Properties

Label 731.2.m.b.87.18
Level $731$
Weight $2$
Character 731.87
Analytic conductor $5.837$
Analytic rank $0$
Dimension $116$
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] = [731,2,Mod(87,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.87");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.m (of order \(8\), 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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(116\)
Relative dimension: \(29\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.18
Character \(\chi\) \(=\) 731.87
Dual form 731.2.m.b.689.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.544996 + 0.544996i) q^{2} +(-1.90994 + 0.791125i) q^{3} -1.40596i q^{4} +(0.670095 + 1.61775i) q^{5} +(-1.47207 - 0.609752i) q^{6} +(1.29182 - 3.11873i) q^{7} +(1.85623 - 1.85623i) q^{8} +(0.900688 - 0.900688i) q^{9} +O(q^{10})\) \(q+(0.544996 + 0.544996i) q^{2} +(-1.90994 + 0.791125i) q^{3} -1.40596i q^{4} +(0.670095 + 1.61775i) q^{5} +(-1.47207 - 0.609752i) q^{6} +(1.29182 - 3.11873i) q^{7} +(1.85623 - 1.85623i) q^{8} +(0.900688 - 0.900688i) q^{9} +(-0.516470 + 1.24687i) q^{10} +(-4.86339 - 2.01448i) q^{11} +(1.11229 + 2.68530i) q^{12} +2.36005i q^{13} +(2.40374 - 0.995660i) q^{14} +(-2.55969 - 2.55969i) q^{15} -0.788636 q^{16} +(-0.687043 + 4.06546i) q^{17} +0.981743 q^{18} +(-3.34074 - 3.34074i) q^{19} +(2.27449 - 0.942126i) q^{20} +6.97860i q^{21} +(-1.55265 - 3.74842i) q^{22} +(-7.31247 - 3.02893i) q^{23} +(-2.07679 + 5.01382i) q^{24} +(1.36744 - 1.36744i) q^{25} +(-1.28622 + 1.28622i) q^{26} +(1.36567 - 3.29701i) q^{27} +(-4.38481 - 1.81625i) q^{28} +(-2.32635 - 5.61631i) q^{29} -2.79004i q^{30} +(-2.55067 + 1.05652i) q^{31} +(-4.14227 - 4.14227i) q^{32} +10.8825 q^{33} +(-2.59010 + 1.84122i) q^{34} +5.91099 q^{35} +(-1.26633 - 1.26633i) q^{36} +(8.24203 - 3.41396i) q^{37} -3.64138i q^{38} +(-1.86709 - 4.50756i) q^{39} +(4.24678 + 1.75908i) q^{40} +(1.86196 - 4.49517i) q^{41} +(-3.80331 + 3.80331i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-2.83228 + 6.83773i) q^{44} +(2.06064 + 0.853545i) q^{45} +(-2.33452 - 5.63602i) q^{46} +11.2746i q^{47} +(1.50625 - 0.623909i) q^{48} +(-3.10796 - 3.10796i) q^{49} +1.49049 q^{50} +(-1.90407 - 8.30834i) q^{51} +3.31813 q^{52} +(-1.82572 - 1.82572i) q^{53} +(2.54114 - 1.05258i) q^{54} -9.21767i q^{55} +(-3.39118 - 8.18703i) q^{56} +(9.02357 + 3.73769i) q^{57} +(1.79301 - 4.32872i) q^{58} +(-0.966745 + 0.966745i) q^{59} +(-3.59882 + 3.59882i) q^{60} +(4.96634 - 11.9898i) q^{61} +(-1.96591 - 0.814306i) q^{62} +(-1.64548 - 3.97254i) q^{63} -2.93777i q^{64} +(-3.81797 + 1.58146i) q^{65} +(5.93093 + 5.93093i) q^{66} -5.57905 q^{67} +(5.71587 + 0.965954i) q^{68} +16.3627 q^{69} +(3.22147 + 3.22147i) q^{70} +(-2.89331 + 1.19845i) q^{71} -3.34378i q^{72} +(-1.38379 - 3.34076i) q^{73} +(6.35247 + 2.63128i) q^{74} +(-1.52991 + 3.69354i) q^{75} +(-4.69694 + 4.69694i) q^{76} +(-12.5653 + 12.5653i) q^{77} +(1.43904 - 3.47416i) q^{78} +(-12.3676 - 5.12281i) q^{79} +(-0.528461 - 1.27582i) q^{80} +11.1988i q^{81} +(3.46461 - 1.43509i) q^{82} +(-6.26970 - 6.26970i) q^{83} +9.81163 q^{84} +(-7.03730 + 1.61278i) q^{85} +0.770741 q^{86} +(8.88640 + 8.88640i) q^{87} +(-12.7670 + 5.28825i) q^{88} +3.29131i q^{89} +(0.657862 + 1.58822i) q^{90} +(7.36036 + 3.04876i) q^{91} +(-4.25854 + 10.2810i) q^{92} +(4.03580 - 4.03580i) q^{93} +(-6.14461 + 6.14461i) q^{94} +(3.16588 - 7.64311i) q^{95} +(11.1886 + 4.63445i) q^{96} +(3.23825 + 7.81783i) q^{97} -3.38765i q^{98} +(-6.19483 + 2.56598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 116 q - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.544996 + 0.544996i 0.385370 + 0.385370i 0.873033 0.487662i \(-0.162150\pi\)
−0.487662 + 0.873033i \(0.662150\pi\)
\(3\) −1.90994 + 0.791125i −1.10271 + 0.456756i −0.858420 0.512947i \(-0.828554\pi\)
−0.244287 + 0.969703i \(0.578554\pi\)
\(4\) 1.40596i 0.702979i
\(5\) 0.670095 + 1.61775i 0.299676 + 0.723481i 0.999954 + 0.00961115i \(0.00305937\pi\)
−0.700278 + 0.713870i \(0.746941\pi\)
\(6\) −1.47207 0.609752i −0.600971 0.248930i
\(7\) 1.29182 3.11873i 0.488263 1.17877i −0.467330 0.884083i \(-0.654784\pi\)
0.955593 0.294688i \(-0.0952158\pi\)
\(8\) 1.85623 1.85623i 0.656278 0.656278i
\(9\) 0.900688 0.900688i 0.300229 0.300229i
\(10\) −0.516470 + 1.24687i −0.163322 + 0.394295i
\(11\) −4.86339 2.01448i −1.46637 0.607390i −0.500341 0.865828i \(-0.666792\pi\)
−0.966028 + 0.258439i \(0.916792\pi\)
\(12\) 1.11229 + 2.68530i 0.321090 + 0.775180i
\(13\) 2.36005i 0.654559i 0.944928 + 0.327280i \(0.106132\pi\)
−0.944928 + 0.327280i \(0.893868\pi\)
\(14\) 2.40374 0.995660i 0.642426 0.266101i
\(15\) −2.55969 2.55969i −0.660909 0.660909i
\(16\) −0.788636 −0.197159
\(17\) −0.687043 + 4.06546i −0.166632 + 0.986019i
\(18\) 0.981743 0.231399
\(19\) −3.34074 3.34074i −0.766419 0.766419i 0.211055 0.977474i \(-0.432310\pi\)
−0.977474 + 0.211055i \(0.932310\pi\)
\(20\) 2.27449 0.942126i 0.508592 0.210666i
\(21\) 6.97860i 1.52286i
\(22\) −1.55265 3.74842i −0.331025 0.799165i
\(23\) −7.31247 3.02893i −1.52476 0.631575i −0.546219 0.837643i \(-0.683933\pi\)
−0.978538 + 0.206068i \(0.933933\pi\)
\(24\) −2.07679 + 5.01382i −0.423923 + 1.02344i
\(25\) 1.36744 1.36744i 0.273487 0.273487i
\(26\) −1.28622 + 1.28622i −0.252248 + 0.252248i
\(27\) 1.36567 3.29701i 0.262823 0.634510i
\(28\) −4.38481 1.81625i −0.828652 0.343239i
\(29\) −2.32635 5.61631i −0.431992 1.04292i −0.978644 0.205562i \(-0.934098\pi\)
0.546652 0.837360i \(-0.315902\pi\)
\(30\) 2.79004i 0.509390i
\(31\) −2.55067 + 1.05652i −0.458115 + 0.189757i −0.599793 0.800156i \(-0.704750\pi\)
0.141678 + 0.989913i \(0.454750\pi\)
\(32\) −4.14227 4.14227i −0.732257 0.732257i
\(33\) 10.8825 1.89440
\(34\) −2.59010 + 1.84122i −0.444198 + 0.315767i
\(35\) 5.91099 0.999139
\(36\) −1.26633 1.26633i −0.211055 0.211055i
\(37\) 8.24203 3.41396i 1.35498 0.561252i 0.417307 0.908766i \(-0.362974\pi\)
0.937675 + 0.347514i \(0.112974\pi\)
\(38\) 3.64138i 0.590710i
\(39\) −1.86709 4.50756i −0.298974 0.721787i
\(40\) 4.24678 + 1.75908i 0.671475 + 0.278134i
\(41\) 1.86196 4.49517i 0.290790 0.702028i −0.709206 0.705001i \(-0.750946\pi\)
0.999996 + 0.00297314i \(0.000946381\pi\)
\(42\) −3.80331 + 3.80331i −0.586864 + 0.586864i
\(43\) 0.707107 0.707107i 0.107833 0.107833i
\(44\) −2.83228 + 6.83773i −0.426982 + 1.03083i
\(45\) 2.06064 + 0.853545i 0.307182 + 0.127239i
\(46\) −2.33452 5.63602i −0.344206 0.830986i
\(47\) 11.2746i 1.64457i 0.569077 + 0.822284i \(0.307301\pi\)
−0.569077 + 0.822284i \(0.692699\pi\)
\(48\) 1.50625 0.623909i 0.217409 0.0900536i
\(49\) −3.10796 3.10796i −0.443994 0.443994i
\(50\) 1.49049 0.210788
\(51\) −1.90407 8.30834i −0.266623 1.16340i
\(52\) 3.31813 0.460141
\(53\) −1.82572 1.82572i −0.250782 0.250782i 0.570509 0.821291i \(-0.306746\pi\)
−0.821291 + 0.570509i \(0.806746\pi\)
\(54\) 2.54114 1.05258i 0.345806 0.143237i
\(55\) 9.21767i 1.24291i
\(56\) −3.39118 8.18703i −0.453165 1.09404i
\(57\) 9.02357 + 3.73769i 1.19520 + 0.495069i
\(58\) 1.79301 4.32872i 0.235434 0.568389i
\(59\) −0.966745 + 0.966745i −0.125860 + 0.125860i −0.767231 0.641371i \(-0.778366\pi\)
0.641371 + 0.767231i \(0.278366\pi\)
\(60\) −3.59882 + 3.59882i −0.464605 + 0.464605i
\(61\) 4.96634 11.9898i 0.635875 1.53514i −0.196252 0.980554i \(-0.562877\pi\)
0.832127 0.554585i \(-0.187123\pi\)
\(62\) −1.96591 0.814306i −0.249671 0.103417i
\(63\) −1.64548 3.97254i −0.207311 0.500493i
\(64\) 2.93777i 0.367222i
\(65\) −3.81797 + 1.58146i −0.473561 + 0.196156i
\(66\) 5.93093 + 5.93093i 0.730047 + 0.730047i
\(67\) −5.57905 −0.681589 −0.340795 0.940138i \(-0.610696\pi\)
−0.340795 + 0.940138i \(0.610696\pi\)
\(68\) 5.71587 + 0.965954i 0.693151 + 0.117139i
\(69\) 16.3627 1.96983
\(70\) 3.22147 + 3.22147i 0.385039 + 0.385039i
\(71\) −2.89331 + 1.19845i −0.343373 + 0.142230i −0.547704 0.836672i \(-0.684498\pi\)
0.204331 + 0.978902i \(0.434498\pi\)
\(72\) 3.34378i 0.394068i
\(73\) −1.38379 3.34076i −0.161960 0.391006i 0.821977 0.569520i \(-0.192871\pi\)
−0.983937 + 0.178514i \(0.942871\pi\)
\(74\) 6.35247 + 2.63128i 0.738460 + 0.305880i
\(75\) −1.52991 + 3.69354i −0.176659 + 0.426493i
\(76\) −4.69694 + 4.69694i −0.538776 + 0.538776i
\(77\) −12.5653 + 12.5653i −1.43195 + 1.43195i
\(78\) 1.43904 3.47416i 0.162940 0.393371i
\(79\) −12.3676 5.12281i −1.39146 0.576362i −0.443939 0.896057i \(-0.646419\pi\)
−0.947520 + 0.319695i \(0.896419\pi\)
\(80\) −0.528461 1.27582i −0.0590838 0.142641i
\(81\) 11.1988i 1.24431i
\(82\) 3.46461 1.43509i 0.382603 0.158479i
\(83\) −6.26970 6.26970i −0.688189 0.688189i 0.273642 0.961832i \(-0.411772\pi\)
−0.961832 + 0.273642i \(0.911772\pi\)
\(84\) 9.81163 1.07054
\(85\) −7.03730 + 1.61278i −0.763302 + 0.174931i
\(86\) 0.770741 0.0831111
\(87\) 8.88640 + 8.88640i 0.952722 + 0.952722i
\(88\) −12.7670 + 5.28825i −1.36096 + 0.563729i
\(89\) 3.29131i 0.348878i 0.984668 + 0.174439i \(0.0558112\pi\)
−0.984668 + 0.174439i \(0.944189\pi\)
\(90\) 0.657862 + 1.58822i 0.0693447 + 0.167413i
\(91\) 7.36036 + 3.04876i 0.771575 + 0.319597i
\(92\) −4.25854 + 10.2810i −0.443984 + 1.07187i
\(93\) 4.03580 4.03580i 0.418493 0.418493i
\(94\) −6.14461 + 6.14461i −0.633768 + 0.633768i
\(95\) 3.16588 7.64311i 0.324813 0.784167i
\(96\) 11.1886 + 4.63445i 1.14193 + 0.473002i
\(97\) 3.23825 + 7.81783i 0.328795 + 0.793780i 0.998682 + 0.0513180i \(0.0163422\pi\)
−0.669888 + 0.742462i \(0.733658\pi\)
\(98\) 3.38765i 0.342204i
\(99\) −6.19483 + 2.56598i −0.622603 + 0.257891i
\(100\) −1.92256 1.92256i −0.192256 0.192256i
\(101\) −10.2345 −1.01837 −0.509186 0.860657i \(-0.670053\pi\)
−0.509186 + 0.860657i \(0.670053\pi\)
\(102\) 3.49030 5.56573i 0.345591 0.551089i
\(103\) 10.9607 1.07999 0.539997 0.841667i \(-0.318425\pi\)
0.539997 + 0.841667i \(0.318425\pi\)
\(104\) 4.38080 + 4.38080i 0.429573 + 0.429573i
\(105\) −11.2897 + 4.67633i −1.10176 + 0.456363i
\(106\) 1.99002i 0.193288i
\(107\) −0.00422798 0.0102073i −0.000408734 0.000986772i 0.923675 0.383177i \(-0.125170\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(108\) −4.63546 1.92007i −0.446047 0.184759i
\(109\) 0.0587593 0.141858i 0.00562812 0.0135875i −0.921040 0.389467i \(-0.872659\pi\)
0.926669 + 0.375879i \(0.122659\pi\)
\(110\) 5.02360 5.02360i 0.478981 0.478981i
\(111\) −13.0409 + 13.0409i −1.23779 + 1.23779i
\(112\) −1.01878 + 2.45955i −0.0962654 + 0.232405i
\(113\) 0.334452 + 0.138535i 0.0314626 + 0.0130322i 0.398359 0.917229i \(-0.369580\pi\)
−0.366897 + 0.930262i \(0.619580\pi\)
\(114\) 2.88079 + 6.95484i 0.269811 + 0.651380i
\(115\) 13.8595i 1.29240i
\(116\) −7.89629 + 3.27075i −0.733153 + 0.303682i
\(117\) 2.12567 + 2.12567i 0.196518 + 0.196518i
\(118\) −1.05374 −0.0970051
\(119\) 11.7916 + 7.39456i 1.08093 + 0.677858i
\(120\) −9.50277 −0.867480
\(121\) 11.8163 + 11.8163i 1.07421 + 1.07421i
\(122\) 9.24104 3.82777i 0.836645 0.346550i
\(123\) 10.0586i 0.906951i
\(124\) 1.48543 + 3.58614i 0.133395 + 0.322045i
\(125\) 11.2173 + 4.64634i 1.00330 + 0.415581i
\(126\) 1.26824 3.06180i 0.112984 0.272767i
\(127\) 8.21518 8.21518i 0.728979 0.728979i −0.241437 0.970416i \(-0.577619\pi\)
0.970416 + 0.241437i \(0.0776188\pi\)
\(128\) −6.68347 + 6.68347i −0.590741 + 0.590741i
\(129\) −0.791125 + 1.90994i −0.0696547 + 0.168161i
\(130\) −2.94267 1.21889i −0.258089 0.106904i
\(131\) 5.92235 + 14.2978i 0.517438 + 1.24921i 0.939472 + 0.342626i \(0.111316\pi\)
−0.422034 + 0.906580i \(0.638684\pi\)
\(132\) 15.3004i 1.33173i
\(133\) −14.7345 + 6.10324i −1.27765 + 0.529218i
\(134\) −3.04056 3.04056i −0.262664 0.262664i
\(135\) 6.24888 0.537818
\(136\) 6.27113 + 8.82176i 0.537745 + 0.756460i
\(137\) 5.02391 0.429221 0.214611 0.976700i \(-0.431152\pi\)
0.214611 + 0.976700i \(0.431152\pi\)
\(138\) 8.91760 + 8.91760i 0.759116 + 0.759116i
\(139\) 8.29640 3.43648i 0.703692 0.291479i −0.00199967 0.999998i \(-0.500637\pi\)
0.705691 + 0.708519i \(0.250637\pi\)
\(140\) 8.31060i 0.702374i
\(141\) −8.91961 21.5338i −0.751167 1.81348i
\(142\) −2.22999 0.923693i −0.187137 0.0775146i
\(143\) 4.75428 11.4778i 0.397572 0.959825i
\(144\) −0.710315 + 0.710315i −0.0591929 + 0.0591929i
\(145\) 7.52692 7.52692i 0.625077 0.625077i
\(146\) 1.06654 2.57486i 0.0882676 0.213097i
\(147\) 8.39480 + 3.47724i 0.692392 + 0.286798i
\(148\) −4.79989 11.5880i −0.394548 0.952524i
\(149\) 19.8308i 1.62461i 0.583236 + 0.812303i \(0.301786\pi\)
−0.583236 + 0.812303i \(0.698214\pi\)
\(150\) −2.84676 + 1.17917i −0.232437 + 0.0962786i
\(151\) 12.1386 + 12.1386i 0.987827 + 0.987827i 0.999927 0.0120998i \(-0.00385157\pi\)
−0.0120998 + 0.999927i \(0.503852\pi\)
\(152\) −12.4024 −1.00597
\(153\) 3.04290 + 4.28052i 0.246004 + 0.346060i
\(154\) −13.6961 −1.10366
\(155\) −3.41839 3.41839i −0.274572 0.274572i
\(156\) −6.33744 + 2.62505i −0.507401 + 0.210172i
\(157\) 5.60725i 0.447508i 0.974646 + 0.223754i \(0.0718311\pi\)
−0.974646 + 0.223754i \(0.928169\pi\)
\(158\) −3.94836 9.53219i −0.314115 0.758340i
\(159\) 4.93140 + 2.04265i 0.391085 + 0.161993i
\(160\) 3.92546 9.47689i 0.310335 0.749214i
\(161\) −18.8928 + 18.8928i −1.48896 + 1.48896i
\(162\) −6.10331 + 6.10331i −0.479522 + 0.479522i
\(163\) 4.94668 11.9424i 0.387454 0.935397i −0.603023 0.797723i \(-0.706037\pi\)
0.990478 0.137674i \(-0.0439625\pi\)
\(164\) −6.32003 2.61784i −0.493511 0.204419i
\(165\) 7.29233 + 17.6052i 0.567707 + 1.37057i
\(166\) 6.83393i 0.530416i
\(167\) 12.5187 5.18542i 0.968727 0.401260i 0.158489 0.987361i \(-0.449338\pi\)
0.810238 + 0.586101i \(0.199338\pi\)
\(168\) 12.9539 + 12.9539i 0.999417 + 0.999417i
\(169\) 7.43018 0.571552
\(170\) −4.71426 2.95634i −0.361567 0.226741i
\(171\) −6.01793 −0.460203
\(172\) −0.994163 0.994163i −0.0758042 0.0758042i
\(173\) −18.6961 + 7.74419i −1.42144 + 0.588780i −0.955222 0.295890i \(-0.904384\pi\)
−0.466218 + 0.884670i \(0.654384\pi\)
\(174\) 9.68611i 0.734302i
\(175\) −2.49818 6.03115i −0.188845 0.455912i
\(176\) 3.83545 + 1.58869i 0.289108 + 0.119752i
\(177\) 1.08161 2.61125i 0.0812990 0.196273i
\(178\) −1.79375 + 1.79375i −0.134447 + 0.134447i
\(179\) −4.15779 + 4.15779i −0.310768 + 0.310768i −0.845207 0.534439i \(-0.820523\pi\)
0.534439 + 0.845207i \(0.320523\pi\)
\(180\) 1.20005 2.89717i 0.0894463 0.215942i
\(181\) −22.5914 9.35768i −1.67921 0.695551i −0.679921 0.733285i \(-0.737986\pi\)
−0.999288 + 0.0377342i \(0.987986\pi\)
\(182\) 2.34980 + 5.67293i 0.174179 + 0.420506i
\(183\) 26.8289i 1.98325i
\(184\) −19.1961 + 7.95127i −1.41515 + 0.586175i
\(185\) 11.0459 + 11.0459i 0.812110 + 0.812110i
\(186\) 4.39899 0.322550
\(187\) 11.5312 18.3879i 0.843243 1.34466i
\(188\) 15.8516 1.15610
\(189\) −8.51831 8.51831i −0.619616 0.619616i
\(190\) 5.89086 2.44007i 0.427368 0.177022i
\(191\) 9.32216i 0.674528i −0.941410 0.337264i \(-0.890499\pi\)
0.941410 0.337264i \(-0.109501\pi\)
\(192\) 2.32415 + 5.61098i 0.167731 + 0.404938i
\(193\) −2.05390 0.850754i −0.147843 0.0612386i 0.307535 0.951537i \(-0.400496\pi\)
−0.455378 + 0.890298i \(0.650496\pi\)
\(194\) −2.49585 + 6.02552i −0.179192 + 0.432607i
\(195\) 6.04099 6.04099i 0.432604 0.432604i
\(196\) −4.36966 + 4.36966i −0.312118 + 0.312118i
\(197\) 6.77556 16.3576i 0.482739 1.16543i −0.475565 0.879681i \(-0.657756\pi\)
0.958303 0.285753i \(-0.0922438\pi\)
\(198\) −4.77461 1.97771i −0.339316 0.140549i
\(199\) 4.51683 + 10.9046i 0.320190 + 0.773007i 0.999242 + 0.0389170i \(0.0123908\pi\)
−0.679053 + 0.734090i \(0.737609\pi\)
\(200\) 5.07656i 0.358967i
\(201\) 10.6557 4.41372i 0.751593 0.311320i
\(202\) −5.57777 5.57777i −0.392450 0.392450i
\(203\) −20.5210 −1.44029
\(204\) −11.6812 + 2.67705i −0.817846 + 0.187431i
\(205\) 8.51978 0.595047
\(206\) 5.97356 + 5.97356i 0.416198 + 0.416198i
\(207\) −9.31438 + 3.85814i −0.647394 + 0.268159i
\(208\) 1.86122i 0.129052i
\(209\) 9.51747 + 22.9772i 0.658337 + 1.58937i
\(210\) −8.70140 3.60424i −0.600454 0.248716i
\(211\) −7.66707 + 18.5100i −0.527823 + 1.27428i 0.405123 + 0.914262i \(0.367229\pi\)
−0.932946 + 0.360016i \(0.882771\pi\)
\(212\) −2.56689 + 2.56689i −0.176295 + 0.176295i
\(213\) 4.57794 4.57794i 0.313675 0.313675i
\(214\) 0.00325868 0.00786715i 0.000222759 0.000537787i
\(215\) 1.61775 + 0.670095i 0.110330 + 0.0457001i
\(216\) −3.58503 8.65502i −0.243930 0.588900i
\(217\) 9.31972i 0.632664i
\(218\) 0.109335 0.0452882i 0.00740513 0.00306731i
\(219\) 5.28591 + 5.28591i 0.357189 + 0.357189i
\(220\) −12.9597 −0.873740
\(221\) −9.59468 1.62145i −0.645408 0.109071i
\(222\) −14.2145 −0.954017
\(223\) 1.47780 + 1.47780i 0.0989609 + 0.0989609i 0.754854 0.655893i \(-0.227708\pi\)
−0.655893 + 0.754854i \(0.727708\pi\)
\(224\) −18.2697 + 7.56757i −1.22070 + 0.505629i
\(225\) 2.46327i 0.164218i
\(226\) 0.106774 + 0.257776i 0.00710252 + 0.0171470i
\(227\) −6.80375 2.81821i −0.451581 0.187051i 0.145289 0.989389i \(-0.453589\pi\)
−0.596869 + 0.802338i \(0.703589\pi\)
\(228\) 5.25503 12.6868i 0.348023 0.840202i
\(229\) 0.306280 0.306280i 0.0202395 0.0202395i −0.696915 0.717154i \(-0.745444\pi\)
0.717154 + 0.696915i \(0.245444\pi\)
\(230\) 7.55335 7.55335i 0.498053 0.498053i
\(231\) 14.0583 33.9397i 0.924967 2.23307i
\(232\) −14.7434 6.10693i −0.967954 0.400940i
\(233\) −8.63619 20.8496i −0.565776 1.36590i −0.905086 0.425229i \(-0.860194\pi\)
0.339310 0.940674i \(-0.389806\pi\)
\(234\) 2.31696i 0.151464i
\(235\) −18.2395 + 7.55505i −1.18981 + 0.492837i
\(236\) 1.35920 + 1.35920i 0.0884766 + 0.0884766i
\(237\) 27.6741 1.79763
\(238\) 2.39635 + 10.4564i 0.155332 + 0.677785i
\(239\) 24.3048 1.57215 0.786073 0.618134i \(-0.212111\pi\)
0.786073 + 0.618134i \(0.212111\pi\)
\(240\) 2.01866 + 2.01866i 0.130304 + 0.130304i
\(241\) −5.13003 + 2.12493i −0.330454 + 0.136879i −0.541741 0.840546i \(-0.682235\pi\)
0.211287 + 0.977424i \(0.432235\pi\)
\(242\) 12.8797i 0.827936i
\(243\) −4.76266 11.4981i −0.305525 0.737602i
\(244\) −16.8572 6.98247i −1.07917 0.447007i
\(245\) 2.94528 7.11053i 0.188167 0.454275i
\(246\) −5.48189 + 5.48189i −0.349512 + 0.349512i
\(247\) 7.88430 7.88430i 0.501666 0.501666i
\(248\) −2.77349 + 6.69580i −0.176117 + 0.425184i
\(249\) 16.9349 + 7.01467i 1.07321 + 0.444536i
\(250\) 3.58112 + 8.64560i 0.226490 + 0.546796i
\(251\) 19.5181i 1.23197i −0.787758 0.615984i \(-0.788758\pi\)
0.787758 0.615984i \(-0.211242\pi\)
\(252\) −5.58522 + 2.31347i −0.351836 + 0.145735i
\(253\) 29.4617 + 29.4617i 1.85224 + 1.85224i
\(254\) 8.95448 0.561854
\(255\) 12.1649 8.64770i 0.761798 0.541540i
\(256\) −13.1605 −0.822530
\(257\) −9.89797 9.89797i −0.617418 0.617418i 0.327450 0.944868i \(-0.393811\pi\)
−0.944868 + 0.327450i \(0.893811\pi\)
\(258\) −1.47207 + 0.609752i −0.0916472 + 0.0379615i
\(259\) 30.1149i 1.87125i
\(260\) 2.22346 + 5.36791i 0.137893 + 0.332904i
\(261\) −7.15386 2.96323i −0.442813 0.183419i
\(262\) −4.56460 + 11.0199i −0.282002 + 0.680812i
\(263\) 16.9773 16.9773i 1.04686 1.04686i 0.0480182 0.998846i \(-0.484709\pi\)
0.998846 0.0480182i \(-0.0152905\pi\)
\(264\) 20.2005 20.2005i 1.24326 1.24326i
\(265\) 1.73016 4.17697i 0.106283 0.256589i
\(266\) −11.3565 4.70402i −0.696312 0.288422i
\(267\) −2.60384 6.28622i −0.159352 0.384710i
\(268\) 7.84391i 0.479143i
\(269\) 17.8616 7.39850i 1.08904 0.451094i 0.235367 0.971907i \(-0.424371\pi\)
0.853671 + 0.520812i \(0.174371\pi\)
\(270\) 3.40562 + 3.40562i 0.207259 + 0.207259i
\(271\) 5.39034 0.327440 0.163720 0.986507i \(-0.447651\pi\)
0.163720 + 0.986507i \(0.447651\pi\)
\(272\) 0.541827 3.20617i 0.0328531 0.194402i
\(273\) −16.4698 −0.996799
\(274\) 2.73801 + 2.73801i 0.165409 + 0.165409i
\(275\) −9.40505 + 3.89570i −0.567146 + 0.234920i
\(276\) 23.0052i 1.38475i
\(277\) −5.27134 12.7261i −0.316724 0.764639i −0.999424 0.0339403i \(-0.989194\pi\)
0.682700 0.730699i \(-0.260806\pi\)
\(278\) 6.39438 + 2.64864i 0.383509 + 0.158855i
\(279\) −1.34576 + 3.24896i −0.0805688 + 0.194510i
\(280\) 10.9722 10.9722i 0.655713 0.655713i
\(281\) 6.47732 6.47732i 0.386405 0.386405i −0.486998 0.873403i \(-0.661908\pi\)
0.873403 + 0.486998i \(0.161908\pi\)
\(282\) 6.87471 16.5970i 0.409383 0.988338i
\(283\) −4.59699 1.90414i −0.273263 0.113189i 0.241844 0.970315i \(-0.422248\pi\)
−0.515107 + 0.857126i \(0.672248\pi\)
\(284\) 1.68497 + 4.06787i 0.0999844 + 0.241384i
\(285\) 17.1025i 1.01307i
\(286\) 8.84644 3.66431i 0.523101 0.216675i
\(287\) −11.6139 11.6139i −0.685549 0.685549i
\(288\) −7.46179 −0.439690
\(289\) −16.0559 5.58630i −0.944467 0.328606i
\(290\) 8.20429 0.481772
\(291\) −12.3698 12.3698i −0.725128 0.725128i
\(292\) −4.69697 + 1.94555i −0.274869 + 0.113855i
\(293\) 12.6198i 0.737258i −0.929577 0.368629i \(-0.879827\pi\)
0.929577 0.368629i \(-0.120173\pi\)
\(294\) 2.68005 + 6.47022i 0.156304 + 0.377351i
\(295\) −2.21177 0.916144i −0.128774 0.0533400i
\(296\) 8.96203 21.6362i 0.520907 1.25758i
\(297\) −13.2836 + 13.2836i −0.770790 + 0.770790i
\(298\) −10.8077 + 10.8077i −0.626075 + 0.626075i
\(299\) 7.14841 17.2578i 0.413403 0.998043i
\(300\) 5.19296 + 2.15099i 0.299816 + 0.124188i
\(301\) −1.29182 3.11873i −0.0744594 0.179761i
\(302\) 13.2310i 0.761359i
\(303\) 19.5473 8.09677i 1.12297 0.465147i
\(304\) 2.63463 + 2.63463i 0.151106 + 0.151106i
\(305\) 22.7245 1.30120
\(306\) −0.674500 + 3.99124i −0.0385586 + 0.228164i
\(307\) −22.7361 −1.29762 −0.648810 0.760950i \(-0.724733\pi\)
−0.648810 + 0.760950i \(0.724733\pi\)
\(308\) 17.6663 + 17.6663i 1.00663 + 1.00663i
\(309\) −20.9344 + 8.67132i −1.19092 + 0.493294i
\(310\) 3.72602i 0.211624i
\(311\) 7.94091 + 19.1711i 0.450288 + 1.08709i 0.972213 + 0.234099i \(0.0752141\pi\)
−0.521925 + 0.852991i \(0.674786\pi\)
\(312\) −11.8328 4.90132i −0.669903 0.277483i
\(313\) −3.65477 + 8.82340i −0.206580 + 0.498728i −0.992880 0.119116i \(-0.961994\pi\)
0.786300 + 0.617844i \(0.211994\pi\)
\(314\) −3.05593 + 3.05593i −0.172456 + 0.172456i
\(315\) 5.32396 5.32396i 0.299971 0.299971i
\(316\) −7.20246 + 17.3883i −0.405170 + 0.978167i
\(317\) 13.8576 + 5.73999i 0.778318 + 0.322390i 0.736236 0.676724i \(-0.236601\pi\)
0.0420814 + 0.999114i \(0.486601\pi\)
\(318\) 1.57436 + 3.80083i 0.0882854 + 0.213140i
\(319\) 32.0007i 1.79170i
\(320\) 4.75259 1.96859i 0.265678 0.110047i
\(321\) 0.0161504 + 0.0161504i 0.000901429 + 0.000901429i
\(322\) −20.5930 −1.14761
\(323\) 15.8769 11.2864i 0.883414 0.627993i
\(324\) 15.7451 0.874726
\(325\) 3.22721 + 3.22721i 0.179013 + 0.179013i
\(326\) 9.20446 3.81261i 0.509788 0.211161i
\(327\) 0.317426i 0.0175537i
\(328\) −4.88786 11.8003i −0.269887 0.651564i
\(329\) 35.1625 + 14.5648i 1.93857 + 0.802982i
\(330\) −5.62050 + 13.5691i −0.309398 + 0.746953i
\(331\) −13.0890 + 13.0890i −0.719438 + 0.719438i −0.968490 0.249052i \(-0.919881\pi\)
0.249052 + 0.968490i \(0.419881\pi\)
\(332\) −8.81494 + 8.81494i −0.483783 + 0.483783i
\(333\) 4.34859 10.4984i 0.238301 0.575310i
\(334\) 9.64868 + 3.99662i 0.527953 + 0.218685i
\(335\) −3.73850 9.02553i −0.204256 0.493117i
\(336\) 5.50358i 0.300245i
\(337\) −2.99213 + 1.23938i −0.162991 + 0.0675133i −0.462687 0.886521i \(-0.653115\pi\)
0.299696 + 0.954035i \(0.403115\pi\)
\(338\) 4.04942 + 4.04942i 0.220259 + 0.220259i
\(339\) −0.748383 −0.0406466
\(340\) 2.26750 + 9.89415i 0.122973 + 0.536586i
\(341\) 14.5333 0.787022
\(342\) −3.27975 3.27975i −0.177349 0.177349i
\(343\) 8.12333 3.36479i 0.438619 0.181682i
\(344\) 2.62511i 0.141537i
\(345\) 10.9646 + 26.4708i 0.590312 + 1.42514i
\(346\) −14.4099 5.96876i −0.774679 0.320883i
\(347\) −10.7000 + 25.8320i −0.574405 + 1.38674i 0.323366 + 0.946274i \(0.395185\pi\)
−0.897771 + 0.440462i \(0.854815\pi\)
\(348\) 12.4939 12.4939i 0.669744 0.669744i
\(349\) 17.7731 17.7731i 0.951372 0.951372i −0.0474988 0.998871i \(-0.515125\pi\)
0.998871 + 0.0474988i \(0.0151250\pi\)
\(350\) 1.92545 4.64846i 0.102920 0.248470i
\(351\) 7.78110 + 3.22304i 0.415324 + 0.172033i
\(352\) 11.8010 + 28.4900i 0.628993 + 1.51852i
\(353\) 1.20551i 0.0641630i −0.999485 0.0320815i \(-0.989786\pi\)
0.999485 0.0320815i \(-0.0102136\pi\)
\(354\) 2.01259 0.833644i 0.106968 0.0443077i
\(355\) −3.87759 3.87759i −0.205801 0.205801i
\(356\) 4.62744 0.245254
\(357\) −28.3712 4.79460i −1.50157 0.253757i
\(358\) −4.53196 −0.239522
\(359\) 9.26083 + 9.26083i 0.488768 + 0.488768i 0.907917 0.419149i \(-0.137672\pi\)
−0.419149 + 0.907917i \(0.637672\pi\)
\(360\) 5.40941 2.24065i 0.285101 0.118093i
\(361\) 3.32111i 0.174795i
\(362\) −7.21235 17.4122i −0.379073 0.915162i
\(363\) −31.9166 13.2203i −1.67519 0.693885i
\(364\) 4.28643 10.3484i 0.224670 0.542401i
\(365\) 4.47725 4.47725i 0.234350 0.234350i
\(366\) −14.6216 + 14.6216i −0.764285 + 0.764285i
\(367\) −6.42276 + 15.5059i −0.335265 + 0.809402i 0.662891 + 0.748716i \(0.269329\pi\)
−0.998157 + 0.0606868i \(0.980671\pi\)
\(368\) 5.76688 + 2.38872i 0.300619 + 0.124521i
\(369\) −2.37170 5.72580i −0.123466 0.298073i
\(370\) 12.0399i 0.625927i
\(371\) −8.05244 + 3.33543i −0.418062 + 0.173167i
\(372\) −5.67417 5.67417i −0.294192 0.294192i
\(373\) −11.9519 −0.618846 −0.309423 0.950924i \(-0.600136\pi\)
−0.309423 + 0.950924i \(0.600136\pi\)
\(374\) 16.3058 3.73689i 0.843152 0.193230i
\(375\) −25.1002 −1.29617
\(376\) 20.9283 + 20.9283i 1.07929 + 1.07929i
\(377\) 13.2547 5.49030i 0.682654 0.282765i
\(378\) 9.28489i 0.477563i
\(379\) 9.19416 + 22.1967i 0.472272 + 1.14017i 0.963157 + 0.268941i \(0.0866737\pi\)
−0.490884 + 0.871225i \(0.663326\pi\)
\(380\) −10.7459 4.45110i −0.551253 0.228336i
\(381\) −9.19130 + 22.1898i −0.470885 + 1.13682i
\(382\) 5.08054 5.08054i 0.259943 0.259943i
\(383\) −12.4160 + 12.4160i −0.634427 + 0.634427i −0.949175 0.314748i \(-0.898080\pi\)
0.314748 + 0.949175i \(0.398080\pi\)
\(384\) 7.47759 18.0525i 0.381589 0.921238i
\(385\) −28.7475 11.9076i −1.46511 0.606867i
\(386\) −0.655711 1.58303i −0.0333748 0.0805739i
\(387\) 1.27377i 0.0647491i
\(388\) 10.9915 4.55285i 0.558011 0.231136i
\(389\) 8.66462 + 8.66462i 0.439313 + 0.439313i 0.891781 0.452467i \(-0.149456\pi\)
−0.452467 + 0.891781i \(0.649456\pi\)
\(390\) 6.58463 0.333426
\(391\) 17.3380 27.6476i 0.876819 1.39820i
\(392\) −11.5382 −0.582766
\(393\) −22.6227 22.6227i −1.14116 1.14116i
\(394\) 12.6075 5.22220i 0.635157 0.263091i
\(395\) 23.4404i 1.17942i
\(396\) 3.60766 + 8.70967i 0.181292 + 0.437677i
\(397\) −19.9517 8.26429i −1.00135 0.414773i −0.179058 0.983839i \(-0.557305\pi\)
−0.822292 + 0.569066i \(0.807305\pi\)
\(398\) −3.48131 + 8.40462i −0.174502 + 0.421286i
\(399\) 23.3137 23.3137i 1.16715 1.16715i
\(400\) −1.07841 + 1.07841i −0.0539204 + 0.0539204i
\(401\) 4.95492 11.9622i 0.247437 0.597365i −0.750548 0.660816i \(-0.770211\pi\)
0.997985 + 0.0634505i \(0.0202105\pi\)
\(402\) 8.21276 + 3.40184i 0.409615 + 0.169668i
\(403\) −2.49344 6.01971i −0.124207 0.299863i
\(404\) 14.3893i 0.715894i
\(405\) −18.1169 + 7.50428i −0.900237 + 0.372891i
\(406\) −11.1839 11.1839i −0.555046 0.555046i
\(407\) −46.9616 −2.32780
\(408\) −18.9566 11.8878i −0.938493 0.588535i
\(409\) −6.50659 −0.321730 −0.160865 0.986976i \(-0.551428\pi\)
−0.160865 + 0.986976i \(0.551428\pi\)
\(410\) 4.64324 + 4.64324i 0.229314 + 0.229314i
\(411\) −9.59538 + 3.97454i −0.473305 + 0.196049i
\(412\) 15.4103i 0.759213i
\(413\) 1.76616 + 4.26389i 0.0869070 + 0.209812i
\(414\) −7.17897 2.97363i −0.352827 0.146146i
\(415\) 5.94154 14.3441i 0.291658 0.704126i
\(416\) 9.77595 9.77595i 0.479306 0.479306i
\(417\) −13.1270 + 13.1270i −0.642831 + 0.642831i
\(418\) −7.33551 + 17.7095i −0.358791 + 0.866199i
\(419\) −8.93282 3.70009i −0.436397 0.180761i 0.153659 0.988124i \(-0.450894\pi\)
−0.590056 + 0.807362i \(0.700894\pi\)
\(420\) 6.57473 + 15.8728i 0.320814 + 0.774513i
\(421\) 34.3093i 1.67213i −0.548629 0.836066i \(-0.684850\pi\)
0.548629 0.836066i \(-0.315150\pi\)
\(422\) −14.2664 + 5.90933i −0.694476 + 0.287662i
\(423\) 10.1549 + 10.1549i 0.493748 + 0.493748i
\(424\) −6.77793 −0.329165
\(425\) 4.61977 + 6.49874i 0.224092 + 0.315235i
\(426\) 4.98992 0.241762
\(427\) −30.9774 30.9774i −1.49910 1.49910i
\(428\) −0.0143510 + 0.00594437i −0.000693680 + 0.000287332i
\(429\) 25.6833i 1.24000i
\(430\) 0.516470 + 1.24687i 0.0249064 + 0.0601294i
\(431\) 4.14191 + 1.71563i 0.199509 + 0.0826392i 0.480201 0.877159i \(-0.340564\pi\)
−0.280692 + 0.959798i \(0.590564\pi\)
\(432\) −1.07701 + 2.60014i −0.0518178 + 0.125099i
\(433\) 14.4126 14.4126i 0.692628 0.692628i −0.270182 0.962809i \(-0.587084\pi\)
0.962809 + 0.270182i \(0.0870838\pi\)
\(434\) −5.07921 + 5.07921i −0.243810 + 0.243810i
\(435\) −8.42127 + 20.3307i −0.403769 + 0.974784i
\(436\) −0.199446 0.0826132i −0.00955172 0.00395645i
\(437\) 14.3102 + 34.5479i 0.684551 + 1.65265i
\(438\) 5.76160i 0.275300i
\(439\) 36.4740 15.1080i 1.74081 0.721068i 0.742101 0.670288i \(-0.233829\pi\)
0.998710 0.0507797i \(-0.0161706\pi\)
\(440\) −17.1102 17.1102i −0.815695 0.815695i
\(441\) −5.59860 −0.266600
\(442\) −4.34537 6.11275i −0.206688 0.290754i
\(443\) 24.4730 1.16275 0.581373 0.813637i \(-0.302516\pi\)
0.581373 + 0.813637i \(0.302516\pi\)
\(444\) 18.3350 + 18.3350i 0.870142 + 0.870142i
\(445\) −5.32453 + 2.20549i −0.252407 + 0.104550i
\(446\) 1.61079i 0.0762732i
\(447\) −15.6887 37.8758i −0.742049 1.79146i
\(448\) −9.16214 3.79508i −0.432870 0.179301i
\(449\) −2.23321 + 5.39145i −0.105392 + 0.254438i −0.967774 0.251819i \(-0.918971\pi\)
0.862383 + 0.506257i \(0.168971\pi\)
\(450\) 1.34247 1.34247i 0.0632847 0.0632847i
\(451\) −18.1109 + 18.1109i −0.852810 + 0.852810i
\(452\) 0.194774 0.470226i 0.00916139 0.0221176i
\(453\) −32.7873 13.5809i −1.54048 0.638088i
\(454\) −2.17211 5.24393i −0.101942 0.246110i
\(455\) 13.9502i 0.653996i
\(456\) 23.6879 9.81184i 1.10929 0.459482i
\(457\) −20.5808 20.5808i −0.962729 0.962729i 0.0366008 0.999330i \(-0.488347\pi\)
−0.999330 + 0.0366008i \(0.988347\pi\)
\(458\) 0.333843 0.0155994
\(459\) 12.4656 + 7.81725i 0.581844 + 0.364878i
\(460\) −19.4858 −0.908531
\(461\) −19.9493 19.9493i −0.929130 0.929130i 0.0685196 0.997650i \(-0.478172\pi\)
−0.997650 + 0.0685196i \(0.978172\pi\)
\(462\) 26.1587 10.8353i 1.21701 0.504104i
\(463\) 1.35223i 0.0628437i 0.999506 + 0.0314218i \(0.0100035\pi\)
−0.999506 + 0.0314218i \(0.989996\pi\)
\(464\) 1.83464 + 4.42922i 0.0851712 + 0.205621i
\(465\) 9.23331 + 3.82456i 0.428184 + 0.177360i
\(466\) 6.65627 16.0696i 0.308346 0.744412i
\(467\) 25.5854 25.5854i 1.18395 1.18395i 0.205242 0.978711i \(-0.434202\pi\)
0.978711 0.205242i \(-0.0657980\pi\)
\(468\) 2.98860 2.98860i 0.138148 0.138148i
\(469\) −7.20714 + 17.3996i −0.332795 + 0.803438i
\(470\) −14.0579 5.82299i −0.648444 0.268594i
\(471\) −4.43604 10.7095i −0.204402 0.493470i
\(472\) 3.58901i 0.165198i
\(473\) −4.86339 + 2.01448i −0.223619 + 0.0926261i
\(474\) 15.0823 + 15.0823i 0.692753 + 0.692753i
\(475\) −9.13650 −0.419211
\(476\) 10.3964 16.5784i 0.476520 0.759871i
\(477\) −3.28881 −0.150584
\(478\) 13.2460 + 13.2460i 0.605859 + 0.605859i
\(479\) −37.0476 + 15.3456i −1.69275 + 0.701159i −0.999803 0.0198334i \(-0.993686\pi\)
−0.692943 + 0.720992i \(0.743686\pi\)
\(480\) 21.2059i 0.967911i
\(481\) 8.05710 + 19.4516i 0.367372 + 0.886915i
\(482\) −3.95392 1.63777i −0.180096 0.0745983i
\(483\) 21.1377 51.0309i 0.961797 2.32198i
\(484\) 16.6132 16.6132i 0.755146 0.755146i
\(485\) −10.4774 + 10.4774i −0.475754 + 0.475754i
\(486\) 3.67078 8.86204i 0.166510 0.401990i
\(487\) 19.6571 + 8.14223i 0.890748 + 0.368960i 0.780656 0.624962i \(-0.214885\pi\)
0.110092 + 0.993921i \(0.464885\pi\)
\(488\) −13.0372 31.4746i −0.590167 1.42479i
\(489\) 26.7227i 1.20844i
\(490\) 5.48038 2.27005i 0.247578 0.102550i
\(491\) −23.9375 23.9375i −1.08028 1.08028i −0.996483 0.0838001i \(-0.973294\pi\)
−0.0838001 0.996483i \(-0.526706\pi\)
\(492\) 14.1419 0.637568
\(493\) 24.4312 5.59904i 1.10033 0.252168i
\(494\) 8.59383 0.386655
\(495\) −8.30225 8.30225i −0.373158 0.373158i
\(496\) 2.01155 0.833212i 0.0903214 0.0374123i
\(497\) 10.5716i 0.474203i
\(498\) 5.40649 + 13.0524i 0.242271 + 0.584893i
\(499\) −22.8399 9.46059i −1.02245 0.423514i −0.192471 0.981303i \(-0.561650\pi\)
−0.829983 + 0.557788i \(0.811650\pi\)
\(500\) 6.53256 15.7710i 0.292145 0.705300i
\(501\) −19.8077 + 19.8077i −0.884944 + 0.884944i
\(502\) 10.6373 10.6373i 0.474764 0.474764i
\(503\) −0.581084 + 1.40286i −0.0259093 + 0.0625505i −0.936305 0.351189i \(-0.885778\pi\)
0.910395 + 0.413739i \(0.135778\pi\)
\(504\) −10.4284 4.31957i −0.464516 0.192409i
\(505\) −6.85810 16.5569i −0.305181 0.736773i
\(506\) 32.1131i 1.42760i
\(507\) −14.1912 + 5.87820i −0.630255 + 0.261060i
\(508\) −11.5502 11.5502i −0.512457 0.512457i
\(509\) 19.5958 0.868570 0.434285 0.900776i \(-0.357001\pi\)
0.434285 + 0.900776i \(0.357001\pi\)
\(510\) 11.3428 + 1.91688i 0.502268 + 0.0848809i
\(511\) −12.2065 −0.539986
\(512\) 6.19453 + 6.19453i 0.273762 + 0.273762i
\(513\) −15.5768 + 6.45212i −0.687733 + 0.284868i
\(514\) 10.7887i 0.475869i
\(515\) 7.34474 + 17.7318i 0.323648 + 0.781356i
\(516\) 2.68530 + 1.11229i 0.118214 + 0.0489658i
\(517\) 22.7125 54.8328i 0.998894 2.41154i
\(518\) 16.4125 16.4125i 0.721125 0.721125i
\(519\) 29.5819 29.5819i 1.29850 1.29850i
\(520\) −4.15150 + 10.0226i −0.182055 + 0.439520i
\(521\) 8.06285 + 3.33974i 0.353240 + 0.146317i 0.552245 0.833682i \(-0.313771\pi\)
−0.199005 + 0.979998i \(0.563771\pi\)
\(522\) −2.28388 5.51377i −0.0999627 0.241331i
\(523\) 1.12779i 0.0493150i −0.999696 0.0246575i \(-0.992150\pi\)
0.999696 0.0246575i \(-0.00784952\pi\)
\(524\) 20.1021 8.32658i 0.878166 0.363748i
\(525\) 9.54279 + 9.54279i 0.416481 + 0.416481i
\(526\) 18.5051 0.806861
\(527\) −2.54283 11.0955i −0.110768 0.483329i
\(528\) −8.58235 −0.373499
\(529\) 28.0344 + 28.0344i 1.21889 + 1.21889i
\(530\) 3.21936 1.33350i 0.139840 0.0579237i
\(531\) 1.74147i 0.0755735i
\(532\) 8.58091 + 20.7161i 0.372029 + 0.898159i
\(533\) 10.6088 + 4.39432i 0.459519 + 0.190339i
\(534\) 2.00688 4.84505i 0.0868463 0.209666i
\(535\) 0.0136797 0.0136797i 0.000591424 0.000591424i
\(536\) −10.3560 + 10.3560i −0.447312 + 0.447312i
\(537\) 4.65182 11.2305i 0.200741 0.484631i
\(538\) 13.7666 + 5.70232i 0.593522 + 0.245845i
\(539\) 8.85429 + 21.3761i 0.381381 + 0.920736i
\(540\) 8.78566i 0.378075i
\(541\) −19.2522 + 7.97453i −0.827717 + 0.342852i −0.755999 0.654573i \(-0.772848\pi\)
−0.0717185 + 0.997425i \(0.522848\pi\)
\(542\) 2.93772 + 2.93772i 0.126186 + 0.126186i
\(543\) 50.5515 2.16937
\(544\) 19.6862 13.9943i 0.844037 0.600002i
\(545\) 0.268865 0.0115169
\(546\) −8.97599 8.97599i −0.384137 0.384137i
\(547\) −2.85098 + 1.18091i −0.121899 + 0.0504922i −0.442799 0.896621i \(-0.646015\pi\)
0.320900 + 0.947113i \(0.396015\pi\)
\(548\) 7.06340i 0.301734i
\(549\) −6.32596 15.2722i −0.269985 0.651802i
\(550\) −7.24886 3.00258i −0.309092 0.128030i
\(551\) −10.9909 + 26.5344i −0.468228 + 1.13040i
\(552\) 30.3730 30.3730i 1.29276 1.29276i
\(553\) −31.9534 + 31.9534i −1.35880 + 1.35880i
\(554\) 4.06283 9.80855i 0.172613 0.416725i
\(555\) −29.8357 12.3584i −1.26646 0.524583i
\(556\) −4.83155 11.6644i −0.204903 0.494681i
\(557\) 35.6120i 1.50893i −0.656340 0.754465i \(-0.727896\pi\)
0.656340 0.754465i \(-0.272104\pi\)
\(558\) −2.50411 + 1.03724i −0.106007 + 0.0439097i
\(559\) 1.66880 + 1.66880i 0.0705829 + 0.0705829i
\(560\) −4.66162 −0.196989
\(561\) −7.47676 + 44.2425i −0.315669 + 1.86792i
\(562\) 7.06023 0.297818
\(563\) 18.0901 + 18.0901i 0.762405 + 0.762405i 0.976757 0.214351i \(-0.0687637\pi\)
−0.214351 + 0.976757i \(0.568764\pi\)
\(564\) −30.2757 + 12.5406i −1.27484 + 0.528055i
\(565\) 0.633893i 0.0266681i
\(566\) −1.46760 3.54309i −0.0616877 0.148927i
\(567\) 34.9261 + 14.4669i 1.46676 + 0.607552i
\(568\) −3.14606 + 7.59526i −0.132006 + 0.318690i
\(569\) −27.0270 + 27.0270i −1.13303 + 1.13303i −0.143361 + 0.989670i \(0.545791\pi\)
−0.989670 + 0.143361i \(0.954209\pi\)
\(570\) −9.32081 + 9.32081i −0.390406 + 0.390406i
\(571\) 4.67128 11.2775i 0.195487 0.471947i −0.795492 0.605964i \(-0.792788\pi\)
0.990979 + 0.134017i \(0.0427875\pi\)
\(572\) −16.1374 6.68431i −0.674737 0.279485i
\(573\) 7.37499 + 17.8048i 0.308095 + 0.743806i
\(574\) 12.6591i 0.528380i
\(575\) −14.1412 + 5.85747i −0.589729 + 0.244274i
\(576\) −2.64602 2.64602i −0.110251 0.110251i
\(577\) 16.7957 0.699213 0.349606 0.936897i \(-0.386315\pi\)
0.349606 + 0.936897i \(0.386315\pi\)
\(578\) −5.70592 11.7949i −0.237335 0.490605i
\(579\) 4.59589 0.190999
\(580\) −10.5825 10.5825i −0.439416 0.439416i
\(581\) −27.6529 + 11.4542i −1.14724 + 0.475200i
\(582\) 13.4829i 0.558886i
\(583\) 5.20131 + 12.5571i 0.215416 + 0.520061i
\(584\) −8.76986 3.63260i −0.362899 0.150318i
\(585\) −2.01440 + 4.86320i −0.0832854 + 0.201069i
\(586\) 6.87775 6.87775i 0.284117 0.284117i
\(587\) 22.2540 22.2540i 0.918520 0.918520i −0.0784014 0.996922i \(-0.524982\pi\)
0.996922 + 0.0784014i \(0.0249816\pi\)
\(588\) 4.88886 11.8027i 0.201613 0.486737i
\(589\) 12.0507 + 4.99157i 0.496541 + 0.205674i
\(590\) −0.706110 1.70470i −0.0290701 0.0701814i
\(591\) 36.6025i 1.50563i
\(592\) −6.49996 + 2.69237i −0.267147 + 0.110656i
\(593\) 4.77643 + 4.77643i 0.196145 + 0.196145i 0.798345 0.602200i \(-0.205709\pi\)
−0.602200 + 0.798345i \(0.705709\pi\)
\(594\) −14.4790 −0.594079
\(595\) −4.06111 + 24.0309i −0.166489 + 0.985171i
\(596\) 27.8813 1.14206
\(597\) −17.2538 17.2538i −0.706151 0.706151i
\(598\) 13.3013 5.50957i 0.543930 0.225303i
\(599\) 33.0854i 1.35183i −0.736979 0.675916i \(-0.763748\pi\)
0.736979 0.675916i \(-0.236252\pi\)
\(600\) 4.01619 + 9.69595i 0.163960 + 0.395835i
\(601\) −27.2027 11.2677i −1.10962 0.459620i −0.248814 0.968551i \(-0.580041\pi\)
−0.860807 + 0.508931i \(0.830041\pi\)
\(602\) 0.995660 2.40374i 0.0405801 0.0979690i
\(603\) −5.02498 + 5.02498i −0.204633 + 0.204633i
\(604\) 17.0664 17.0664i 0.694422 0.694422i
\(605\) −11.1978 + 27.0339i −0.455255 + 1.09908i
\(606\) 15.0659 + 6.24051i 0.612012 + 0.253504i
\(607\) −15.3859 37.1449i −0.624495 1.50766i −0.846374 0.532590i \(-0.821219\pi\)
0.221879 0.975074i \(-0.428781\pi\)
\(608\) 27.6765i 1.12243i
\(609\) 39.1940 16.2347i 1.58822 0.657862i
\(610\) 12.3848 + 12.3848i 0.501444 + 0.501444i
\(611\) −26.6086 −1.07647
\(612\) 6.01824 4.27819i 0.243273 0.172936i
\(613\) −30.5740 −1.23487 −0.617435 0.786622i \(-0.711828\pi\)
−0.617435 + 0.786622i \(0.711828\pi\)
\(614\) −12.3911 12.3911i −0.500064 0.500064i
\(615\) −16.2723 + 6.74021i −0.656162 + 0.271791i
\(616\) 46.6482i 1.87951i
\(617\) −10.3840 25.0693i −0.418046 1.00925i −0.982913 0.184070i \(-0.941073\pi\)
0.564867 0.825182i \(-0.308927\pi\)
\(618\) −16.1350 6.68334i −0.649045 0.268843i
\(619\) 2.58904 6.25050i 0.104062 0.251229i −0.863269 0.504744i \(-0.831587\pi\)
0.967331 + 0.253515i \(0.0815868\pi\)
\(620\) −4.80611 + 4.80611i −0.193018 + 0.193018i
\(621\) −19.9728 + 19.9728i −0.801481 + 0.801481i
\(622\) −6.12039 + 14.7759i −0.245405 + 0.592460i
\(623\) 10.2647 + 4.25179i 0.411247 + 0.170344i
\(624\) 1.47245 + 3.55482i 0.0589454 + 0.142307i
\(625\) 11.5910i 0.463641i
\(626\) −6.80055 + 2.81688i −0.271805 + 0.112585i
\(627\) −36.3557 36.3557i −1.45191 1.45191i
\(628\) 7.88356 0.314588
\(629\) 8.21669 + 35.8532i 0.327621 + 1.42956i
\(630\) 5.80307 0.231200
\(631\) 26.3629 + 26.3629i 1.04949 + 1.04949i 0.998710 + 0.0507787i \(0.0161703\pi\)
0.0507787 + 0.998710i \(0.483830\pi\)
\(632\) −32.4662 + 13.4480i −1.29144 + 0.534931i
\(633\) 41.4186i 1.64624i
\(634\) 4.42404 + 10.6806i 0.175701 + 0.424180i
\(635\) 18.7951 + 7.78518i 0.745860 + 0.308946i
\(636\) 2.87188 6.93334i 0.113878 0.274925i
\(637\) 7.33492 7.33492i 0.290620 0.290620i
\(638\) −17.4403 + 17.4403i −0.690467 + 0.690467i
\(639\) −1.52654 + 3.68540i −0.0603890 + 0.145792i
\(640\) −15.2908 6.33364i −0.604421 0.250359i
\(641\) −12.6971 30.6535i −0.501506 1.21074i −0.948664 0.316287i \(-0.897564\pi\)
0.447158 0.894455i \(-0.352436\pi\)
\(642\) 0.0176038i 0.000694768i
\(643\) 2.99720 1.24148i 0.118198 0.0489593i −0.322801 0.946467i \(-0.604624\pi\)
0.440999 + 0.897508i \(0.354624\pi\)
\(644\) 26.5625 + 26.5625i 1.04671 + 1.04671i
\(645\) −3.61995 −0.142535
\(646\) 14.8039 + 2.50179i 0.582452 + 0.0984315i
\(647\) −8.42170 −0.331091 −0.165546 0.986202i \(-0.552939\pi\)
−0.165546 + 0.986202i \(0.552939\pi\)
\(648\) 20.7876 + 20.7876i 0.816615 + 0.816615i
\(649\) 6.64916 2.75417i 0.261002 0.108111i
\(650\) 3.51763i 0.137973i
\(651\) −7.37306 17.8001i −0.288973 0.697643i
\(652\) −16.7904 6.95483i −0.657565 0.272372i
\(653\) −8.95953 + 21.6302i −0.350613 + 0.846455i 0.645931 + 0.763396i \(0.276469\pi\)
−0.996545 + 0.0830598i \(0.973531\pi\)
\(654\) −0.172996 + 0.172996i −0.00676468 + 0.00676468i
\(655\) −19.1618 + 19.1618i −0.748714 + 0.748714i
\(656\) −1.46841 + 3.54505i −0.0573318 + 0.138411i
\(657\) −4.25534 1.76262i −0.166017 0.0687664i
\(658\) 11.2257 + 27.1012i 0.437622 + 1.05651i
\(659\) 32.9683i 1.28426i 0.766595 + 0.642131i \(0.221949\pi\)
−0.766595 + 0.642131i \(0.778051\pi\)
\(660\) 24.7522 10.2527i 0.963479 0.399086i
\(661\) 15.0077 + 15.0077i 0.583730 + 0.583730i 0.935926 0.352196i \(-0.114565\pi\)
−0.352196 + 0.935926i \(0.614565\pi\)
\(662\) −14.2669 −0.554500
\(663\) 19.6081 4.49370i 0.761514 0.174521i
\(664\) −23.2761 −0.903287
\(665\) −19.7471 19.7471i −0.765759 0.765759i
\(666\) 8.09156 3.35163i 0.313541 0.129873i
\(667\) 48.1154i 1.86304i
\(668\) −7.29049 17.6008i −0.282077 0.680995i
\(669\) −3.99164 1.65339i −0.154326 0.0639239i
\(670\) 2.88141 6.95634i 0.111319 0.268747i
\(671\) −48.3066 + 48.3066i −1.86486 + 1.86486i
\(672\) 28.9073 28.9073i 1.11512 1.11512i
\(673\) 2.19614 5.30194i 0.0846548 0.204375i −0.875883 0.482523i \(-0.839721\pi\)
0.960538 + 0.278148i \(0.0897206\pi\)
\(674\) −2.30615 0.955240i −0.0888297 0.0367945i
\(675\) −2.64099 6.37591i −0.101652 0.245409i
\(676\) 10.4465i 0.401789i
\(677\) 25.3105 10.4840i 0.972763 0.402931i 0.161023 0.986951i \(-0.448521\pi\)
0.811740 + 0.584019i \(0.198521\pi\)
\(678\) −0.407866 0.407866i −0.0156640 0.0156640i
\(679\) 28.5650 1.09622
\(680\) −10.0692 + 16.0566i −0.386135 + 0.615741i
\(681\) 15.2243 0.583398
\(682\) 7.92058 + 7.92058i 0.303295 + 0.303295i
\(683\) 31.1640 12.9086i 1.19246 0.493933i 0.303904 0.952703i \(-0.401710\pi\)
0.888555 + 0.458770i \(0.151710\pi\)
\(684\) 8.46096i 0.323513i
\(685\) 3.36650 + 8.12744i 0.128627 + 0.310534i
\(686\) 6.26098 + 2.59338i 0.239045 + 0.0990159i
\(687\) −0.342672 + 0.827283i −0.0130737 + 0.0315628i
\(688\) −0.557650 + 0.557650i −0.0212602 + 0.0212602i
\(689\) 4.30878 4.30878i 0.164152 0.164152i
\(690\) −8.45083 + 20.4021i −0.321718 + 0.776695i
\(691\) −4.88582 2.02377i −0.185865 0.0769880i 0.287810 0.957688i \(-0.407073\pi\)
−0.473675 + 0.880700i \(0.657073\pi\)
\(692\) 10.8880 + 26.2860i 0.413900 + 0.999243i
\(693\) 22.6348i 0.859825i
\(694\) −19.9098 + 8.24691i −0.755766 + 0.313049i
\(695\) 11.1188 + 11.1188i 0.421759 + 0.421759i
\(696\) 32.9905 1.25050
\(697\) 16.9957 + 10.6581i 0.643758 + 0.403705i
\(698\) 19.3725 0.733262
\(699\) 32.9893 + 32.9893i 1.24777 + 1.24777i
\(700\) −8.47955 + 3.51234i −0.320497 + 0.132754i
\(701\) 12.0343i 0.454529i 0.973833 + 0.227264i \(0.0729781\pi\)
−0.973833 + 0.227264i \(0.927022\pi\)
\(702\) 2.48413 + 5.99721i 0.0937573 + 0.226350i
\(703\) −38.9396 16.1293i −1.46864 0.608329i
\(704\) −5.91810 + 14.2875i −0.223047 + 0.538482i
\(705\) 28.8595 28.8595i 1.08691 1.08691i
\(706\) 0.657000 0.657000i 0.0247265 0.0247265i
\(707\) −13.2212 + 31.9187i −0.497233 + 1.20043i
\(708\) −3.67130 1.52070i −0.137976 0.0571515i
\(709\) 5.56300 + 13.4303i 0.208923 + 0.504384i 0.993254 0.115958i \(-0.0369937\pi\)
−0.784331 + 0.620342i \(0.786994\pi\)
\(710\) 4.22654i 0.158619i
\(711\) −15.7534 + 6.52526i −0.590798 + 0.244717i
\(712\) 6.10944 + 6.10944i 0.228961 + 0.228961i
\(713\) 21.8519 0.818359
\(714\) −12.8492 18.0753i −0.480868 0.676449i
\(715\) 21.7541 0.813558
\(716\) 5.84569 + 5.84569i 0.218464 + 0.218464i
\(717\) −46.4208 + 19.2281i −1.73362 + 0.718087i
\(718\) 10.0942i 0.376714i
\(719\) −2.59407 6.26263i −0.0967423 0.233557i 0.868098 0.496392i \(-0.165342\pi\)
−0.964841 + 0.262836i \(0.915342\pi\)
\(720\) −1.62509 0.673136i −0.0605637 0.0250863i
\(721\) 14.1593 34.1837i 0.527321 1.27307i
\(722\) −1.80999 + 1.80999i −0.0673609 + 0.0673609i
\(723\) 8.11699 8.11699i 0.301874 0.301874i
\(724\) −13.1565 + 31.7626i −0.488958 + 1.18045i
\(725\) −10.8611 4.49880i −0.403370 0.167081i
\(726\) −10.1894 24.5994i −0.378165 0.912971i
\(727\) 1.40583i 0.0521393i −0.999660 0.0260697i \(-0.991701\pi\)
0.999660 0.0260697i \(-0.00829917\pi\)
\(728\) 19.3218 8.00334i 0.716112 0.296623i
\(729\) −5.56344 5.56344i −0.206053 0.206053i
\(730\) 4.88017 0.180623
\(731\) 2.38890 + 3.36053i 0.0883567 + 0.124294i
\(732\) 37.7203 1.39418
\(733\) −31.8645 31.8645i −1.17694 1.17694i −0.980519 0.196424i \(-0.937067\pi\)
−0.196424 0.980519i \(-0.562933\pi\)
\(734\) −11.9510 + 4.95029i −0.441121 + 0.182718i
\(735\) 15.9108i 0.586879i
\(736\) 17.7436 + 42.8369i 0.654039 + 1.57899i
\(737\) 27.1331 + 11.2389i 0.999461 + 0.413990i
\(738\) 1.82797 4.41311i 0.0672885 0.162449i
\(739\) −17.3877 + 17.3877i −0.639617 + 0.639617i −0.950461 0.310844i \(-0.899388\pi\)
0.310844 + 0.950461i \(0.399388\pi\)
\(740\) 15.5301 15.5301i 0.570897 0.570897i
\(741\) −8.82111 + 21.2961i −0.324052 + 0.782330i
\(742\) −6.20635 2.57075i −0.227842 0.0943753i
\(743\) −9.12312 22.0252i −0.334695 0.808025i −0.998207 0.0598593i \(-0.980935\pi\)
0.663512 0.748166i \(-0.269065\pi\)
\(744\) 14.9828i 0.549296i
\(745\) −32.0814 + 13.2886i −1.17537 + 0.486855i
\(746\) −6.51374 6.51374i −0.238485 0.238485i
\(747\) −11.2941 −0.413229
\(748\) −25.8526 16.2123i −0.945266 0.592782i
\(749\) −0.0372955 −0.00136275
\(750\) −13.6795 13.6795i −0.499504 0.499504i
\(751\) 34.9604 14.4811i 1.27572 0.528422i 0.361024 0.932557i \(-0.382427\pi\)
0.914700 + 0.404135i \(0.132427\pi\)
\(752\) 8.89155i 0.324241i
\(753\) 15.4412 + 37.2784i 0.562709 + 1.35850i
\(754\) 10.2160 + 4.23160i 0.372044 + 0.154106i
\(755\) −11.5033 + 27.7713i −0.418647 + 1.01070i
\(756\) −11.9764 + 11.9764i −0.435577 + 0.435577i
\(757\) 14.9302 14.9302i 0.542647 0.542647i −0.381657 0.924304i \(-0.624646\pi\)
0.924304 + 0.381657i \(0.124646\pi\)
\(758\) −7.08631 + 17.1079i −0.257386 + 0.621386i
\(759\) −79.5782 32.9624i −2.88850 1.19646i
\(760\) −8.31079 20.0640i −0.301464 0.727799i
\(761\) 27.9358i 1.01267i 0.862337 + 0.506335i \(0.169000\pi\)
−0.862337 + 0.506335i \(0.831000\pi\)
\(762\) −17.1026 + 7.08411i −0.619561 + 0.256630i
\(763\) −0.366510 0.366510i −0.0132685 0.0132685i
\(764\) −13.1066 −0.474179
\(765\) −4.88580 + 7.79102i −0.176646 + 0.281685i
\(766\) −13.5333 −0.488979
\(767\) −2.28156 2.28156i −0.0823825 0.0823825i
\(768\) 25.1358 10.4116i 0.907009 0.375695i
\(769\) 6.47377i 0.233450i 0.993164 + 0.116725i \(0.0372397\pi\)
−0.993164 + 0.116725i \(0.962760\pi\)
\(770\) −9.17767 22.1569i −0.330740 0.798478i
\(771\) 26.7351 + 11.0740i 0.962841 + 0.398822i
\(772\) −1.19612 + 2.88770i −0.0430495 + 0.103931i
\(773\) 28.4108 28.4108i 1.02186 1.02186i 0.0221087 0.999756i \(-0.492962\pi\)
0.999756 0.0221087i \(-0.00703798\pi\)
\(774\) 0.694197 0.694197i 0.0249524 0.0249524i
\(775\) −2.04315 + 4.93261i −0.0733923 + 0.177185i
\(776\) 20.5227 + 8.50077i 0.736721 + 0.305160i
\(777\) 23.8247 + 57.5178i 0.854705 + 2.06344i
\(778\) 9.44436i 0.338597i
\(779\) −21.2375 + 8.79688i −0.760914 + 0.315181i
\(780\) −8.49338 8.49338i −0.304112 0.304112i
\(781\) 16.4856 0.589900
\(782\) 24.5169 5.61870i 0.876724 0.200924i
\(783\) −21.6941 −0.775282
\(784\) 2.45104 + 2.45104i 0.0875373 + 0.0875373i
\(785\) −9.07115 + 3.75739i −0.323763 + 0.134107i
\(786\) 24.6586i 0.879542i
\(787\) −20.1603 48.6714i −0.718638 1.73495i −0.677193 0.735806i \(-0.736804\pi\)
−0.0414458 0.999141i \(-0.513196\pi\)
\(788\) −22.9982 9.52615i −0.819276 0.339355i
\(789\) −18.9945 + 45.8568i −0.676223 + 1.63255i
\(790\) 12.7750 12.7750i 0.454512 0.454512i
\(791\) 0.864105 0.864105i 0.0307241 0.0307241i
\(792\) −6.73599 + 16.2621i −0.239353 + 0.577849i
\(793\) 28.2965 + 11.7208i 1.00484 + 0.416218i
\(794\) −6.36962 15.3776i −0.226049 0.545732i
\(795\) 9.34656i 0.331488i
\(796\) 15.3314 6.35048i 0.543407 0.225087i
\(797\) −23.5951 23.5951i −0.835781 0.835781i 0.152520 0.988300i \(-0.451261\pi\)
−0.988300 + 0.152520i \(0.951261\pi\)
\(798\) 25.4118 0.899567
\(799\) −45.8364 7.74613i −1.62158 0.274038i
\(800\) −11.3286 −0.400526
\(801\) 2.96444 + 2.96444i 0.104743 + 0.104743i
\(802\) 9.21978 3.81896i 0.325562 0.134852i
\(803\) 19.0350i 0.671732i
\(804\) −6.20551 14.9814i −0.218852 0.528354i
\(805\) −43.2240 17.9039i −1.52344 0.631031i
\(806\) 1.92180 4.63964i 0.0676925 0.163424i
\(807\) −28.2614 + 28.2614i −0.994850 + 0.994850i
\(808\) −18.9976 + 18.9976i −0.668335 + 0.668335i
\(809\) 16.2814 39.3067i 0.572422 1.38195i −0.327065 0.945002i \(-0.606060\pi\)
0.899487 0.436948i \(-0.143940\pi\)
\(810\) −13.9635 5.78385i −0.490626 0.203224i
\(811\) 3.78500 + 9.13779i 0.132909 + 0.320871i 0.976297 0.216434i \(-0.0694425\pi\)
−0.843388 + 0.537305i \(0.819442\pi\)
\(812\) 28.8517i 1.01250i
\(813\) −10.2953 + 4.26444i −0.361070 + 0.149560i
\(814\) −25.5939 25.5939i −0.897066 0.897066i
\(815\) 22.6345 0.792853
\(816\) 1.50162 + 6.55225i 0.0525672 + 0.229375i
\(817\) −4.72452 −0.165290
\(818\) −3.54607 3.54607i −0.123985 0.123985i
\(819\) 9.37537 3.88341i 0.327602 0.135697i
\(820\) 11.9784i 0.418306i
\(821\) −1.35519 3.27173i −0.0472966 0.114184i 0.898466 0.439044i \(-0.144683\pi\)
−0.945762 + 0.324860i \(0.894683\pi\)
\(822\) −7.39555 3.06334i −0.257950 0.106846i
\(823\) −15.2899 + 36.9131i −0.532973 + 1.28671i 0.396573 + 0.918003i \(0.370199\pi\)
−0.929546 + 0.368707i \(0.879801\pi\)
\(824\) 20.3457 20.3457i 0.708776 0.708776i
\(825\) 14.8811 14.8811i 0.518095 0.518095i
\(826\) −1.36125 + 3.28635i −0.0473640 + 0.114347i
\(827\) 14.9697 + 6.20065i 0.520548 + 0.215618i 0.627457 0.778651i \(-0.284096\pi\)
−0.106910 + 0.994269i \(0.534096\pi\)
\(828\) 5.42439 + 13.0956i 0.188510 + 0.455105i
\(829\) 32.6413i 1.13368i −0.823828 0.566839i \(-0.808166\pi\)
0.823828 0.566839i \(-0.191834\pi\)
\(830\) 11.0556 4.57938i 0.383746 0.158953i
\(831\) 20.1359 + 20.1359i 0.698507 + 0.698507i
\(832\) 6.93328 0.240368
\(833\) 14.7706 10.5000i 0.511770 0.363802i
\(834\) −14.3083 −0.495456
\(835\) 16.7775 + 16.7775i 0.580608 + 0.580608i
\(836\) 32.3050 13.3812i 1.11729 0.462798i
\(837\) 9.85246i 0.340551i
\(838\) −2.85181 6.88489i −0.0985143 0.237835i
\(839\) 46.9502 + 19.4474i 1.62090 + 0.671400i 0.994169 0.107834i \(-0.0343915\pi\)
0.626733 + 0.779234i \(0.284392\pi\)
\(840\) −12.2759 + 29.6366i −0.423558 + 1.02256i
\(841\) −5.62490 + 5.62490i −0.193962 + 0.193962i
\(842\) 18.6984 18.6984i 0.644390 0.644390i
\(843\) −7.24695 + 17.4957i −0.249598 + 0.602584i
\(844\) 26.0242 + 10.7796i 0.895791 + 0.371049i
\(845\) 4.97893 + 12.0202i 0.171280 + 0.413508i
\(846\) 11.0688i 0.380552i
\(847\) 52.1164 21.5873i 1.79074 0.741749i
\(848\) 1.43983 + 1.43983i 0.0494439 + 0.0494439i
\(849\) 10.2864 0.353029
\(850\) −1.02403 + 6.05954i −0.0351241 + 0.207841i
\(851\) −70.6103 −2.42049
\(852\) −6.43639 6.43639i −0.220507 0.220507i
\(853\) −23.7822 + 9.85091i −0.814287 + 0.337289i −0.750663 0.660685i \(-0.770266\pi\)
−0.0636239 + 0.997974i \(0.520266\pi\)
\(854\) 33.7652i 1.15542i
\(855\) −4.03259 9.73553i −0.137912 0.332948i
\(856\) −0.0267952 0.0110989i −0.000915840 0.000379353i
\(857\) −1.45074 + 3.50241i −0.0495565 + 0.119640i −0.946719 0.322060i \(-0.895625\pi\)
0.897163 + 0.441700i \(0.145625\pi\)
\(858\) −13.9973 + 13.9973i −0.477859 + 0.477859i
\(859\) 28.2076 28.2076i 0.962431 0.962431i −0.0368882 0.999319i \(-0.511745\pi\)
0.999319 + 0.0368882i \(0.0117446\pi\)
\(860\) 0.942126 2.27449i 0.0321262 0.0775596i
\(861\) 31.3700 + 12.9939i 1.06909 + 0.442831i
\(862\) 1.32231 + 3.19234i 0.0450381 + 0.108731i
\(863\) 4.33919i 0.147708i 0.997269 + 0.0738539i \(0.0235299\pi\)
−0.997269 + 0.0738539i \(0.976470\pi\)
\(864\) −19.3141 + 8.00015i −0.657078 + 0.272171i
\(865\) −25.0564 25.0564i −0.851942 0.851942i
\(866\) 15.7097 0.533837
\(867\) 35.0854 2.03274i 1.19156 0.0690355i
\(868\) 13.1031 0.444749
\(869\) 49.8285 + 49.8285i 1.69032 + 1.69032i
\(870\) −15.6697 + 6.49062i −0.531254 + 0.220053i
\(871\) 13.1668i 0.446140i
\(872\) −0.154250 0.372392i −0.00522356 0.0126108i
\(873\) 9.95808 + 4.12477i 0.337030 + 0.139602i
\(874\) −11.0295 + 26.6275i −0.373078 + 0.900689i
\(875\) 28.9814 28.9814i 0.979750 0.979750i
\(876\) 7.43177 7.43177i 0.251096 0.251096i
\(877\) 9.29907 22.4499i 0.314007 0.758080i −0.685541 0.728034i \(-0.740434\pi\)
0.999548 0.0300466i \(-0.00956556\pi\)
\(878\) 28.1120 + 11.6444i 0.948735 + 0.392979i
\(879\) 9.98385 + 24.1031i 0.336747 + 0.812979i
\(880\) 7.26939i 0.245051i
\(881\) 26.7489 11.0797i 0.901193 0.373286i 0.116514 0.993189i \(-0.462828\pi\)
0.784679 + 0.619903i \(0.212828\pi\)
\(882\) −3.05121 3.05121i −0.102740 0.102740i
\(883\) 56.3473 1.89624 0.948119 0.317914i \(-0.102982\pi\)
0.948119 + 0.317914i \(0.102982\pi\)
\(884\) −2.27970 + 13.4897i −0.0766745 + 0.453708i
\(885\) 4.94914 0.166363
\(886\) 13.3377 + 13.3377i 0.448088 + 0.448088i
\(887\) 17.7779 7.36386i 0.596925 0.247254i −0.0637019 0.997969i \(-0.520291\pi\)
0.660627 + 0.750715i \(0.270291\pi\)
\(888\) 48.4141i 1.62467i
\(889\) −15.0084 36.2335i −0.503366 1.21523i
\(890\) −4.10383 1.69986i −0.137561 0.0569795i
\(891\) 22.5598 54.4643i 0.755783 1.82462i
\(892\) 2.07773 2.07773i 0.0695675 0.0695675i
\(893\) 37.6655 37.6655i 1.26043 1.26043i
\(894\) 12.0919 29.1924i 0.404414 0.976341i
\(895\) −9.51241 3.94017i −0.317965 0.131705i
\(896\) 12.2101 + 29.4778i 0.407911 + 0.984785i
\(897\) 38.6167i 1.28937i
\(898\) −4.15541 + 1.72123i −0.138668 + 0.0574381i
\(899\) 11.8675 + 11.8675i 0.395804 + 0.395804i
\(900\) −3.46325 −0.115442
\(901\) 8.67674 6.16805i 0.289064 0.205487i
\(902\) −19.7408 −0.657295
\(903\) 4.93462 + 4.93462i 0.164214 + 0.164214i
\(904\) 0.877974 0.363669i 0.0292010 0.0120954i
\(905\) 42.8179i 1.42332i
\(906\) −10.4674 25.2705i −0.347755 0.839555i
\(907\) −30.5989 12.6745i −1.01602 0.420849i −0.188372 0.982098i \(-0.560321\pi\)
−0.827647 + 0.561249i \(0.810321\pi\)
\(908\) −3.96228 + 9.56579i −0.131493 + 0.317452i
\(909\) −9.21810 + 9.21810i −0.305745 + 0.305745i
\(910\) −7.60281 + 7.60281i −0.252031 + 0.252031i
\(911\) −5.31036 + 12.8203i −0.175940 + 0.424757i −0.987108 0.160057i \(-0.948832\pi\)
0.811168 + 0.584813i \(0.198832\pi\)
\(912\) −7.11631 2.94767i −0.235645 0.0976072i
\(913\) 17.8618 + 43.1223i 0.591140 + 1.42714i
\(914\) 22.4329i 0.742015i
\(915\) −43.4025 + 17.9779i −1.43484 + 0.594331i
\(916\) −0.430616 0.430616i −0.0142280 0.0142280i
\(917\) 52.2417 1.72517
\(918\) 2.53333 + 11.0541i 0.0836123 + 0.364839i
\(919\) −19.1000 −0.630052 −0.315026 0.949083i \(-0.602013\pi\)
−0.315026 + 0.949083i \(0.602013\pi\)
\(920\) −25.7264 25.7264i −0.848174 0.848174i
\(921\) 43.4248 17.9871i 1.43089 0.592696i
\(922\) 21.7446i 0.716119i
\(923\) −2.82839 6.82834i −0.0930976 0.224758i
\(924\) −47.7178 19.7654i −1.56980 0.650233i
\(925\) 6.60207 15.9388i 0.217075 0.524065i
\(926\) −0.736963 + 0.736963i −0.0242181 + 0.0242181i
\(927\) 9.87221 9.87221i 0.324246 0.324246i
\(928\) −13.6279 + 32.9006i −0.447358 + 1.08002i
\(929\) −3.08240 1.27677i −0.101130 0.0418895i 0.331545 0.943439i \(-0.392430\pi\)
−0.432675 + 0.901550i \(0.642430\pi\)
\(930\) 2.94775 + 7.11649i 0.0966604 + 0.233359i
\(931\) 20.7658i 0.680570i
\(932\) −29.3137 + 12.1421i −0.960201 + 0.397728i
\(933\) −30.3334 30.3334i −0.993071 0.993071i
\(934\) 27.8879 0.912521
\(935\) 37.4741 + 6.33294i 1.22553 + 0.207109i
\(936\) 7.89147 0.257941
\(937\) 10.5894 + 10.5894i 0.345940 + 0.345940i 0.858595 0.512655i \(-0.171338\pi\)
−0.512655 + 0.858595i \(0.671338\pi\)
\(938\) −13.4106 + 5.55484i −0.437871 + 0.181372i
\(939\) 19.7436i 0.644307i
\(940\) 10.6221 + 25.6440i 0.346454 + 0.836415i
\(941\) −48.5576 20.1132i −1.58293 0.655673i −0.594059 0.804422i \(-0.702475\pi\)
−0.988875 + 0.148749i \(0.952475\pi\)
\(942\) 3.41904 8.25428i 0.111398 0.268939i
\(943\) −27.2311 + 27.2311i −0.886767 + 0.886767i
\(944\) 0.762410 0.762410i 0.0248143 0.0248143i
\(945\) 8.07244 19.4886i 0.262597 0.633964i
\(946\) −3.74842 1.55265i −0.121872 0.0504809i
\(947\) −5.68318 13.7204i −0.184679 0.445854i 0.804241 0.594303i \(-0.202572\pi\)
−0.988920 + 0.148449i \(0.952572\pi\)
\(948\) 38.9087i 1.26370i
\(949\) 7.88434 3.26580i 0.255937 0.106012i
\(950\) −4.97935 4.97935i −0.161552 0.161552i
\(951\) −31.0082 −1.00551
\(952\) 35.6139 8.16186i 1.15425 0.264527i
\(953\) −15.8397 −0.513099 −0.256549 0.966531i \(-0.582586\pi\)
−0.256549 + 0.966531i \(0.582586\pi\)
\(954\) −1.79239 1.79239i −0.0580307 0.0580307i
\(955\) 15.0810 6.24674i 0.488008 0.202140i
\(956\) 34.1715i 1.10519i
\(957\) −25.3166 61.1196i −0.818368 1.97572i
\(958\) −28.5541 11.8275i −0.922540 0.382129i
\(959\) 6.49000 15.6682i 0.209573 0.505954i
\(960\) −7.51979 + 7.51979i −0.242700 + 0.242700i
\(961\) −16.5306 + 16.5306i −0.533246 + 0.533246i
\(962\) −6.20994 + 14.9921i −0.200217 + 0.483365i
\(963\) −0.0130016 0.00538546i −0.000418972 0.000173544i
\(964\) 2.98756 + 7.21261i 0.0962228 + 0.232302i
\(965\) 3.89279i 0.125313i
\(966\) 39.3316 16.2917i 1.26547 0.524176i
\(967\) −8.47076 8.47076i −0.272401 0.272401i 0.557665 0.830066i \(-0.311697\pi\)
−0.830066 + 0.557665i \(0.811697\pi\)
\(968\) 43.8676 1.40996
\(969\) −21.3950 + 34.1170i −0.687307 + 1.09600i
\(970\) −11.4203 −0.366683
\(971\) −29.1418 29.1418i −0.935206 0.935206i 0.0628186 0.998025i \(-0.479991\pi\)
−0.998025 + 0.0628186i \(0.979991\pi\)
\(972\) −16.1658 + 6.69610i −0.518519 + 0.214778i
\(973\) 30.3136i 0.971810i
\(974\) 6.27555 + 15.1505i 0.201082 + 0.485454i
\(975\) −8.71692 3.61067i −0.279165 0.115634i
\(976\) −3.91664 + 9.45560i −0.125368 + 0.302666i
\(977\) −22.5933 + 22.5933i −0.722824 + 0.722824i −0.969179 0.246356i \(-0.920767\pi\)
0.246356 + 0.969179i \(0.420767\pi\)
\(978\) −14.5638 + 14.5638i −0.465697 + 0.465697i
\(979\) 6.63029 16.0069i 0.211905 0.511584i
\(980\) −9.99711 4.14094i −0.319346 0.132277i
\(981\) −0.0748456 0.180693i −0.00238964 0.00576909i
\(982\) 26.0917i 0.832618i
\(983\) −24.8228 + 10.2819i −0.791723 + 0.327942i −0.741636 0.670802i \(-0.765950\pi\)
−0.0500870 + 0.998745i \(0.515950\pi\)
\(984\) 18.6711 + 18.6711i 0.595212 + 0.595212i
\(985\) 31.0029 0.987835
\(986\) 16.3664 + 10.2634i 0.521211 + 0.326855i
\(987\) −78.6809 −2.50444
\(988\) −11.0850 11.0850i −0.352661 0.352661i
\(989\) −7.31247 + 3.02893i −0.232523 + 0.0963142i
\(990\) 9.04939i 0.287608i
\(991\) 21.3204 + 51.4720i 0.677265 + 1.63506i 0.768977 + 0.639277i \(0.220766\pi\)
−0.0917117 + 0.995786i \(0.529234\pi\)
\(992\) 14.9420 + 6.18918i 0.474409 + 0.196507i
\(993\) 14.6443 35.3544i 0.464721 1.12194i
\(994\) −5.76150 + 5.76150i −0.182744 + 0.182744i
\(995\) −14.6142 + 14.6142i −0.463303 + 0.463303i
\(996\) 9.86233 23.8098i 0.312500 0.754441i
\(997\) 19.8945 + 8.24055i 0.630064 + 0.260981i 0.674780 0.738019i \(-0.264238\pi\)
−0.0447165 + 0.999000i \(0.514238\pi\)
\(998\) −7.29167 17.6036i −0.230814 0.557233i
\(999\) 31.8364i 1.00726i
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 731.2.m.b.87.18 116
17.9 even 8 inner 731.2.m.b.689.18 yes 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.m.b.87.18 116 1.1 even 1 trivial
731.2.m.b.689.18 yes 116 17.9 even 8 inner