0.994072i \(-0.534675\pi\)
0.806532 + 0.591191i \(0.201342\pi\)
\(44\) 5.30846i 0.800280i
\(45\) 4.78054 + 4.06883i 0.712641 + 0.606546i
\(46\) −2.30933 + 1.33329i −0.340493 + 0.196583i
\(47\) 1.79070 0.261200 0.130600 0.991435i \(-0.458310\pi\)
0.130600 + 0.991435i \(0.458310\pi\)
\(48\) −2.08700 + 1.20493i −0.301233 + 0.173917i
\(49\) 2.51214 4.35115i 0.358877 0.621592i
\(50\) 0.799077 + 4.93573i 0.113007 + 0.698018i
\(51\) −16.9667 −2.37581
\(52\) 3.59726 0.244364i 0.498850 0.0338872i
\(53\) 7.93952i 1.09058i 0.838248 + 0.545288i \(0.183580\pi\)
−0.838248 + 0.545288i \(0.816420\pi\)
\(54\) 0.401847 + 0.232006i 0.0546844 + 0.0315721i
\(55\) −11.6750 2.14317i −1.57426 0.288984i
\(56\) −0.702803 1.21729i −0.0939160 0.162667i
\(57\) 6.36656 0.843271
\(58\) −2.10653 3.64862i −0.276601 0.479087i
\(59\) 5.59815 3.23210i 0.728817 0.420783i −0.0891719 0.996016i \(-0.528422\pi\)
0.817989 + 0.575233i \(0.195089\pi\)
\(60\) −1.80745 5.07645i −0.233341 0.655367i
\(61\) 7.36754 + 12.7610i 0.943317 + 1.63387i 0.759086 + 0.650991i \(0.225646\pi\)
0.184232 + 0.982883i \(0.441020\pi\)
\(62\) 4.39634 + 2.53823i 0.558335 + 0.322355i
\(63\) 1.97309 3.41749i 0.248586 0.430563i
\(64\) 1.00000 0.125000
\(65\) −0.914875 + 8.01018i −0.113476 + 0.993541i
\(66\) 12.7927 1.57467
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 6.09726 + 3.52026i 0.739401 + 0.426894i
\(69\) 3.21306 + 5.56518i 0.386807 + 0.669969i
\(70\) 2.96095 1.05424i 0.353901 0.126005i
\(71\) −8.34802 + 4.81973i −0.990728 + 0.571997i −0.905492 0.424364i \(-0.860498\pi\)
−0.0852359 + 0.996361i \(0.527164\pi\)
\(72\) 1.40373 + 2.43133i 0.165431 + 0.286534i
\(73\) 7.04281 0.824298 0.412149 0.911116i \(-0.364778\pi\)
0.412149 + 0.911116i \(0.364778\pi\)
\(74\) 0.412995 + 0.715328i 0.0480097 + 0.0831552i
\(75\) 11.8945 1.92567i 1.37345 0.222357i
\(76\) −2.28793 1.32094i −0.262443 0.151522i
\(77\) 7.46160i 0.850329i
\(78\) −0.588885 8.66892i −0.0666781 0.981561i
\(79\) 4.05956 0.456736 0.228368 0.973575i \(-0.426661\pi\)
0.228368 + 0.973575i \(0.426661\pi\)
\(80\) −0.403726 + 2.19932i −0.0451380 + 0.245891i
\(81\) 4.77028 8.26237i 0.530031 0.918041i
\(82\) −2.43440 + 1.40550i −0.268834 + 0.155212i
\(83\) −8.55910 −0.939484 −0.469742 0.882804i \(-0.655653\pi\)
−0.469742 + 0.882804i \(0.655653\pi\)
\(84\) −2.93351 + 1.69366i −0.320072 + 0.184794i
\(85\) −10.2038 + 11.9886i −1.10676 + 1.30035i
\(86\) 5.28374i 0.569761i
\(87\) −8.79268 + 5.07645i −0.942674 + 0.544253i
\(88\) −4.59726 2.65423i −0.490070 0.282942i
\(89\) −13.1289 7.57999i −1.39166 0.803477i −0.398163 0.917314i \(-0.630352\pi\)
−0.993499 + 0.113838i \(0.963686\pi\)
\(90\) −5.91398 + 2.10565i −0.623388 + 0.221955i
\(91\) 5.05633 0.343480i 0.530048 0.0360065i
\(92\) 2.66659i 0.278011i
\(93\) 6.11679 10.5946i 0.634281 1.09861i
\(94\) −0.895350 + 1.55079i −0.0923483 + 0.159952i
\(95\) 3.82886 4.49859i 0.392832 0.461545i
\(96\) 2.40987i 0.245956i
\(97\) −2.18328 3.78155i −0.221678 0.383958i 0.733639 0.679539i \(-0.237820\pi\)
−0.955318 + 0.295581i \(0.904487\pi\)
\(98\) 2.51214 + 4.35115i 0.253764 + 0.439532i
\(99\) 14.9033i 1.49783i
\(100\) −4.67401 1.77585i −0.467401 0.177585i
\(101\) 4.19353 7.26341i 0.417272 0.722737i −0.578392 0.815759i \(-0.696319\pi\)
0.995664 + 0.0930224i \(0.0296528\pi\)
\(102\) 8.48334 14.6936i 0.839976 1.45488i
\(103\) 5.56518i 0.548354i 0.961679 + 0.274177i \(0.0884054\pi\)
−0.961679 + 0.274177i \(0.911595\pi\)
\(104\) −1.58700 + 3.23750i −0.155619 + 0.317463i
\(105\) −2.54057 7.13549i −0.247934 0.696353i
\(106\) −6.87583 3.96976i −0.667839 0.385577i
\(107\) −13.1503 7.59234i −1.27129 0.733980i −0.296059 0.955170i \(-0.595673\pi\)
−0.975231 + 0.221190i \(0.929006\pi\)
\(108\) −0.401847 + 0.232006i −0.0386677 + 0.0223248i
\(109\) 0.667003i 0.0638873i 0.999490 + 0.0319436i \(0.0101697\pi\)
−0.999490 + 0.0319436i \(0.989830\pi\)
\(110\) 7.69353 9.03926i 0.733550 0.861860i
\(111\) 1.72385 0.995263i 0.163620 0.0944661i
\(112\) 1.40561 0.132817
\(113\) −2.91774 + 1.68456i −0.274478 + 0.158470i −0.630921 0.775847i \(-0.717323\pi\)
0.356443 + 0.934317i \(0.383989\pi\)
\(114\) −3.18328 + 5.51360i −0.298141 + 0.516396i
\(115\) 5.86468 + 1.07657i 0.546884 + 0.100391i
\(116\) 4.21306 0.391173
\(117\) −10.0991 + 0.686041i −0.933666 + 0.0634245i
\(118\) 6.46419i 0.595077i
\(119\) 8.57035 + 4.94809i 0.785642 + 0.453591i
\(120\) 5.30006 + 0.972927i 0.483827 + 0.0888156i
\(121\) 8.58987 + 14.8781i 0.780897 + 1.35255i
\(122\) −14.7351 −1.33405
\(123\) 3.38707 + 5.86658i 0.305402 + 0.528971i
\(124\) −4.39634 + 2.53823i −0.394803 + 0.227939i
\(125\) 5.79268 9.56268i 0.518113 0.855312i
\(126\) 1.97309 + 3.41749i 0.175777 + 0.304454i
\(127\) −9.39545 5.42446i −0.833711 0.481343i 0.0214106 0.999771i \(-0.493184\pi\)
−0.855122 + 0.518428i \(0.826518\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 12.7331 1.12109
\(130\) −6.47958 4.79740i −0.568297 0.420759i
\(131\) 15.3500 1.34114 0.670568 0.741848i \(-0.266051\pi\)
0.670568 + 0.741848i \(0.266051\pi\)
\(132\) −6.39634 + 11.0788i −0.556730 + 0.964284i
\(133\) −3.21593 1.85672i −0.278856 0.160998i
\(134\) −2.00000 3.46410i −0.172774 0.299253i
\(135\) −0.348020 0.977456i −0.0299528 0.0841260i
\(136\) −6.09726 + 3.52026i −0.522836 + 0.301859i
\(137\) 5.69541 + 9.86475i 0.486592 + 0.842802i 0.999881 0.0154136i \(-0.00490648\pi\)
−0.513289 + 0.858216i \(0.671573\pi\)
\(138\) −6.42612 −0.547028
\(139\) −5.67500 9.82938i −0.481347 0.833717i 0.518424 0.855124i \(-0.326519\pi\)
−0.999771 + 0.0214063i \(0.993186\pi\)
\(140\) −0.567480 + 3.09138i −0.0479608 + 0.261269i
\(141\) 3.73720 + 2.15767i 0.314729 + 0.181709i
\(142\) 9.63946i 0.808926i
\(143\) 15.8889 10.6714i 1.32870 0.892384i
\(144\) −2.80745 −0.233954
\(145\) −1.70092 + 9.26586i −0.141254 + 0.769488i
\(146\) −3.52140 + 6.09925i −0.291433 + 0.504778i
\(147\) 10.4857 6.05391i 0.864844 0.499318i
\(148\) −0.825990 −0.0678960
\(149\) 1.70092 0.982029i 0.139345 0.0804509i −0.428707 0.903444i \(-0.641031\pi\)
0.568052 + 0.822993i \(0.307697\pi\)
\(150\) −4.27955 + 11.2637i −0.349424 + 0.919680i
\(151\) 10.3602i 0.843101i 0.906805 + 0.421550i \(0.138514\pi\)
−0.906805 + 0.421550i \(0.861486\pi\)
\(152\) 2.28793 1.32094i 0.185575 0.107142i
\(153\) −17.1178 9.88295i −1.38389 0.798989i
\(154\) −6.46194 3.73080i −0.520718 0.300637i
\(155\) −3.80745 10.6937i −0.305822 0.858939i
\(156\) 7.80194 + 3.82447i 0.624655 + 0.306203i
\(157\) 5.83105i 0.465368i −0.972552 0.232684i \(-0.925249\pi\)
0.972552 0.232684i \(-0.0747508\pi\)
\(158\) −2.02978 + 3.51568i −0.161481 + 0.279693i
\(159\) −9.56659 + 16.5698i −0.758680 + 1.31407i
\(160\) −1.70280 1.44930i −0.134618 0.114577i
\(161\) 3.74817i 0.295397i
\(162\) 4.77028 + 8.26237i 0.374789 + 0.649153i
\(163\) 5.87592 + 10.1774i 0.460238 + 0.797155i 0.998973 0.0453204i \(-0.0144309\pi\)
−0.538735 + 0.842475i \(0.681098\pi\)
\(164\) 2.81100i 0.219502i
\(165\) −21.7834 18.5404i −1.69584 1.44337i
\(166\) 4.27955 7.41240i 0.332158 0.575314i
\(167\) −5.58799 + 9.67869i −0.432412 + 0.748959i −0.997080 0.0763585i \(-0.975671\pi\)
0.564669 + 0.825318i \(0.309004\pi\)
\(168\) 3.38732i 0.261338i
\(169\) −7.96283 10.2759i −0.612525 0.790451i
\(170\) −5.28054 14.8310i −0.404999 1.13749i
\(171\) 6.42325 + 3.70847i 0.491198 + 0.283593i
\(172\) −4.57586 2.64187i −0.348906 0.201441i
\(173\) −0.461938 + 0.266700i −0.0351205 + 0.0202768i −0.517457 0.855709i \(-0.673121\pi\)
0.482337 + 0.875986i \(0.339788\pi\)
\(174\) 10.1529i 0.769690i
\(175\) −6.56982 2.49614i −0.496631 0.188691i
\(176\) 4.59726 2.65423i 0.346532 0.200070i
\(177\) 15.5778 1.17090
\(178\) 13.1289 7.57999i 0.984054 0.568144i
\(179\) −4.61867 + 7.99976i −0.345215 + 0.597930i −0.985393 0.170297i \(-0.945527\pi\)
0.640178 + 0.768227i \(0.278861\pi\)
\(180\) 1.13344 6.17449i 0.0844819 0.460219i
\(181\) −4.76464 −0.354153 −0.177077 0.984197i \(-0.556664\pi\)
−0.177077 + 0.984197i \(0.556664\pi\)
\(182\) −2.23070 + 4.55065i −0.165351 + 0.337317i
\(183\) 35.5096i 2.62494i
\(184\) 2.30933 + 1.33329i 0.170246 + 0.0982917i
\(185\) 0.333474 1.81662i 0.0245175 0.133560i
\(186\) 6.11679 + 10.5946i 0.448504 + 0.776833i
\(187\) 37.3743 2.73308
\(188\) −0.895350 1.55079i −0.0653001 0.113103i
\(189\) −0.564838 + 0.326110i −0.0410859 + 0.0237210i
\(190\) 1.98146 + 5.56518i 0.143750 + 0.403741i
\(191\) 8.97219 + 15.5403i 0.649205 + 1.12446i 0.983313 + 0.181922i \(0.0582317\pi\)
−0.334108 + 0.942535i \(0.608435\pi\)
\(192\) 2.08700 + 1.20493i 0.150617 + 0.0869585i
\(193\) −10.4731 + 18.1399i −0.753869 + 1.30574i 0.192065 + 0.981382i \(0.438481\pi\)
−0.945934 + 0.324358i \(0.894852\pi\)
\(194\) 4.36656 0.313501
\(195\) −11.5611 + 15.6149i −0.827906 + 1.11821i
\(196\) −5.02427 −0.358877
\(197\) 13.3862 23.1855i 0.953726 1.65190i 0.216468 0.976290i \(-0.430546\pi\)
0.737258 0.675611i \(-0.236120\pi\)
\(198\) 12.9066 + 7.45163i 0.917232 + 0.529564i
\(199\) −7.19452 12.4613i −0.510006 0.883357i −0.999933 0.0115929i \(-0.996310\pi\)
0.489927 0.871764i \(-0.337024\pi\)
\(200\) 3.87493 3.15989i 0.273999 0.223438i
\(201\) −8.34802 + 4.81973i −0.588824 + 0.339958i
\(202\) 4.19353 + 7.26341i 0.295056 + 0.511052i
\(203\) 5.92190 0.415636
\(204\) 8.48334 + 14.6936i 0.593953 + 1.02876i
\(205\) 6.18229 + 1.13488i 0.431790 + 0.0792632i
\(206\) −4.81959 2.78259i −0.335797 0.193872i
\(207\) 7.48632i 0.520335i
\(208\) −2.01026 2.99314i −0.139386 0.207537i
\(209\) −14.0243 −0.970079
\(210\) 7.44980 + 1.36755i 0.514085 + 0.0943700i
\(211\) 12.1954 21.1231i 0.839567 1.45417i −0.0506903 0.998714i \(-0.516142\pi\)
0.890257 0.455458i \(-0.150525\pi\)
\(212\) 6.87583 3.96976i 0.472234 0.272644i
\(213\) −23.2298 −1.59168
\(214\) 13.1503 7.59234i 0.898938 0.519002i
\(215\) 7.65771 8.99718i 0.522252 0.613602i
\(216\) 0.464013i 0.0315721i
\(217\) −6.17952 + 3.56775i −0.419493 + 0.242194i
\(218\) −0.577641 0.333501i −0.0391228 0.0225876i
\(219\) 14.6984 + 8.48611i 0.993224 + 0.573438i
\(220\) 3.98146 + 11.1824i 0.268430 + 0.753919i
\(221\) −1.72045 25.3266i −0.115730 1.70365i
\(222\) 1.99053i 0.133595i
\(223\) 1.48974 2.58031i 0.0997606 0.172790i −0.811825 0.583901i \(-0.801526\pi\)
0.911586 + 0.411110i \(0.134859\pi\)
\(224\) −0.702803 + 1.21729i −0.0469580 + 0.0813337i
\(225\) 13.1221 + 4.98561i 0.874804 + 0.332374i
\(226\) 3.36912i 0.224110i
\(227\) −1.98146 3.43199i −0.131514 0.227789i 0.792746 0.609552i \(-0.208651\pi\)
−0.924260 + 0.381762i \(0.875317\pi\)
\(228\) −3.18328 5.51360i −0.210818 0.365147i
\(229\) 9.85151i 0.651006i 0.945541 + 0.325503i \(0.105534\pi\)
−0.945541 + 0.325503i \(0.894466\pi\)
\(230\) −3.86468 + 4.54067i −0.254829 + 0.299403i
\(231\) −8.99073 + 15.5724i −0.591547 + 1.02459i
\(232\) −2.10653 + 3.64862i −0.138300 + 0.239543i
\(233\) 19.3821i 1.26976i −0.772610 0.634881i \(-0.781049\pi\)
0.772610 0.634881i \(-0.218951\pi\)
\(234\) 4.45544 9.08913i 0.291261 0.594175i
\(235\) 3.77216 1.34307i 0.246069 0.0876119i
\(236\) −5.59815 3.23210i −0.364409 0.210391i
\(237\) 8.47232 + 4.89150i 0.550337 + 0.317737i
\(238\) −8.57035 + 4.94809i −0.555533 + 0.320737i
\(239\) 30.0138i 1.94143i 0.240232 + 0.970715i \(0.422776\pi\)
−0.240232 + 0.970715i \(0.577224\pi\)
\(240\) −3.49261 + 4.10353i −0.225447 + 0.264882i
\(241\) −16.5815 + 9.57333i −1.06811 + 0.616672i −0.927664 0.373416i \(-0.878186\pi\)
−0.140444 + 0.990089i \(0.544853\pi\)
\(242\) −17.1797 −1.10436
\(243\) 18.7057 10.7997i 1.19997 0.692803i
\(244\) 7.36754 12.7610i 0.471659 0.816937i
\(245\) 2.02843 11.0500i 0.129592 0.705957i
\(246\) −6.77414 −0.431903
\(247\) 0.645579 + 9.50350i 0.0410772 + 0.604693i
\(248\) 5.07645i 0.322355i
\(249\) −17.8629 10.3131i −1.13201 0.653569i
\(250\) 5.38519 + 9.79795i 0.340589 + 0.619676i
\(251\) −8.52150 14.7597i −0.537872 0.931622i −0.999018 0.0442979i \(-0.985895\pi\)
0.461146 0.887324i \(-0.347438\pi\)
\(252\) −3.94617 −0.248586
\(253\) −7.07774 12.2590i −0.444973 0.770717i
\(254\) 9.39545 5.42446i 0.589523 0.340361i
\(255\) −35.7408 + 12.7254i −2.23818 + 0.796895i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.12328 + 4.11263i 0.444338 + 0.256539i 0.705436 0.708774i \(-0.250751\pi\)
−0.261098 + 0.965312i \(0.584085\pi\)
\(258\) −6.36656 + 11.0272i −0.396365 + 0.686523i
\(259\) −1.16102 −0.0721421
\(260\) 7.39446 3.21279i 0.458585 0.199249i
\(261\) −11.8280 −0.732133
\(262\) −7.67500 + 13.2935i −0.474163 + 0.821274i
\(263\) −9.03229 5.21479i −0.556955 0.321558i 0.194968 0.980810i \(-0.437540\pi\)
−0.751922 + 0.659252i \(0.770873\pi\)
\(264\) −6.39634 11.0788i −0.393667 0.681852i
\(265\) 5.95482 + 16.7248i 0.365801 + 1.02740i
\(266\) 3.21593 1.85672i 0.197181 0.113843i
\(267\) −18.2667 31.6389i −1.11791 1.93627i
\(268\) 4.00000 0.244339
\(269\) 11.3206 + 19.6078i 0.690228 + 1.19551i 0.971763 + 0.235959i \(0.0758230\pi\)
−0.281535 + 0.959551i \(0.590844\pi\)
\(270\) 1.02051 + 0.187334i 0.0621064 + 0.0114008i
\(271\) 0.218603 + 0.126211i 0.0132792 + 0.00766675i 0.506625 0.862167i \(-0.330893\pi\)
−0.493346 + 0.869833i \(0.664226\pi\)
\(272\) 7.04051i 0.426894i
\(273\) 10.9665 + 5.37570i 0.663720 + 0.325352i
\(274\) −11.3908 −0.688145
\(275\) −26.2011 + 4.24187i −1.57999 + 0.255794i
\(276\) 3.21306 5.56518i 0.193403 0.334985i
\(277\) −4.03166 + 2.32768i −0.242239 + 0.139857i −0.616205 0.787586i \(-0.711331\pi\)
0.373966 + 0.927442i \(0.377998\pi\)
\(278\) 11.3500 0.680727
\(279\) 12.3425 7.12595i 0.738927 0.426620i
\(280\) −2.39347 2.03714i −0.143037 0.121742i
\(281\) 3.70262i 0.220880i 0.993883 + 0.110440i \(0.0352260\pi\)
−0.993883 + 0.110440i \(0.964774\pi\)
\(282\) −3.73720 + 2.15767i −0.222547 + 0.128488i
\(283\) −4.63147 2.67398i −0.275312 0.158952i 0.355987 0.934491i \(-0.384145\pi\)
−0.631299 + 0.775539i \(0.717478\pi\)
\(284\) 8.34802 + 4.81973i 0.495364 + 0.285998i
\(285\) 13.4113 4.77506i 0.794419 0.282850i
\(286\) 1.29720 + 19.0959i 0.0767049 + 1.12917i
\(287\) 3.95116i 0.233230i
\(288\) 1.40373 2.43133i 0.0827154 0.143267i
\(289\) 16.2844 28.2054i 0.957906 1.65914i
\(290\) −7.17401 6.10597i −0.421272 0.358555i
\(291\) 10.5228i 0.616858i
\(292\) −3.52140 6.09925i −0.206075 0.356932i
\(293\) −12.0871 20.9355i −0.706136 1.22306i −0.966280 0.257493i \(-0.917103\pi\)
0.260144 0.965570i \(-0.416230\pi\)
\(294\) 12.1078i 0.706142i
\(295\) 9.36853 11.0072i 0.545457 0.640866i
\(296\) 0.412995 0.715328i 0.0240048 0.0415776i
\(297\) −1.23160 + 2.13319i −0.0714645 + 0.123780i
\(298\) 1.96406i 0.113775i
\(299\) −7.98146 + 5.36052i −0.461580 + 0.310007i
\(300\) −7.61491 9.33807i −0.439647 0.539134i
\(301\) −6.43185 3.71343i −0.370726 0.214039i
\(302\) −8.97219 5.18010i −0.516292 0.298081i
\(303\) 17.5039 10.1059i 1.00557 0.580566i
\(304\) 2.64187i 0.151522i
\(305\) 25.0910 + 21.3555i 1.43670 + 1.22281i
\(306\) 17.1178 9.88295i 0.978558 0.564971i
\(307\) −27.5443 −1.57204 −0.786019 0.618203i \(-0.787861\pi\)
−0.786019 + 0.618203i \(0.787861\pi\)
\(308\) 6.46194 3.73080i 0.368203 0.212582i
\(309\) −6.70567 + 11.6146i −0.381472 + 0.660729i
\(310\) 11.1647 + 2.04950i 0.634115 + 0.116404i
\(311\) 12.8262 0.727306 0.363653 0.931534i \(-0.381529\pi\)
0.363653 + 0.931534i \(0.381529\pi\)
\(312\) −7.21306 + 4.84445i −0.408359 + 0.274263i
\(313\) 2.72604i 0.154085i 0.997028 + 0.0770425i \(0.0245477\pi\)
−0.997028 + 0.0770425i \(0.975452\pi\)
\(314\) 5.04984 + 2.91552i 0.284979 + 0.164533i
\(315\) 1.59317 8.67889i 0.0897652 0.489000i
\(316\) −2.02978 3.51568i −0.114184 0.197773i
\(317\) 1.89961 0.106692 0.0533462 0.998576i \(-0.483011\pi\)
0.0533462 + 0.998576i \(0.483011\pi\)
\(318\) −9.56659 16.5698i −0.536468 0.929189i
\(319\) 19.3685 11.1824i 1.08443 0.626096i
\(320\) 2.10653 0.750022i 0.117759 0.0419275i
\(321\) −18.2965 31.6905i −1.02121 1.76879i
\(322\) 3.24601 + 1.87409i 0.180893 + 0.104439i
\(323\) −9.30006 + 16.1082i −0.517469 + 0.896283i
\(324\) −9.54057 −0.530031
\(325\) 4.08060 + 17.5599i 0.226351 + 0.974046i
\(326\) −11.7518 −0.650874
\(327\) −0.803694 + 1.39204i −0.0444444 + 0.0769799i
\(328\) 2.43440 + 1.40550i 0.134417 + 0.0776058i
\(329\) −1.25851 2.17980i −0.0693839 0.120176i
\(330\) 26.9481 9.59479i 1.48345 0.528176i
\(331\) 7.78318 4.49362i 0.427802 0.246992i −0.270608 0.962690i \(-0.587225\pi\)
0.698410 + 0.715698i \(0.253891\pi\)
\(332\) 4.27955 + 7.41240i 0.234871 + 0.406808i
\(333\) 2.31893 0.127076
\(334\) −5.58799 9.67869i −0.305761 0.529594i
\(335\) −1.61491 + 8.79728i −0.0882317 + 0.480647i
\(336\) 2.93351 + 1.69366i 0.160036 + 0.0923968i
\(337\) 1.37859i 0.0750967i −0.999295 0.0375484i \(-0.988045\pi\)
0.999295 0.0375484i \(-0.0119548\pi\)
\(338\) 12.8806 1.75808i 0.700611 0.0956271i
\(339\) −8.11912 −0.440970
\(340\) 15.4843 + 2.84244i 0.839756 + 0.154153i
\(341\) −13.4741 + 23.3378i −0.729662 + 1.26381i
\(342\) −6.42325 + 3.70847i −0.347330 + 0.200531i
\(343\) −16.9014 −0.912589
\(344\) 4.57586 2.64187i 0.246714 0.142440i
\(345\) 10.9424 + 9.31335i 0.589120 + 0.501414i
\(346\) 0.533400i 0.0286758i
\(347\) 10.3020 5.94788i 0.553042 0.319299i −0.197306 0.980342i \(-0.563219\pi\)
0.750348 + 0.661043i \(0.229886\pi\)
\(348\) 8.79268 + 5.07645i 0.471337 + 0.272126i
\(349\) 3.95580 + 2.28388i 0.211749 + 0.122254i 0.602124 0.798403i \(-0.294321\pi\)
−0.390375 + 0.920656i \(0.627655\pi\)
\(350\) 5.44663 4.44156i 0.291135 0.237411i
\(351\) 1.50224 + 0.736390i 0.0801837 + 0.0393056i
\(352\) 5.30846i 0.282942i
\(353\) −0.421009 + 0.729210i −0.0224081 + 0.0388119i −0.877012 0.480468i \(-0.840467\pi\)
0.854604 + 0.519280i \(0.173800\pi\)
\(354\) −7.78892 + 13.4908i −0.413976 + 0.717028i
\(355\) −13.9704 + 16.4141i −0.741474 + 0.871170i
\(356\) 15.1600i 0.803477i
\(357\) 11.9242 + 20.6534i 0.631098 + 1.09309i
\(358\) −4.61867 7.99976i −0.244104 0.422801i
\(359\) 8.05922i 0.425349i −0.977123 0.212675i \(-0.931783\pi\)
0.977123 0.212675i \(-0.0682174\pi\)
\(360\) 4.78054 + 4.06883i 0.251957 + 0.214446i
\(361\) −6.01026 + 10.4101i −0.316329 + 0.547898i
\(362\) 2.38232 4.12630i 0.125212 0.216874i
\(363\) 41.4009i 2.17298i
\(364\) −2.82563 4.20717i −0.148103 0.220516i
\(365\) 14.8359 5.28226i 0.776546 0.276486i
\(366\) −30.7522 17.7548i −1.60744 0.928058i
\(367\) 14.3052 + 8.25912i 0.746726 + 0.431122i 0.824510 0.565848i \(-0.191451\pi\)
−0.0777837 + 0.996970i \(0.524784\pi\)
\(368\) −2.30933 + 1.33329i −0.120382 + 0.0695027i
\(369\) 7.89176i 0.410828i
\(370\) 1.40650 + 1.19710i 0.0731204 + 0.0622345i
\(371\) 9.66470 5.57992i 0.501766 0.289695i
\(372\) −12.2336 −0.634281
\(373\) 22.9969 13.2773i 1.19073 0.687471i 0.232261 0.972653i \(-0.425388\pi\)
0.958473 + 0.285183i \(0.0920543\pi\)
\(374\) −18.6871 + 32.3671i −0.966289 + 1.67366i
\(375\) 23.6117 12.9776i 1.21930 0.670160i
\(376\) 1.79070 0.0923483
\(377\) −8.46933 12.6103i −0.436193 0.649462i
\(378\) 0.652219i 0.0335465i
\(379\) −1.00089 0.577865i −0.0514124 0.0296830i 0.474073 0.880485i \(-0.342783\pi\)
−0.525486 + 0.850802i \(0.676116\pi\)
\(380\) −5.81032 1.06659i −0.298063 0.0547151i
\(381\) −13.0722 22.6418i −0.669710 1.15997i
\(382\) −17.9444 −0.918115
\(383\) −17.5039 30.3176i −0.894405 1.54916i −0.834539 0.550949i \(-0.814266\pi\)
−0.0598661 0.998206i \(-0.519067\pi\)
\(384\) −2.08700 + 1.20493i −0.106502 + 0.0614890i
\(385\) 5.59637 + 15.7181i 0.285217 + 0.801068i
\(386\) −10.4731 18.1399i −0.533066 0.923298i
\(387\) 12.8465 + 7.41693i 0.653024 + 0.377024i
\(388\) −2.18328 + 3.78155i −0.110839 + 0.191979i
\(389\) 11.3135 0.573615 0.286807 0.957988i \(-0.407406\pi\)
0.286807 + 0.957988i \(0.407406\pi\)
\(390\) −7.74238 17.8197i −0.392051 0.902333i
\(391\) −18.7741 −0.949449
\(392\) 2.51214 4.35115i 0.126882 0.219766i
\(393\) 32.0355 + 18.4957i 1.61598 + 0.932985i
\(394\) 13.3862 + 23.1855i 0.674386 + 1.16807i
\(395\) 8.55159 3.04476i 0.430277 0.153199i
\(396\) −12.9066 + 7.45163i −0.648581 + 0.374458i
\(397\) 9.00287 + 15.5934i 0.451841 + 0.782611i 0.998500 0.0547435i \(-0.0174341\pi\)
−0.546660 + 0.837355i \(0.684101\pi\)
\(398\) 14.3890 0.721258
\(399\) −4.47444 7.74995i −0.224002 0.387983i
\(400\) 0.799077 + 4.93573i 0.0399538 + 0.246787i
\(401\) 3.97385 + 2.29430i 0.198445 + 0.114572i 0.595930 0.803037i \(-0.296784\pi\)
−0.397485 + 0.917609i \(0.630117\pi\)
\(402\) 9.63946i 0.480773i
\(403\) 16.4350 + 8.05636i 0.818687 + 0.401316i
\(404\) −8.38707 −0.417272
\(405\) 3.85178 20.9828i 0.191396 1.04264i
\(406\) −2.96095 + 5.12852i −0.146950 + 0.254524i
\(407\) −3.79729 + 2.19237i −0.188225 + 0.108672i
\(408\) −16.9667 −0.839976
\(409\) −22.7332 + 13.1250i −1.12408 + 0.648991i −0.942441 0.334374i \(-0.891475\pi\)
−0.181644 + 0.983364i \(0.558142\pi\)
\(410\) −4.07398 + 4.78658i −0.201199 + 0.236392i
\(411\) 27.4504i 1.35403i
\(412\) 4.81959 2.78259i 0.237444 0.137088i
\(413\) −7.86880 4.54305i −0.387198 0.223549i
\(414\) −6.48334 3.74316i −0.318639 0.183966i
\(415\) −18.0300 + 6.41952i −0.885058 + 0.315122i
\(416\) 3.59726 0.244364i 0.176370 0.0119809i
\(417\) 27.3520i 1.33943i
\(418\) 7.01214 12.1454i 0.342975 0.594050i
\(419\) 6.03869 10.4593i 0.295009 0.510971i −0.679978 0.733233i \(-0.738011\pi\)
0.974987 + 0.222262i \(0.0713440\pi\)
\(420\) −4.90924 + 5.76794i −0.239546 + 0.281447i
\(421\) 3.11716i 0.151921i −0.997111 0.0759604i \(-0.975798\pi\)
0.997111 0.0759604i \(-0.0242023\pi\)
\(422\) 12.1954 + 21.1231i 0.593663 + 1.02826i
\(423\) 2.51365 + 4.35378i 0.122218 + 0.211688i
\(424\) 7.93952i 0.385577i
\(425\) −12.5029 + 32.9074i −0.606478 + 1.59624i
\(426\) 11.6149 20.1176i 0.562744 0.974701i
\(427\) 10.3559 17.9369i 0.501155 0.868027i
\(428\) 15.1847i 0.733980i
\(429\) 46.0186 3.12607i 2.22180 0.150928i
\(430\) 3.96293 + 11.1304i 0.191109 + 0.536754i
\(431\) 4.52932 + 2.61501i 0.218170 + 0.125960i 0.605103 0.796148i \(-0.293132\pi\)
−0.386933 + 0.922108i \(0.626465\pi\)
\(432\) 0.401847 + 0.232006i 0.0193339 + 0.0111624i
\(433\) −19.3178 + 11.1531i −0.928354 + 0.535986i −0.886291 0.463129i \(-0.846727\pi\)
−0.0420637 + 0.999115i \(0.513393\pi\)
\(434\) 7.13549i 0.342515i
\(435\) −14.7146 + 17.2884i −0.705510 + 0.828915i
\(436\) 0.577641 0.333501i 0.0276640 0.0159718i
\(437\) 7.04478 0.336998
\(438\) −14.6984 + 8.48611i −0.702316 + 0.405482i
\(439\) 2.62417 4.54520i 0.125245 0.216931i −0.796584 0.604528i \(-0.793362\pi\)
0.921829 + 0.387598i \(0.126695\pi\)
\(440\) −11.6750 2.14317i −0.556584 0.102171i
\(441\) 14.1054 0.671686
\(442\) 22.7937 + 11.1733i 1.08418 + 0.531461i
\(443\) 1.11623i 0.0530338i −0.999648 0.0265169i \(-0.991558\pi\)
0.999648 0.0265169i \(-0.00844158\pi\)
\(444\) −1.72385 0.995263i −0.0818101 0.0472331i
\(445\) −33.3416 6.12048i −1.58054 0.290139i
\(446\) 1.48974 + 2.58031i 0.0705414 + 0.122181i
\(447\) 4.73311 0.223869
\(448\) −0.702803 1.21729i −0.0332043 0.0575116i
\(449\) 29.8678 17.2442i 1.40955 0.813802i 0.414203 0.910185i \(-0.364060\pi\)
0.995344 + 0.0963822i \(0.0307271\pi\)
\(450\) −10.8787 + 8.87124i −0.512826 + 0.418194i
\(451\) −7.46105 12.9229i −0.351327 0.608516i
\(452\) 2.91774 + 1.68456i 0.137239 + 0.0792350i
\(453\) −12.4833 + 21.6218i −0.586519 + 1.01588i
\(454\) 3.96293 0.185989
\(455\) 10.3937 4.51591i 0.487264 0.211709i
\(456\) 6.36656 0.298141
\(457\) 2.03770 3.52940i 0.0953196 0.165098i −0.814422 0.580273i \(-0.802946\pi\)
0.909742 + 0.415174i \(0.136279\pi\)
\(458\) −8.53166 4.92576i −0.398658 0.230165i
\(459\) 1.63344 + 2.82921i 0.0762426 + 0.132056i
\(460\) −2.00000 5.61725i −0.0932505 0.261905i
\(461\) 26.2766 15.1708i 1.22383 0.706576i 0.258094 0.966120i \(-0.416906\pi\)
0.965731 + 0.259544i \(0.0835722\pi\)
\(462\) −8.99073 15.5724i −0.418287 0.724494i
\(463\) 25.2291 1.17250 0.586248 0.810132i \(-0.300605\pi\)
0.586248 + 0.810132i \(0.300605\pi\)
\(464\) −2.10653 3.64862i −0.0977932 0.169383i
\(465\) 4.93902 26.9055i 0.229041 1.24771i
\(466\) 16.7854 + 9.69104i 0.777568 + 0.448929i
\(467\) 21.9997i 1.01802i 0.860759 + 0.509012i \(0.169989\pi\)
−0.860759 + 0.509012i \(0.830011\pi\)
\(468\) 5.64370 + 8.40309i 0.260880 + 0.388433i
\(469\) 5.62242 0.259619
\(470\) −0.722953 + 3.93832i −0.0333473 + 0.181661i
\(471\) 7.02602 12.1694i 0.323742 0.560738i
\(472\) 5.59815 3.23210i 0.257676 0.148769i
\(473\) −28.0485 −1.28967
\(474\) −8.47232 + 4.89150i −0.389147 + 0.224674i
\(475\) 4.69156 12.3481i 0.215264 0.566571i
\(476\) 9.89618i 0.453591i
\(477\) −19.3036 + 11.1449i −0.883849 + 0.510291i
\(478\) −25.9927 15.0069i −1.18888 0.686399i
\(479\) −19.1462 11.0541i −0.874812 0.505073i −0.00586793 0.999983i \(-0.501868\pi\)
−0.868944 + 0.494910i \(0.835201\pi\)
\(480\) −1.80745 5.07645i −0.0824986 0.231707i
\(481\) 1.66045 + 2.47230i 0.0757101 + 0.112727i
\(482\) 19.1467i 0.872107i
\(483\) 4.51630 7.82245i 0.205499 0.355934i
\(484\) 8.58987 14.8781i 0.390449 0.676277i
\(485\) −7.43539 6.32844i −0.337624 0.287360i
\(486\) 21.5994i 0.979771i
\(487\) −1.83437 3.17722i −0.0831231 0.143973i 0.821467 0.570256i \(-0.193156\pi\)
−0.904590 + 0.426283i \(0.859823\pi\)
\(488\) 7.36754 + 12.7610i 0.333513 + 0.577662i
\(489\) 28.3204i 1.28069i
\(490\) 8.55534 + 7.28166i 0.386491 + 0.328952i
\(491\) −13.2345 + 22.9228i −0.597263 + 1.03449i 0.395960 + 0.918268i \(0.370412\pi\)
−0.993223 + 0.116222i \(0.962922\pi\)
\(492\) 3.38707 5.86658i 0.152701 0.264486i
\(493\) 29.6621i 1.33591i
\(494\) −8.55306 4.19266i −0.384821 0.188637i
\(495\) −11.1778 31.3941i −0.502403 1.41106i
\(496\) 4.39634 + 2.53823i 0.197401 + 0.113970i
\(497\) 11.7340 + 6.77464i 0.526343 + 0.303884i
\(498\) 17.8629 10.3131i 0.800455 0.462143i
\(499\) 37.0404i 1.65816i −0.559133 0.829078i \(-0.688866\pi\)
0.559133 0.829078i \(-0.311134\pi\)
\(500\) −11.1779 0.235262i −0.499889 0.0105212i
\(501\) −23.3243 + 13.4663i −1.04205 + 0.601630i
\(502\) 17.0430 0.760666
\(503\) −29.4618 + 17.0098i −1.31364 + 0.758429i −0.982696 0.185223i \(-0.940699\pi\)
−0.330940 + 0.943652i \(0.607366\pi\)
\(504\) 1.97309 3.41749i 0.0878883 0.152227i
\(505\) 3.38608 18.4458i 0.150679 0.820829i
\(506\) 14.1555 0.629288
\(507\) −4.23674 31.0405i −0.188160 1.37855i
\(508\) 10.8489i 0.481343i
\(509\) −13.9811 8.07197i −0.619700 0.357784i 0.157052 0.987590i \(-0.449801\pi\)
−0.776752 + 0.629806i \(0.783134\pi\)
\(510\) 6.84990 37.3152i 0.303319 1.65234i
\(511\) −4.94971 8.57314i −0.218962 0.379254i
\(512\) 1.00000 0.0441942
\(513\) −0.612931 1.06163i −0.0270616 0.0468720i
\(514\) −7.12328 + 4.11263i −0.314195 + 0.181400i
\(515\) 4.17401 + 11.7232i 0.183929 + 0.516587i
\(516\) −6.36656 11.0272i −0.280272 0.485445i
\(517\) −8.23232 4.75293i −0.362057 0.209034i
\(518\) 0.580508 1.00547i 0.0255061 0.0441778i
\(519\) −1.28542 −0.0564238
\(520\) −0.914875 + 8.01018i −0.0401199 + 0.351270i
\(521\) −36.5483 −1.60121 −0.800605 0.599193i \(-0.795488\pi\)
−0.800605 + 0.599193i \(0.795488\pi\)
\(522\) 5.91398 10.2433i 0.258848 0.448338i
\(523\) 0.577641 + 0.333501i 0.0252585 + 0.0145830i 0.512576 0.858642i \(-0.328691\pi\)
−0.487318 + 0.873225i \(0.662025\pi\)
\(524\) −7.67500 13.2935i −0.335284 0.580729i
\(525\) −10.7036 13.1256i −0.467142 0.572850i
\(526\) 9.03229 5.21479i 0.393826 0.227376i
\(527\) 17.8704 + 30.9525i 0.778447 + 1.34831i
\(528\) 12.7927 0.556730
\(529\) −7.94466 13.7605i −0.345420 0.598285i
\(530\) −17.4615 3.20539i −0.758481 0.139233i
\(531\) 15.7166 + 9.07396i 0.682040 + 0.393776i
\(532\) 3.71343i 0.160998i
\(533\) −8.41372 + 5.65083i −0.364438 + 0.244765i
\(534\) 36.5335 1.58096
\(535\) −33.3960 6.13046i −1.44383 0.265043i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) −19.2784 + 11.1304i −0.831922 + 0.480311i
\(538\) −22.6412 −0.976129
\(539\) −23.0979 + 13.3356i −0.994896 + 0.574404i
\(540\) −0.672492 + 0.790122i −0.0289395 + 0.0340014i
\(541\) 7.70275i 0.331167i −0.986196 0.165584i \(-0.947049\pi\)
0.986196 0.165584i \(-0.0529508\pi\)
\(542\) −0.218603 + 0.126211i −0.00938981 + 0.00542121i
\(543\) −9.94384 5.74108i −0.426731 0.246373i
\(544\) 6.09726 + 3.52026i 0.261418 + 0.150930i
\(545\) 0.500267 + 1.40506i 0.0214291 + 0.0601862i
\(546\) −10.1387 + 6.80938i −0.433897 + 0.291415i
\(547\) 27.5445i 1.17772i −0.808236 0.588858i \(-0.799578\pi\)
0.808236 0.588858i \(-0.200422\pi\)
\(548\) 5.69541 9.86475i 0.243296 0.421401i
\(549\) −20.6840 + 35.8258i −0.882773 + 1.52901i
\(550\) 9.42701 24.8118i 0.401969 1.05798i
\(551\) 11.1304i 0.474169i
\(552\) 3.21306 + 5.56518i 0.136757 + 0.236870i
\(553\) −2.85307 4.94167i −0.121325 0.210141i
\(554\) 4.65536i 0.197787i
\(555\) 2.88486 3.38947i 0.122456 0.143875i
\(556\) −5.67500 + 9.82938i −0.240673 + 0.416859i
\(557\) −2.08137 + 3.60503i −0.0881903 + 0.152750i −0.906746 0.421677i \(-0.861442\pi\)
0.818556 + 0.574427i \(0.194775\pi\)
\(558\) 14.2519i 0.603331i
\(559\) 1.29116 + 19.0070i 0.0546101 + 0.803911i
\(560\) 2.96095 1.05424i 0.125123 0.0445496i
\(561\) 78.0003 + 45.0335i 3.29317 + 1.90132i
\(562\) −3.20656 1.85131i −0.135261 0.0780928i
\(563\) 27.3575 15.7949i 1.15298 0.665674i 0.203370 0.979102i \(-0.434811\pi\)
0.949612 + 0.313428i \(0.101477\pi\)
\(564\) 4.31535i 0.181709i
\(565\) −4.88285 + 5.73694i −0.205423 + 0.241355i
\(566\) 4.63147 2.67398i 0.194675 0.112396i
\(567\) −13.4103 −0.563179
\(568\) −8.34802 + 4.81973i −0.350275 + 0.202231i
\(569\) 11.9583 20.7124i 0.501318 0.868309i −0.498680 0.866786i \(-0.666182\pi\)
0.999999 0.00152301i \(-0.000484788\pi\)
\(570\) −2.57035 + 14.0021i −0.107660 + 0.586483i
\(571\) 0.653231 0.0273369 0.0136684 0.999907i \(-0.495649\pi\)
0.0136684 + 0.999907i \(0.495649\pi\)
\(572\) −17.1861 8.42455i −0.718589 0.352248i
\(573\) 43.2436i 1.80653i
\(574\) 3.42181 + 1.97558i 0.142823 + 0.0824592i
\(575\) 13.1616 2.13081i 0.548875 0.0888608i
\(576\) 1.40373 + 2.43133i 0.0584886 + 0.101305i
\(577\) −21.3167 −0.887425 −0.443712 0.896169i \(-0.646339\pi\)
−0.443712 + 0.896169i \(0.646339\pi\)
\(578\) 16.2844 + 28.2054i 0.677341 + 1.17319i
\(579\) −43.7148 + 25.2387i −1.81672 + 1.04889i
\(580\) 8.87493 3.15989i 0.368512 0.131207i
\(581\) 6.01536 + 10.4189i 0.249559 + 0.432250i
\(582\) 9.11303 + 5.26141i 0.377747 + 0.218092i
\(583\) 21.0733 36.5000i 0.872767 1.51168i
\(584\) 7.04281 0.291433
\(585\) −20.7596 + 9.01975i −0.858304 + 0.372921i
\(586\) 24.1742 0.998627
\(587\) −7.61491 + 13.1894i −0.314301 + 0.544385i −0.979289 0.202469i \(-0.935103\pi\)
0.664988 + 0.746854i \(0.268437\pi\)
\(588\) −10.4857 6.05391i −0.432422 0.249659i
\(589\) −6.70567 11.6146i −0.276302 0.478570i
\(590\) 4.84829 + 13.6170i 0.199601 + 0.560603i
\(591\) 55.8740 32.2589i 2.29835 1.32695i
\(592\) 0.412995 + 0.715328i 0.0169740 + 0.0293998i
\(593\) −9.70527 −0.398548 −0.199274 0.979944i \(-0.563858\pi\)
−0.199274 + 0.979944i \(0.563858\pi\)
\(594\) −1.23160 2.13319i −0.0505330 0.0875257i
\(595\) 21.7649 + 3.99535i 0.892273 + 0.163793i
\(596\) −1.70092 0.982029i −0.0696725 0.0402255i
\(597\) 34.6757i 1.41918i
\(598\) −0.651618 9.59241i −0.0266467 0.392263i
\(599\) −1.20026 −0.0490411 −0.0245206 0.999699i \(-0.507806\pi\)
−0.0245206 + 0.999699i \(0.507806\pi\)
\(600\) 11.8945 1.92567i 0.485589 0.0786150i
\(601\) −7.03681 + 12.1881i −0.287037 + 0.497163i −0.973101 0.230378i \(-0.926004\pi\)
0.686064 + 0.727541i \(0.259337\pi\)
\(602\) 6.43185 3.71343i 0.262143 0.151348i
\(603\) −11.2298 −0.457313
\(604\) 8.97219 5.18010i 0.365073 0.210775i
\(605\) 29.2537 + 24.8986i 1.18933 + 1.01227i
\(606\) 20.2117i 0.821045i
\(607\) −27.3053 + 15.7647i −1.10829 + 0.639870i −0.938385 0.345591i \(-0.887678\pi\)
−0.169902 + 0.985461i \(0.554345\pi\)
\(608\) −2.28793 1.32094i −0.0927877 0.0535710i
\(609\) 12.3590 + 7.13549i 0.500814 + 0.289145i
\(610\) −31.0399 + 11.0516i −1.25677 + 0.447468i
\(611\) −2.84185 + 5.79739i −0.114969 + 0.234537i
\(612\) 19.7659i 0.798989i
\(613\) −1.41675 + 2.45389i −0.0572222 + 0.0991117i −0.893217 0.449625i \(-0.851558\pi\)
0.835995 + 0.548737i \(0.184891\pi\)
\(614\) 13.7722 23.8541i 0.555799 0.962673i
\(615\) 11.5350 + 9.81774i 0.465137 + 0.395889i
\(616\) 7.46160i 0.300637i
\(617\) −1.12704 1.95209i −0.0453730 0.0785883i 0.842447 0.538779i \(-0.181114\pi\)
−0.887820 + 0.460191i \(0.847781\pi\)
\(618\) −6.70567 11.6146i −0.269742 0.467206i
\(619\) 6.37526i 0.256243i 0.991758 + 0.128122i \(0.0408948\pi\)
−0.991758 + 0.128122i \(0.959105\pi\)
\(620\) −7.35729 + 8.64420i −0.295476 + 0.347159i
\(621\) 0.618665 1.07156i 0.0248262 0.0430002i
\(622\) −6.41309 + 11.1078i −0.257141 + 0.445382i
\(623\) 21.3090i 0.853725i
\(624\) −0.588885 8.66892i −0.0235743 0.347034i
\(625\) 5.03022 24.4887i 0.201209 0.979548i
\(626\) −2.36082 1.36302i −0.0943575 0.0544773i
\(627\) −29.2687 16.8983i −1.16888 0.674853i
\(628\) −5.04984 + 2.91552i −0.201510 + 0.116342i
\(629\) 5.81539i 0.231875i
\(630\) 6.71956 + 5.71918i 0.267714 + 0.227857i
\(631\) −26.7025 + 15.4167i −1.06301 + 0.613729i −0.926263 0.376877i \(-0.876998\pi\)
−0.136746 + 0.990606i \(0.543665\pi\)
\(632\) 4.05956 0.161481
\(633\) 50.9038 29.3893i 2.02324 1.16812i
\(634\) −0.949803 + 1.64511i −0.0377215 + 0.0653355i
\(635\) −23.8603 4.38000i −0.946865 0.173815i
\(636\) 19.1332 0.758680
\(637\) 10.1001 + 15.0383i 0.400179 + 0.595840i
\(638\) 22.3649i 0.885433i
\(639\) −23.4367 13.5312i −0.927140 0.535285i
\(640\) −0.403726 + 2.19932i −0.0159587 + 0.0869357i
\(641\) 9.59449 + 16.6181i 0.378960 + 0.656377i 0.990911 0.134518i \(-0.0429486\pi\)
−0.611952 + 0.790895i \(0.709615\pi\)
\(642\) 36.5931 1.44421
\(643\) 12.2778 + 21.2657i 0.484188 + 0.838638i 0.999835 0.0181630i \(-0.00578179\pi\)
−0.515647 + 0.856801i \(0.672448\pi\)
\(644\) −3.24601 + 1.87409i −0.127911 + 0.0738493i
\(645\) 26.8227 9.55012i 1.05614 0.376036i
\(646\) −9.30006 16.1082i −0.365906 0.633768i
\(647\) 25.4323 + 14.6834i 0.999849 + 0.577263i 0.908204 0.418529i \(-0.137454\pi\)
0.0916452 + 0.995792i \(0.470787\pi\)
\(648\) 4.77028 8.26237i 0.187394 0.324577i
\(649\) −34.3149 −1.34698
\(650\) −17.2476 5.24602i −0.676506 0.205766i
\(651\) −17.1956 −0.673948
\(652\) 5.87592 10.1774i 0.230119 0.398577i
\(653\) 21.6951 + 12.5257i 0.848997 + 0.490168i 0.860312 0.509767i \(-0.170269\pi\)
−0.0113155 + 0.999936i \(0.503602\pi\)
\(654\) −0.803694 1.39204i −0.0314269 0.0544330i
\(655\) 32.3352 11.5128i 1.26344 0.449844i
\(656\) −2.43440 + 1.40550i −0.0950473 + 0.0548756i
\(657\) 9.88618 + 17.1234i 0.385696 + 0.668046i
\(658\) 2.51702 0.0981236
\(659\) 17.5467 + 30.3917i 0.683521 + 1.18389i 0.973899 + 0.226981i \(0.0728855\pi\)
−0.290378 + 0.956912i \(0.593781\pi\)
\(660\) −5.16474 + 28.1352i −0.201037 + 1.09516i
\(661\) 26.9586 + 15.5646i 1.04857 + 0.605392i 0.922248 0.386598i \(-0.126350\pi\)
0.126321 + 0.991989i \(0.459683\pi\)
\(662\) 8.98724i 0.349299i
\(663\) 26.9262 54.9297i 1.04573 2.13329i
\(664\) −8.55910 −0.332158
\(665\) −8.16702 1.49921i −0.316704 0.0581369i
\(666\) −1.15946 + 2.00825i −0.0449283 + 0.0778181i
\(667\) −9.72935 + 5.61725i −0.376722 + 0.217501i
\(668\) 11.1760 0.432412
\(669\) 6.21821 3.59008i 0.240410 0.138801i
\(670\) −6.81121 5.79719i −0.263140 0.223965i
\(671\) 78.2206i 3.01967i
\(672\) −2.93351 + 1.69366i −0.113162 + 0.0653344i
\(673\) −0.167875 0.0969228i −0.00647112 0.00373610i 0.496761 0.867887i \(-0.334523\pi\)
−0.503232 + 0.864151i \(0.667856\pi\)
\(674\) 1.19390 + 0.689296i 0.0459872 + 0.0265507i
\(675\) −1.46623 1.79802i −0.0564351 0.0692057i
\(676\) −4.91774 + 12.0339i −0.189144 + 0.462844i
\(677\) 21.9008i 0.841718i −0.907126 0.420859i \(-0.861729\pi\)
0.907126 0.420859i \(-0.138271\pi\)
\(678\) 4.05956 7.03137i 0.155907 0.270038i
\(679\) −3.06883 + 5.31537i −0.117771 + 0.203985i
\(680\) −10.2038 + 11.9886i −0.391298 + 0.459742i
\(681\) 9.55012i 0.365961i
\(682\) −13.4741 23.3378i −0.515949 0.893650i
\(683\) 2.55910 + 4.43250i 0.0979214 + 0.169605i 0.910824 0.412795i \(-0.135447\pi\)
−0.812903 + 0.582399i \(0.802114\pi\)
\(684\) 7.41693i 0.283593i
\(685\) 19.3963 + 16.5087i 0.741096 + 0.630765i
\(686\) 8.45069 14.6370i 0.322649 0.558845i
\(687\) −11.8704 + 20.5602i −0.452884 + 0.784419i
\(688\) 5.28374i 0.201441i
\(689\) −25.7042 12.6001i −0.979252 0.480024i
\(690\) −13.5368 + 4.81973i −0.515337 + 0.183484i
\(691\) −1.66003 0.958418i −0.0631505 0.0364600i 0.468092 0.883680i \(-0.344941\pi\)
−0.531243 + 0.847220i \(0.678275\pi\)
\(692\) 0.461938 + 0.266700i 0.0175603 + 0.0101384i
\(693\) −18.1416 + 10.4741i −0.689142 + 0.397876i
\(694\) 11.8958i 0.451557i
\(695\) −19.3268 16.4495i −0.733108 0.623966i
\(696\) −8.79268 + 5.07645i −0.333285 + 0.192422i
\(697\) −19.7909 −0.749633
\(698\) −3.95580 + 2.28388i −0.149729 + 0.0864463i
\(699\) 23.3541 40.4505i 0.883334 1.52998i
\(700\) 1.12319 + 6.93770i 0.0424525 + 0.262220i
\(701\) −23.4448 −0.885500 −0.442750 0.896645i \(-0.645997\pi\)
−0.442750 + 0.896645i \(0.645997\pi\)
\(702\) −1.38885 + 0.932784i −0.0524189 + 0.0352057i
\(703\) 2.18216i 0.0823017i
\(704\) −4.59726 2.65423i −0.173266 0.100035i
\(705\) 9.49083 + 1.74222i 0.357445 + 0.0656158i
\(706\) −0.421009 0.729210i −0.0158449 0.0274442i
\(707\) −11.7889 −0.443368
\(708\) −7.78892 13.4908i −0.292725 0.507015i
\(709\) −4.33100 + 2.50051i −0.162654 + 0.0939085i −0.579118 0.815244i \(-0.696603\pi\)
0.416463 + 0.909153i \(0.363269\pi\)
\(710\) −7.22981 20.3058i −0.271330 0.762064i
\(711\) 5.69851 + 9.87011i 0.213711 + 0.370158i
\(712\) −13.1289 7.57999i −0.492027 0.284072i
\(713\) 6.76840 11.7232i 0.253479 0.439038i
\(714\) −23.8485 −0.892507
\(715\) 25.4668 34.3966i 0.952404 1.28636i
\(716\) 9.23733 0.345215
\(717\) −36.1646 + 62.6389i −1.35059 + 2.33929i
\(718\) 6.97949 + 4.02961i 0.260472 + 0.150384i
\(719\) 22.7388 + 39.3848i 0.848016 + 1.46881i 0.882976 + 0.469418i \(0.155536\pi\)
−0.0349601 + 0.999389i \(0.511130\pi\)
\(720\) −5.91398 + 2.10565i −0.220401 + 0.0784730i
\(721\) 6.77444 3.91123i 0.252293 0.145662i
\(722\) −6.01026 10.4101i −0.223679 0.387423i
\(723\) −46.1409 −1.71600
\(724\) 2.38232 + 4.12630i 0.0885383 + 0.153353i
\(725\) 3.36656 + 20.7945i 0.125031 + 0.772290i
\(726\) −35.8542 20.7004i −1.33067 0.768265i
\(727\) 6.38432i 0.236781i 0.992967 + 0.118391i \(0.0377735\pi\)
−0.992967 + 0.118391i \(0.962226\pi\)
\(728\) 5.05633 0.343480i 0.187400 0.0127302i
\(729\) 23.4301 0.867780
\(730\) −2.84337 + 15.4894i −0.105238 + 0.573288i
\(731\) −18.6001 + 32.2164i −0.687951 + 1.19157i
\(732\) 30.7522 17.7548i 1.13663 0.656236i
\(733\) 46.0006 1.69907 0.849536 0.527530i \(-0.176882\pi\)
0.849536 + 0.527530i \(0.176882\pi\)
\(734\) −14.3052 + 8.25912i −0.528015 + 0.304850i
\(735\) 17.5478 20.6172i 0.647261 0.760478i
\(736\) 2.66659i 0.0982917i
\(737\) 18.3890 10.6169i 0.677369 0.391079i
\(738\) −6.83446 3.94588i −0.251580 0.145250i
\(739\) −4.14392 2.39250i −0.152437 0.0880094i 0.421841 0.906670i \(-0.361384\pi\)
−0.574278 + 0.818660i \(0.694717\pi\)
\(740\) −1.73997 + 0.619511i −0.0639627 + 0.0227737i
\(741\) −10.1038 + 20.6117i −0.371171 + 0.757191i
\(742\) 11.1598i 0.409691i
\(743\) −7.90749 + 13.6962i −0.290098 + 0.502464i −0.973833 0.227267i \(-0.927021\pi\)
0.683735 + 0.729730i \(0.260354\pi\)
\(744\) 6.11679 10.5946i 0.224252 0.388416i
\(745\) 2.84650 3.34440i 0.104288 0.122529i
\(746\) 26.5545i 0.972231i
\(747\) −12.0146 20.8100i −0.439593 0.761397i
\(748\) −18.6871 32.3671i −0.683269 1.18346i
\(749\) 21.3437i 0.779881i
\(750\) −0.566950 + 26.9372i −0.0207021 + 0.983606i
\(751\) −4.94420 + 8.56360i −0.180416 + 0.312490i −0.942022 0.335550i \(-0.891078\pi\)
0.761606 + 0.648040i \(0.224411\pi\)
\(752\) −0.895350 + 1.55079i −0.0326501 + 0.0565516i
\(753\) 41.0713i 1.49672i
\(754\) 15.1555 1.02952i 0.551930 0.0374929i
\(755\) 7.77038 + 21.8241i 0.282793 + 0.794259i
\(756\) 0.564838 + 0.326110i 0.0205430 + 0.0118605i
\(757\) 7.56985 + 4.37046i 0.275131 + 0.158847i 0.631217 0.775606i \(-0.282556\pi\)
−0.356086 + 0.934453i \(0.615889\pi\)
\(758\) 1.00089 0.577865i 0.0363540 0.0209890i
\(759\) 34.1128i 1.23822i
\(760\) 3.82886 4.49859i 0.138887 0.163181i
\(761\) 42.8460 24.7372i 1.55317 0.896721i 0.555286 0.831659i \(-0.312609\pi\)
0.997881 0.0650620i \(-0.0207245\pi\)
\(762\) 26.1445 0.947114
\(763\) 0.811936 0.468772i 0.0293941 0.0169707i
\(764\) 8.97219 15.5403i 0.324603 0.562228i
\(765\) −43.4715 7.98002i −1.57172 0.288518i
\(766\) 35.0077 1.26488
\(767\) 1.57962 + 23.2534i 0.0570366 + 0.839631i
\(768\) 2.40987i 0.0869585i
\(769\) 20.2409 + 11.6861i 0.729906 + 0.421412i 0.818388 0.574666i \(-0.194868\pi\)
−0.0884817 + 0.996078i \(0.528201\pi\)
\(770\) −16.4104 3.01245i −0.591391 0.108561i
\(771\) 9.91088 + 17.1662i 0.356932 + 0.618224i
\(772\) 20.9462 0.753869
\(773\) 0.828857 + 1.43562i 0.0298119 + 0.0516358i 0.880546 0.473960i \(-0.157176\pi\)
−0.850735 + 0.525596i \(0.823842\pi\)
\(774\) −12.8465 + 7.41693i −0.461758 + 0.266596i
\(775\) −16.0410 19.6709i −0.576211 0.706600i
\(776\) −2.18328 3.78155i −0.0783751 0.135750i
\(777\) −2.42305 1.39895i −0.0869264 0.0501870i
\(778\) −5.65673 + 9.79774i −0.202803 + 0.351266i
\(779\) 7.42631 0.266075
\(780\) 19.3035 + 2.20473i 0.691175 + 0.0789418i
\(781\) 51.1707 1.83103
\(782\) 9.38707 16.2589i 0.335681 0.581416i
\(783\) 1.69300 + 0.977456i 0.0605030 + 0.0349314i
\(784\) 2.51214 + 4.35115i 0.0897191 + 0.155398i
\(785\) −4.37342 12.2833i −0.156094 0.438409i
\(786\) −32.0355 + 18.4957i −1.14267 + 0.659720i
\(787\) −21.6724 37.5376i −0.772536 1.33807i −0.936169 0.351550i \(-0.885655\pi\)
0.163633 0.986521i \(-0.447679\pi\)
\(788\) −26.7724 −0.953726
\(789\) −12.5669 21.7666i −0.447395 0.774911i
\(790\) −1.63895 + 8.92827i −0.0583113 + 0.317654i
\(791\) 4.10120 + 2.36783i 0.145822 + 0.0841902i
\(792\) 14.9033i 0.529564i
\(793\) −53.0060 + 3.60073i −1.88230 + 0.127866i
\(794\) −18.0057 −0.639000
\(795\) −7.72457 + 42.0800i −0.273962 + 1.49242i
\(796\) −7.19452 + 12.4613i −0.255003 + 0.441678i
\(797\) 17.6871 10.2117i 0.626509 0.361715i −0.152890 0.988243i \(-0.548858\pi\)
0.779399 + 0.626528i \(0.215525\pi\)
\(798\) 8.94887 0.316787
\(799\) −10.9184 + 6.30372i −0.386264 + 0.223010i
\(800\) −4.67401 1.77585i −0.165251 0.0627857i
\(801\) 42.5609i 1.50382i
\(802\) −3.97385 + 2.29430i −0.140321 + 0.0810146i
\(803\) −32.3776 18.6932i −1.14258 0.659670i
\(804\) 8.34802 + 4.81973i 0.294412 + 0.169979i
\(805\) −2.81121 7.89563i −0.0990822 0.278285i
\(806\) −15.1945 + 10.2050i −0.535204 + 0.359455i
\(807\) 54.5621i 1.92068i
\(808\) 4.19353 7.26341i 0.147528 0.255526i
\(809\) 11.5118 19.9390i 0.404732 0.701017i −0.589558 0.807726i \(-0.700698\pi\)
0.994290 + 0.106709i \(0.0340313\pi\)
\(810\) 16.2457 + 13.8271i 0.570816 + 0.485835i
\(811\) 5.67837i 0.199395i 0.995018 + 0.0996973i \(0.0317874\pi\)
−0.995018 + 0.0996973i \(0.968213\pi\)
\(812\) −2.96095 5.12852i −0.103909 0.179976i
\(813\) 0.304150 + 0.526804i 0.0106670 + 0.0184758i
\(814\) 4.38474i 0.153685i
\(815\) 20.0111 + 17.0319i 0.700957 + 0.596602i
\(816\) 8.48334 14.6936i 0.296976 0.514378i
\(817\) 6.97949 12.0888i 0.244181 0.422935i
\(818\) 26.2500i 0.917811i
\(819\) 7.93282 + 11.8114i 0.277195 + 0.412725i
\(820\) −2.10831 5.92146i −0.0736255 0.206786i
\(821\) −11.2259 6.48129i −0.391787 0.226198i 0.291147 0.956678i \(-0.405963\pi\)
−0.682934 + 0.730480i \(0.739296\pi\)
\(822\) −23.7727 13.7252i −0.829169 0.478721i
\(823\) −7.09023 + 4.09355i −0.247150 + 0.142692i −0.618459 0.785817i \(-0.712243\pi\)
0.371309 + 0.928510i \(0.378909\pi\)
\(824\) 5.56518i 0.193872i
\(825\) −59.7931 22.7178i −2.08173 0.790933i
\(826\) 7.86880 4.54305i 0.273791 0.158073i
\(827\) 9.13747 0.317741 0.158870 0.987299i \(-0.449215\pi\)
0.158870 + 0.987299i \(0.449215\pi\)
\(828\) 6.48334 3.74316i 0.225312 0.130084i
\(829\) 2.45257 4.24798i 0.0851814 0.147539i −0.820287 0.571952i \(-0.806186\pi\)
0.905469 + 0.424413i \(0.139520\pi\)
\(830\) 3.45554 18.8242i 0.119943 0.653398i
\(831\) −11.2188 −0.389176
\(832\) −1.58700 + 3.23750i −0.0550195 + 0.112240i
\(833\) 35.3734i 1.22562i
\(834\) 23.6875 + 13.6760i 0.820231 + 0.473561i
\(835\) −4.51204 + 24.5796i −0.156146 + 0.850611i
\(836\) 7.01214 + 12.1454i 0.242520 + 0.420057i
\(837\) −2.35554 −0.0814193
\(838\) 6.03869 + 10.4593i 0.208603 + 0.361311i
\(839\) −1.95525 + 1.12887i −0.0675028 + 0.0389727i −0.533372 0.845881i \(-0.679075\pi\)
0.465869 + 0.884854i \(0.345742\pi\)
\(840\) −2.54057 7.13549i −0.0876579 0.246198i
\(841\) 5.62507 + 9.74290i 0.193968 + 0.335962i
\(842\) 2.69954 + 1.55858i 0.0930321 + 0.0537121i
\(843\) −4.46141 + 7.72739i −0.153659 + 0.266145i
\(844\) −24.3908 −0.839567
\(845\) −24.4811 15.6741i −0.842174 0.539206i
\(846\) −5.02731 −0.172842
\(847\) 12.0740 20.9127i 0.414867 0.718570i
\(848\) −6.87583 3.96976i −0.236117 0.136322i
\(849\) −6.44393 11.1612i −0.221155 0.383052i
\(850\) −22.2472 27.2815i −0.763074 0.935748i
\(851\) 1.90749 1.10129i 0.0653878 0.0377516i
\(852\) 11.6149 + 20.1176i 0.397920 + 0.689218i
\(853\) 14.7832 0.506166 0.253083 0.967445i \(-0.418555\pi\)
0.253083 + 0.967445i \(0.418555\pi\)
\(854\) 10.3559 + 17.9369i 0.354370 + 0.613788i
\(855\) 16.3122 + 2.99441i 0.557865 + 0.102407i
\(856\) −13.1503 7.59234i −0.449469 0.259501i
\(857\) 19.3235i 0.660079i −0.943967 0.330039i \(-0.892938\pi\)
0.943967 0.330039i \(-0.107062\pi\)
\(858\) −20.3020 + 41.4163i −0.693100 + 1.41393i
\(859\) 48.8245 1.66587 0.832935 0.553371i \(-0.186659\pi\)
0.832935 + 0.553371i \(0.186659\pi\)
\(860\) −11.6206 2.13319i −0.396261 0.0727411i
\(861\) 4.76088 8.24609i 0.162251 0.281026i
\(862\) −4.52932 + 2.61501i −0.154269 + 0.0890675i
\(863\) −15.2366 −0.518660 −0.259330 0.965789i \(-0.583502\pi\)
−0.259330 + 0.965789i \(0.583502\pi\)
\(864\) −0.401847 + 0.232006i −0.0136711 + 0.00789302i
\(865\) −0.773055 + 0.908276i −0.0262847 + 0.0308823i
\(866\) 22.3063i 0.757998i
\(867\) 67.9712 39.2432i 2.30842 1.33277i
\(868\) 6.17952 + 3.56775i 0.209747 + 0.121097i
\(869\) −18.6629 10.7750i −0.633094 0.365517i
\(870\) −7.61491 21.3874i −0.258169 0.725101i
\(871\) −8.04102 11.9725i −0.272460 0.405674i
\(872\) 0.667003i 0.0225876i
\(873\) 6.12945 10.6165i 0.207451 0.359315i
\(874\) −3.52239 + 6.10096i −0.119147 + 0.206368i
\(875\) −15.7117 0.330686i −0.531152 0.0111792i
\(876\) 16.9722i 0.573438i
\(877\) 0.222953 + 0.386166i 0.00752859 + 0.0130399i 0.869765 0.493466i \(-0.164270\pi\)
−0.862237 + 0.506506i \(0.830937\pi\)
\(878\) 2.62417 + 4.54520i 0.0885616 + 0.153393i
\(879\) 58.2566i 1.96495i
\(880\) 7.69353 9.03926i 0.259349 0.304713i
\(881\) −19.4053 + 33.6110i −0.653782 + 1.13238i 0.328415 + 0.944534i \(0.393486\pi\)
−0.982198 + 0.187851i \(0.939848\pi\)
\(882\) −7.05270 + 12.2156i −0.237477 + 0.411322i
\(883\) 25.2239i 0.848853i 0.905462 + 0.424427i \(0.139524\pi\)
−0.905462 + 0.424427i \(0.860476\pi\)
\(884\) −21.0732 + 14.1532i −0.708769 + 0.476025i
\(885\) 32.8152 11.6837i 1.10307 0.392744i
\(886\) 0.966685 + 0.558116i 0.0324764 + 0.0187503i
\(887\) 0.226808 + 0.130947i 0.00761545 + 0.00439678i 0.503803 0.863819i \(-0.331934\pi\)
−0.496187 + 0.868215i \(0.665267\pi\)
\(888\) 1.72385 0.995263i 0.0578485 0.0333988i
\(889\) 15.2493i 0.511446i
\(890\) 21.9713 25.8144i 0.736480 0.865302i
\(891\) −43.8605 + 25.3229i −1.46938 + 0.848348i
\(892\) −2.97949 −0.0997606
\(893\) 4.09699 2.36540i 0.137101 0.0791551i
\(894\) −2.36656 + 4.09900i −0.0791495 + 0.137091i
\(895\) −3.72935 + 20.3158i −0.124659 + 0.679084i
\(896\) 1.40561 0.0469580
\(897\) −23.1164 + 1.57031i −0.771835 + 0.0524312i
\(898\) 34.4883i 1.15089i
\(899\) 18.5220 + 10.6937i 0.617744 + 0.356655i
\(900\) −2.24337 13.8568i −0.0747790 0.461895i
\(901\) −27.9491 48.4093i −0.931121 1.61275i
\(902\) 14.9221 0.496851
\(903\) −8.94887 15.4999i −0.297800 0.515804i
\(904\) −2.91774 + 1.68456i −0.0970426 + 0.0560276i
\(905\) −10.0369 + 3.57359i −0.333637 + 0.118790i
\(906\) −12.4833 21.6218i −0.414731 0.718336i
\(907\) 32.9635 + 19.0315i 1.09454 + 0.631930i 0.934780 0.355226i \(-0.115596\pi\)
0.159755 + 0.987157i \(0.448930\pi\)
\(908\) −1.98146 + 3.43199i −0.0657572 + 0.113895i
\(909\) 23.5463 0.780982
\(910\) −1.28595 + 11.2592i −0.0426289 + 0.373238i
\(911\) −50.4261 −1.67069 −0.835346 0.549725i \(-0.814733\pi\)
−0.835346 + 0.549725i \(0.814733\pi\)
\(912\) −3.18328 + 5.51360i −0.105409 + 0.182574i
\(913\) 39.3484 + 22.7178i 1.30224 + 0.751850i
\(914\) 2.03770 + 3.52940i 0.0674011 + 0.116742i
\(915\) 26.6330 + 74.8020i 0.880459 + 2.47288i
\(916\) 8.53166 4.92576i 0.281894 0.162752i
\(917\) −10.7880 18.6854i −0.356252 0.617046i
\(918\) −3.26689 −0.107823
\(919\) −3.36458 5.82763i −0.110987 0.192236i 0.805181 0.593029i \(-0.202068\pi\)
−0.916169 + 0.400793i \(0.868735\pi\)
\(920\) 5.86468 + 1.07657i 0.193353 + 0.0354935i
\(921\) −57.4851 33.1891i −1.89420 1.09362i
\(922\) 30.3417i 0.999249i
\(923\) −2.35554 34.6757i −0.0775335 1.14136i
\(924\) 17.9815 0.591547
\(925\) −0.660029 4.07687i −0.0217016 0.134047i
\(926\) −12.6145 + 21.8490i −0.414540 + 0.718004i
\(927\) −13.5308 + 7.81199i −0.444409 + 0.256579i
\(928\) 4.21306 0.138300
\(929\) 13.8526 7.99782i 0.454490 0.262400i −0.255234 0.966879i \(-0.582153\pi\)
0.709725 + 0.704479i \(0.248819\pi\)
\(930\) 20.8314 + 17.7301i 0.683087 + 0.581392i
\(931\) 13.2735i 0.435021i
\(932\) −16.7854 + 9.69104i −0.549823 + 0.317441i
\(933\) 26.7683 + 15.4547i 0.876355 + 0.505964i
\(934\) −19.0523 10.9999i −0.623410 0.359926i
\(935\) 78.7300 28.0315i 2.57475 0.916729i
\(936\) −10.0991 + 0.686041i −0.330101 + 0.0224239i
\(937\) 32.2129i 1.05235i 0.850376 + 0.526176i \(0.176375\pi\)
−0.850376 + 0.526176i \(0.823625\pi\)
\(938\) −2.81121 + 4.86916i −0.0917893 + 0.158984i
\(939\) −3.28470 + 5.68927i −0.107192 + 0.185662i
\(940\) −3.04921 2.59526i −0.0994543 0.0846479i
\(941\) 14.9874i 0.488576i −0.969703 0.244288i \(-0.921446\pi\)
0.969703 0.244288i \(-0.0785542\pi\)
\(942\) 7.02602 + 12.1694i 0.228920 + 0.396501i
\(943\) 3.74789 + 6.49154i 0.122048 + 0.211394i
\(944\) 6.46419i 0.210391i
\(945\) −0.945259 + 1.11060i −0.0307493 + 0.0361278i
\(946\) 14.0243 24.2908i 0.455968 0.789760i
\(947\) 7.43878 12.8844i 0.241728 0.418685i −0.719479 0.694515i \(-0.755619\pi\)
0.961207 + 0.275829i \(0.0889525\pi\)
\(948\) 9.78300i 0.317737i
\(949\) −11.1770 + 22.8011i −0.362820 + 0.740155i
\(950\) 8.34802 + 10.2371i 0.270846 + 0.332135i
\(951\) 3.96449 + 2.28890i 0.128557 + 0.0742226i
\(952\) 8.57035 + 4.94809i 0.277767 + 0.160369i
\(953\) 5.73486 3.31103i 0.185770 0.107255i −0.404231 0.914657i \(-0.632461\pi\)
0.590001 + 0.807402i \(0.299127\pi\)
\(954\) 22.2898i 0.721660i
\(955\) 30.5558 + 26.0067i 0.988761 + 0.841559i
\(956\) 25.9927 15.0069i 0.840664 0.485358i
\(957\) 53.8963 1.74222
\(958\) 19.1462 11.0541i 0.618586 0.357141i
\(959\) 8.00551 13.8659i 0.258511 0.447755i
\(960\) 5.30006 + 0.972927i 0.171059 + 0.0314011i
\(961\) 5.22962 0.168697
\(962\) −2.97130 + 0.201842i −0.0957986 + 0.00650766i
\(963\) 42.6303i 1.37374i
\(964\) 16.5815 + 9.57333i 0.534054 + 0.308336i
\(965\) −8.45652 + 46.0673i −0.272225 + 1.48296i
\(966\) 4.51630 + 7.82245i 0.145309 + 0.251683i
\(967\) 24.8355 0.798655 0.399328 0.916808i \(-0.369244\pi\)
0.399328 + 0.916808i \(0.369244\pi\)
\(968\) 8.58987 + 14.8781i 0.276089 + 0.478200i
\(969\) −38.8186 + 22.4119i −1.24703 + 0.719974i
\(970\) 9.19828 3.27501i 0.295339 0.105154i
\(971\) 11.5415 + 19.9904i 0.370383 + 0.641522i 0.989624 0.143678i \(-0.0458931\pi\)
−0.619241 + 0.785201i \(0.712560\pi\)
\(972\) −18.7057 10.7997i −0.599985 0.346401i
\(973\) −7.97681 + 13.8162i −0.255725 + 0.442928i
\(974\) 3.66873 0.117554
\(975\) −12.6422 + 41.5644i −0.404875 + 1.33113i
\(976\) −14.7351 −0.471659
\(977\) 4.00989 6.94534i 0.128288 0.222201i −0.794725 0.606969i \(-0.792385\pi\)
0.923013 + 0.384768i \(0.125719\pi\)
\(978\) −24.5262 14.1602i −0.784260 0.452793i
\(979\) 40.2381 + 69.6943i 1.28601 + 2.22744i
\(980\) −10.5838 + 3.76832i −0.338086 + 0.120374i
\(981\) −1.62170 + 0.936289i −0.0517769 + 0.0298934i
\(982\) −13.2345 22.9228i −0.422329 0.731495i
\(983\) 16.0606 0.512254 0.256127 0.966643i \(-0.417553\pi\)
0.256127 + 0.966643i \(0.417553\pi\)
\(984\) 3.38707 + 5.86658i 0.107976 + 0.187020i
\(985\) 10.8087 58.8810i 0.344394 1.87610i
\(986\) 25.6881 + 14.8310i 0.818076 + 0.472317i
\(987\) 6.06568i 0.193073i
\(988\) 7.90749 5.31084i 0.251571 0.168960i
\(989\) 14.0896 0.448022
\(990\) 32.7770 + 6.01684i 1.04172 + 0.191228i
\(991\) 17.2373 29.8559i 0.547562 0.948405i −0.450879 0.892585i \(-0.648889\pi\)
0.998441 0.0558199i \(-0.0177773\pi\)
\(992\) −4.39634 + 2.53823i −0.139584 + 0.0805888i
\(993\) 21.6581 0.687297
\(994\) −11.7340 + 6.77464i −0.372181 + 0.214879i
\(995\) −24.5017 20.8540i −0.776756 0.661116i
\(996\) 20.6263i 0.653569i
\(997\) −38.3187 + 22.1233i −1.21357 + 0.700652i −0.963534 0.267586i \(-0.913774\pi\)
−0.250031 + 0.968238i \(0.580441\pi\)
\(998\) 32.0779 + 18.5202i 1.01541 + 0.586247i
\(999\) −0.331921 0.191635i −0.0105015 0.00606306i
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 130.2.m.a.69.4 yes 8
3.2 odd 2 1170.2.bj.b.199.1 8
4.3 odd 2 1040.2.df.c.849.1 8
5.2 odd 4 650.2.m.e.251.4 16
5.3 odd 4 650.2.m.e.251.5 16
5.4 even 2 130.2.m.b.69.1 yes 8
13.4 even 6 1690.2.c.e.1689.2 8
13.6 odd 12 1690.2.b.e.339.2 16
13.7 odd 12 1690.2.b.e.339.10 16
13.9 even 3 1690.2.c.f.1689.2 8
13.10 even 6 130.2.m.b.49.1 yes 8
15.14 odd 2 1170.2.bj.a.199.4 8
20.19 odd 2 1040.2.df.a.849.4 8
39.23 odd 6 1170.2.bj.a.829.4 8
52.23 odd 6 1040.2.df.a.49.4 8
65.4 even 6 1690.2.c.f.1689.7 8
65.7 even 12 8450.2.a.cr.1.2 8
65.9 even 6 1690.2.c.e.1689.7 8
65.19 odd 12 1690.2.b.e.339.15 16
65.23 odd 12 650.2.m.e.101.5 16
65.32 even 12 8450.2.a.cs.1.2 8
65.33 even 12 8450.2.a.cs.1.7 8
65.49 even 6 inner 130.2.m.a.49.4 8
65.58 even 12 8450.2.a.cr.1.7 8
65.59 odd 12 1690.2.b.e.339.7 16
65.62 odd 12 650.2.m.e.101.4 16
195.179 odd 6 1170.2.bj.b.829.1 8
260.179 odd 6 1040.2.df.c.49.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.m.a.49.4 8 65.49 even 6 inner
130.2.m.a.69.4 yes 8 1.1 even 1 trivial
130.2.m.b.49.1 yes 8 13.10 even 6
130.2.m.b.69.1 yes 8 5.4 even 2
650.2.m.e.101.4 16 65.62 odd 12
650.2.m.e.101.5 16 65.23 odd 12
650.2.m.e.251.4 16 5.2 odd 4
650.2.m.e.251.5 16 5.3 odd 4
1040.2.df.a.49.4 8 52.23 odd 6
1040.2.df.a.849.4 8 20.19 odd 2
1040.2.df.c.49.1 8 260.179 odd 6
1040.2.df.c.849.1 8 4.3 odd 2
1170.2.bj.a.199.4 8 15.14 odd 2
1170.2.bj.a.829.4 8 39.23 odd 6
1170.2.bj.b.199.1 8 3.2 odd 2
1170.2.bj.b.829.1 8 195.179 odd 6
1690.2.b.e.339.2 16 13.6 odd 12
1690.2.b.e.339.7 16 65.59 odd 12
1690.2.b.e.339.10 16 13.7 odd 12
1690.2.b.e.339.15 16 65.19 odd 12
1690.2.c.e.1689.2 8 13.4 even 6
1690.2.c.e.1689.7 8 65.9 even 6
1690.2.c.f.1689.2 8 13.9 even 3
1690.2.c.f.1689.7 8 65.4 even 6
8450.2.a.cr.1.2 8 65.7 even 12
8450.2.a.cr.1.7 8 65.58 even 12
8450.2.a.cs.1.2 8 65.32 even 12
8450.2.a.cs.1.7 8 65.33 even 12