Properties

Label 1014.2.e.m.529.2
Level $1014$
Weight $2$
Character 1014.529
Analytic conductor $8.097$
Analytic rank $0$
Dimension $6$
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] = [1014,2,Mod(529,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not 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: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.2
Root \(0.222521 + 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.m.991.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.356896 q^{5} +(0.500000 + 0.866025i) q^{6} +(2.02446 + 3.50647i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -0.356896 q^{5} +(0.500000 + 0.866025i) q^{6} +(2.02446 + 3.50647i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.178448 + 0.309081i) q^{10} +(-0.455927 + 0.789689i) q^{11} +1.00000 q^{12} +4.04892 q^{14} +(0.178448 - 0.309081i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.04892 + 1.81678i) q^{17} -1.00000 q^{18} +(-2.49396 - 4.31966i) q^{19} +(0.178448 + 0.309081i) q^{20} -4.04892 q^{21} +(0.455927 + 0.789689i) q^{22} +(-4.24698 + 7.35598i) q^{23} +(0.500000 - 0.866025i) q^{24} -4.87263 q^{25} +1.00000 q^{27} +(2.02446 - 3.50647i) q^{28} +(-4.25786 + 7.37484i) q^{29} +(-0.178448 - 0.309081i) q^{30} +10.7899 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.455927 - 0.789689i) q^{33} +2.09783 q^{34} +(-0.722521 - 1.25144i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.307979 + 0.533434i) q^{37} -4.98792 q^{38} +0.356896 q^{40} +(-3.80194 + 6.58515i) q^{41} +(-2.02446 + 3.50647i) q^{42} +(3.13706 + 5.43355i) q^{43} +0.911854 q^{44} +(0.178448 + 0.309081i) q^{45} +(4.24698 + 7.35598i) q^{46} -1.78017 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-4.69687 + 8.13521i) q^{49} +(-2.43631 + 4.21982i) q^{50} -2.09783 q^{51} +10.4112 q^{53} +(0.500000 - 0.866025i) q^{54} +(0.162718 - 0.281837i) q^{55} +(-2.02446 - 3.50647i) q^{56} +4.98792 q^{57} +(4.25786 + 7.37484i) q^{58} +(-3.02446 - 5.23852i) q^{59} -0.356896 q^{60} +(1.55496 + 2.69327i) q^{61} +(5.39493 - 9.34429i) q^{62} +(2.02446 - 3.50647i) q^{63} +1.00000 q^{64} -0.911854 q^{66} +(6.78986 - 11.7604i) q^{67} +(1.04892 - 1.81678i) q^{68} +(-4.24698 - 7.35598i) q^{69} -1.44504 q^{70} +(5.74094 + 9.94360i) q^{71} +(0.500000 + 0.866025i) q^{72} -0.533188 q^{73} +(0.307979 + 0.533434i) q^{74} +(2.43631 - 4.21982i) q^{75} +(-2.49396 + 4.31966i) q^{76} -3.69202 q^{77} -11.7071 q^{79} +(0.178448 - 0.309081i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.80194 + 6.58515i) q^{82} +6.49934 q^{83} +(2.02446 + 3.50647i) q^{84} +(-0.374354 - 0.648401i) q^{85} +6.27413 q^{86} +(-4.25786 - 7.37484i) q^{87} +(0.455927 - 0.789689i) q^{88} +(-3.24698 + 5.62393i) q^{89} +0.356896 q^{90} +8.49396 q^{92} +(-5.39493 + 9.34429i) q^{93} +(-0.890084 + 1.54167i) q^{94} +(0.890084 + 1.54167i) q^{95} -1.00000 q^{96} +(-0.980386 - 1.69808i) q^{97} +(4.69687 + 8.13521i) q^{98} +0.911854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{5} + 3 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + q^{11} + 6 q^{12} + 6 q^{14} - 3 q^{15} - 3 q^{16} - 12 q^{17} - 6 q^{18} + 4 q^{19} - 3 q^{20} - 6 q^{21} - q^{22} - 16 q^{23} + 3 q^{24} + 4 q^{25} + 6 q^{27} + 3 q^{28} - 13 q^{29} + 3 q^{30} + 18 q^{31} + 3 q^{32} + q^{33} - 24 q^{34} - 4 q^{35} - 3 q^{36} - 12 q^{37} + 8 q^{38} - 6 q^{40} - 14 q^{41} - 3 q^{42} + 8 q^{43} - 2 q^{44} - 3 q^{45} + 16 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{49} + 2 q^{50} + 24 q^{51} + 30 q^{53} + 3 q^{54} + 22 q^{55} - 3 q^{56} - 8 q^{57} + 13 q^{58} - 9 q^{59} + 6 q^{60} + 10 q^{61} + 9 q^{62} + 3 q^{63} + 6 q^{64} + 2 q^{66} - 6 q^{67} - 12 q^{68} - 16 q^{69} - 8 q^{70} + 6 q^{71} + 3 q^{72} - 10 q^{73} + 12 q^{74} - 2 q^{75} + 4 q^{76} - 12 q^{77} - 10 q^{79} - 3 q^{80} - 3 q^{81} + 14 q^{82} + 14 q^{83} + 3 q^{84} - 26 q^{85} + 16 q^{86} - 13 q^{87} - q^{88} - 10 q^{89} - 6 q^{90} + 32 q^{92} - 9 q^{93} - 4 q^{94} + 4 q^{95} - 6 q^{96} + 7 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.356896 −0.159609 −0.0798043 0.996811i \(-0.525430\pi\)
−0.0798043 + 0.996811i \(0.525430\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 2.02446 + 3.50647i 0.765173 + 1.32532i 0.940155 + 0.340748i \(0.110680\pi\)
−0.174981 + 0.984572i \(0.555987\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.178448 + 0.309081i −0.0564302 + 0.0977400i
\(11\) −0.455927 + 0.789689i −0.137467 + 0.238100i −0.926537 0.376203i \(-0.877229\pi\)
0.789070 + 0.614303i \(0.210563\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 4.04892 1.08212
\(15\) 0.178448 0.309081i 0.0460751 0.0798043i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.04892 + 1.81678i 0.254400 + 0.440633i 0.964732 0.263233i \(-0.0847888\pi\)
−0.710333 + 0.703866i \(0.751455\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.49396 4.31966i −0.572153 0.990999i −0.996345 0.0854262i \(-0.972775\pi\)
0.424191 0.905573i \(-0.360559\pi\)
\(20\) 0.178448 + 0.309081i 0.0399022 + 0.0691126i
\(21\) −4.04892 −0.883546
\(22\) 0.455927 + 0.789689i 0.0972040 + 0.168362i
\(23\) −4.24698 + 7.35598i −0.885556 + 1.53383i −0.0404819 + 0.999180i \(0.512889\pi\)
−0.845075 + 0.534649i \(0.820444\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −4.87263 −0.974525
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 2.02446 3.50647i 0.382587 0.662660i
\(29\) −4.25786 + 7.37484i −0.790666 + 1.36947i 0.134890 + 0.990861i \(0.456932\pi\)
−0.925555 + 0.378612i \(0.876401\pi\)
\(30\) −0.178448 0.309081i −0.0325800 0.0564302i
\(31\) 10.7899 1.93792 0.968958 0.247227i \(-0.0795192\pi\)
0.968958 + 0.247227i \(0.0795192\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.455927 0.789689i −0.0793667 0.137467i
\(34\) 2.09783 0.359776
\(35\) −0.722521 1.25144i −0.122128 0.211532i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −0.307979 + 0.533434i −0.0506314 + 0.0876961i −0.890230 0.455511i \(-0.849457\pi\)
0.839599 + 0.543207i \(0.182790\pi\)
\(38\) −4.98792 −0.809147
\(39\) 0 0
\(40\) 0.356896 0.0564302
\(41\) −3.80194 + 6.58515i −0.593763 + 1.02843i 0.399957 + 0.916534i \(0.369025\pi\)
−0.993720 + 0.111894i \(0.964308\pi\)
\(42\) −2.02446 + 3.50647i −0.312381 + 0.541059i
\(43\) 3.13706 + 5.43355i 0.478398 + 0.828609i 0.999693 0.0247671i \(-0.00788442\pi\)
−0.521296 + 0.853376i \(0.674551\pi\)
\(44\) 0.911854 0.137467
\(45\) 0.178448 + 0.309081i 0.0266014 + 0.0460751i
\(46\) 4.24698 + 7.35598i 0.626183 + 1.08458i
\(47\) −1.78017 −0.259664 −0.129832 0.991536i \(-0.541444\pi\)
−0.129832 + 0.991536i \(0.541444\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −4.69687 + 8.13521i −0.670981 + 1.16217i
\(50\) −2.43631 + 4.21982i −0.344547 + 0.596772i
\(51\) −2.09783 −0.293756
\(52\) 0 0
\(53\) 10.4112 1.43009 0.715043 0.699080i \(-0.246407\pi\)
0.715043 + 0.699080i \(0.246407\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0.162718 0.281837i 0.0219410 0.0380028i
\(56\) −2.02446 3.50647i −0.270530 0.468571i
\(57\) 4.98792 0.660666
\(58\) 4.25786 + 7.37484i 0.559085 + 0.968364i
\(59\) −3.02446 5.23852i −0.393751 0.681997i 0.599190 0.800607i \(-0.295489\pi\)
−0.992941 + 0.118610i \(0.962156\pi\)
\(60\) −0.356896 −0.0460751
\(61\) 1.55496 + 2.69327i 0.199092 + 0.344837i 0.948234 0.317572i \(-0.102867\pi\)
−0.749142 + 0.662409i \(0.769534\pi\)
\(62\) 5.39493 9.34429i 0.685157 1.18673i
\(63\) 2.02446 3.50647i 0.255058 0.441773i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.911854 −0.112241
\(67\) 6.78986 11.7604i 0.829513 1.43676i −0.0689079 0.997623i \(-0.521951\pi\)
0.898421 0.439136i \(-0.144715\pi\)
\(68\) 1.04892 1.81678i 0.127200 0.220317i
\(69\) −4.24698 7.35598i −0.511276 0.885556i
\(70\) −1.44504 −0.172716
\(71\) 5.74094 + 9.94360i 0.681324 + 1.18009i 0.974577 + 0.224053i \(0.0719289\pi\)
−0.293253 + 0.956035i \(0.594738\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −0.533188 −0.0624049 −0.0312025 0.999513i \(-0.509934\pi\)
−0.0312025 + 0.999513i \(0.509934\pi\)
\(74\) 0.307979 + 0.533434i 0.0358018 + 0.0620105i
\(75\) 2.43631 4.21982i 0.281321 0.487263i
\(76\) −2.49396 + 4.31966i −0.286077 + 0.495499i
\(77\) −3.69202 −0.420745
\(78\) 0 0
\(79\) −11.7071 −1.31715 −0.658575 0.752515i \(-0.728841\pi\)
−0.658575 + 0.752515i \(0.728841\pi\)
\(80\) 0.178448 0.309081i 0.0199511 0.0345563i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.80194 + 6.58515i 0.419854 + 0.727208i
\(83\) 6.49934 0.713395 0.356697 0.934220i \(-0.383903\pi\)
0.356697 + 0.934220i \(0.383903\pi\)
\(84\) 2.02446 + 3.50647i 0.220887 + 0.382587i
\(85\) −0.374354 0.648401i −0.0406044 0.0703289i
\(86\) 6.27413 0.676556
\(87\) −4.25786 7.37484i −0.456491 0.790666i
\(88\) 0.455927 0.789689i 0.0486020 0.0841811i
\(89\) −3.24698 + 5.62393i −0.344179 + 0.596136i −0.985204 0.171384i \(-0.945176\pi\)
0.641025 + 0.767520i \(0.278509\pi\)
\(90\) 0.356896 0.0376201
\(91\) 0 0
\(92\) 8.49396 0.885556
\(93\) −5.39493 + 9.34429i −0.559428 + 0.968958i
\(94\) −0.890084 + 1.54167i −0.0918051 + 0.159011i
\(95\) 0.890084 + 1.54167i 0.0913207 + 0.158172i
\(96\) −1.00000 −0.102062
\(97\) −0.980386 1.69808i −0.0995431 0.172414i 0.811953 0.583723i \(-0.198405\pi\)
−0.911496 + 0.411310i \(0.865071\pi\)
\(98\) 4.69687 + 8.13521i 0.474455 + 0.821780i
\(99\) 0.911854 0.0916448
\(100\) 2.43631 + 4.21982i 0.243631 + 0.421982i
\(101\) −3.49127 + 6.04706i −0.347394 + 0.601705i −0.985786 0.168007i \(-0.946267\pi\)
0.638391 + 0.769712i \(0.279600\pi\)
\(102\) −1.04892 + 1.81678i −0.103858 + 0.179888i
\(103\) 4.94869 0.487609 0.243804 0.969824i \(-0.421604\pi\)
0.243804 + 0.969824i \(0.421604\pi\)
\(104\) 0 0
\(105\) 1.44504 0.141022
\(106\) 5.20560 9.01636i 0.505612 0.875746i
\(107\) 2.13437 3.69685i 0.206338 0.357388i −0.744220 0.667934i \(-0.767179\pi\)
0.950558 + 0.310547i \(0.100512\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 6.21983 0.595752 0.297876 0.954605i \(-0.403722\pi\)
0.297876 + 0.954605i \(0.403722\pi\)
\(110\) −0.162718 0.281837i −0.0155146 0.0268721i
\(111\) −0.307979 0.533434i −0.0292320 0.0506314i
\(112\) −4.04892 −0.382587
\(113\) −6.49396 11.2479i −0.610900 1.05811i −0.991089 0.133201i \(-0.957474\pi\)
0.380189 0.924909i \(-0.375859\pi\)
\(114\) 2.49396 4.31966i 0.233581 0.404574i
\(115\) 1.51573 2.62532i 0.141343 0.244812i
\(116\) 8.51573 0.790666
\(117\) 0 0
\(118\) −6.04892 −0.556848
\(119\) −4.24698 + 7.35598i −0.389320 + 0.674322i
\(120\) −0.178448 + 0.309081i −0.0162900 + 0.0282151i
\(121\) 5.08426 + 8.80620i 0.462206 + 0.800564i
\(122\) 3.10992 0.281559
\(123\) −3.80194 6.58515i −0.342809 0.593763i
\(124\) −5.39493 9.34429i −0.484479 0.839142i
\(125\) 3.52350 0.315151
\(126\) −2.02446 3.50647i −0.180353 0.312381i
\(127\) −4.61141 + 7.98719i −0.409196 + 0.708749i −0.994800 0.101849i \(-0.967524\pi\)
0.585604 + 0.810598i \(0.300858\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −6.27413 −0.552406
\(130\) 0 0
\(131\) −14.5526 −1.27146 −0.635732 0.771910i \(-0.719302\pi\)
−0.635732 + 0.771910i \(0.719302\pi\)
\(132\) −0.455927 + 0.789689i −0.0396834 + 0.0687336i
\(133\) 10.0978 17.4900i 0.875593 1.51657i
\(134\) −6.78986 11.7604i −0.586554 1.01594i
\(135\) −0.356896 −0.0307167
\(136\) −1.04892 1.81678i −0.0899439 0.155787i
\(137\) −7.70171 13.3398i −0.658002 1.13969i −0.981132 0.193338i \(-0.938069\pi\)
0.323131 0.946354i \(-0.395265\pi\)
\(138\) −8.49396 −0.723054
\(139\) −1.35690 2.35021i −0.115090 0.199342i 0.802725 0.596349i \(-0.203382\pi\)
−0.917816 + 0.397006i \(0.870049\pi\)
\(140\) −0.722521 + 1.25144i −0.0610642 + 0.105766i
\(141\) 0.890084 1.54167i 0.0749586 0.129832i
\(142\) 11.4819 0.963538
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 1.51961 2.63205i 0.126197 0.218580i
\(146\) −0.266594 + 0.461754i −0.0220635 + 0.0382151i
\(147\) −4.69687 8.13521i −0.387391 0.670981i
\(148\) 0.615957 0.0506314
\(149\) −7.36778 12.7614i −0.603592 1.04545i −0.992272 0.124079i \(-0.960402\pi\)
0.388680 0.921373i \(-0.372931\pi\)
\(150\) −2.43631 4.21982i −0.198924 0.344547i
\(151\) 15.8213 1.28752 0.643760 0.765227i \(-0.277373\pi\)
0.643760 + 0.765227i \(0.277373\pi\)
\(152\) 2.49396 + 4.31966i 0.202287 + 0.350371i
\(153\) 1.04892 1.81678i 0.0847999 0.146878i
\(154\) −1.84601 + 3.19738i −0.148756 + 0.257653i
\(155\) −3.85086 −0.309308
\(156\) 0 0
\(157\) −4.27413 −0.341112 −0.170556 0.985348i \(-0.554556\pi\)
−0.170556 + 0.985348i \(0.554556\pi\)
\(158\) −5.85354 + 10.1386i −0.465683 + 0.806586i
\(159\) −5.20560 + 9.01636i −0.412831 + 0.715043i
\(160\) −0.178448 0.309081i −0.0141075 0.0244350i
\(161\) −34.3913 −2.71042
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −0.158834 0.275108i −0.0124408 0.0215481i 0.859738 0.510735i \(-0.170627\pi\)
−0.872179 + 0.489187i \(0.837293\pi\)
\(164\) 7.60388 0.593763
\(165\) 0.162718 + 0.281837i 0.0126676 + 0.0219410i
\(166\) 3.24967 5.62859i 0.252223 0.436863i
\(167\) 6.18060 10.7051i 0.478269 0.828387i −0.521420 0.853300i \(-0.674598\pi\)
0.999690 + 0.0249130i \(0.00793089\pi\)
\(168\) 4.04892 0.312381
\(169\) 0 0
\(170\) −0.748709 −0.0574233
\(171\) −2.49396 + 4.31966i −0.190718 + 0.330333i
\(172\) 3.13706 5.43355i 0.239199 0.414305i
\(173\) 8.53199 + 14.7778i 0.648675 + 1.12354i 0.983440 + 0.181237i \(0.0580100\pi\)
−0.334764 + 0.942302i \(0.608657\pi\)
\(174\) −8.51573 −0.645576
\(175\) −9.86443 17.0857i −0.745681 1.29156i
\(176\) −0.455927 0.789689i −0.0343668 0.0595250i
\(177\) 6.04892 0.454664
\(178\) 3.24698 + 5.62393i 0.243371 + 0.421532i
\(179\) 12.4840 21.6230i 0.933100 1.61618i 0.155114 0.987897i \(-0.450426\pi\)
0.777987 0.628281i \(-0.216241\pi\)
\(180\) 0.178448 0.309081i 0.0133007 0.0230375i
\(181\) 5.26205 0.391125 0.195562 0.980691i \(-0.437347\pi\)
0.195562 + 0.980691i \(0.437347\pi\)
\(182\) 0 0
\(183\) −3.10992 −0.229892
\(184\) 4.24698 7.35598i 0.313091 0.542290i
\(185\) 0.109916 0.190381i 0.00808120 0.0139971i
\(186\) 5.39493 + 9.34429i 0.395575 + 0.685157i
\(187\) −1.91292 −0.139886
\(188\) 0.890084 + 1.54167i 0.0649160 + 0.112438i
\(189\) 2.02446 + 3.50647i 0.147258 + 0.255058i
\(190\) 1.78017 0.129147
\(191\) −5.26875 9.12574i −0.381233 0.660316i 0.610005 0.792397i \(-0.291167\pi\)
−0.991239 + 0.132082i \(0.957834\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) 1.71379 2.96837i 0.123361 0.213668i −0.797730 0.603015i \(-0.793966\pi\)
0.921091 + 0.389347i \(0.127299\pi\)
\(194\) −1.96077 −0.140775
\(195\) 0 0
\(196\) 9.39373 0.670981
\(197\) 1.88740 3.26906i 0.134471 0.232911i −0.790924 0.611914i \(-0.790400\pi\)
0.925395 + 0.379003i \(0.123733\pi\)
\(198\) 0.455927 0.789689i 0.0324013 0.0561207i
\(199\) −8.97703 15.5487i −0.636365 1.10222i −0.986224 0.165414i \(-0.947104\pi\)
0.349859 0.936802i \(-0.386229\pi\)
\(200\) 4.87263 0.344547
\(201\) 6.78986 + 11.7604i 0.478920 + 0.829513i
\(202\) 3.49127 + 6.04706i 0.245645 + 0.425470i
\(203\) −34.4795 −2.41999
\(204\) 1.04892 + 1.81678i 0.0734389 + 0.127200i
\(205\) 1.35690 2.35021i 0.0947697 0.164146i
\(206\) 2.47434 4.28569i 0.172396 0.298598i
\(207\) 8.49396 0.590371
\(208\) 0 0
\(209\) 4.54825 0.314609
\(210\) 0.722521 1.25144i 0.0498587 0.0863578i
\(211\) 6.26875 10.8578i 0.431559 0.747481i −0.565449 0.824783i \(-0.691297\pi\)
0.997008 + 0.0773018i \(0.0246305\pi\)
\(212\) −5.20560 9.01636i −0.357522 0.619246i
\(213\) −11.4819 −0.786725
\(214\) −2.13437 3.69685i −0.145903 0.252711i
\(215\) −1.11960 1.93921i −0.0763564 0.132253i
\(216\) −1.00000 −0.0680414
\(217\) 21.8436 + 37.8343i 1.48284 + 2.56836i
\(218\) 3.10992 5.38653i 0.210630 0.364822i
\(219\) 0.266594 0.461754i 0.0180147 0.0312025i
\(220\) −0.325437 −0.0219410
\(221\) 0 0
\(222\) −0.615957 −0.0413403
\(223\) 2.71379 4.70043i 0.181729 0.314764i −0.760740 0.649056i \(-0.775164\pi\)
0.942469 + 0.334292i \(0.108497\pi\)
\(224\) −2.02446 + 3.50647i −0.135265 + 0.234286i
\(225\) 2.43631 + 4.21982i 0.162421 + 0.281321i
\(226\) −12.9879 −0.863943
\(227\) 8.28836 + 14.3559i 0.550118 + 0.952832i 0.998265 + 0.0588728i \(0.0187506\pi\)
−0.448147 + 0.893960i \(0.647916\pi\)
\(228\) −2.49396 4.31966i −0.165166 0.286077i
\(229\) 23.8780 1.57790 0.788951 0.614456i \(-0.210624\pi\)
0.788951 + 0.614456i \(0.210624\pi\)
\(230\) −1.51573 2.62532i −0.0999442 0.173109i
\(231\) 1.84601 3.19738i 0.121459 0.210372i
\(232\) 4.25786 7.37484i 0.279543 0.484182i
\(233\) 13.9952 0.916857 0.458428 0.888731i \(-0.348413\pi\)
0.458428 + 0.888731i \(0.348413\pi\)
\(234\) 0 0
\(235\) 0.635334 0.0414446
\(236\) −3.02446 + 5.23852i −0.196875 + 0.340998i
\(237\) 5.85354 10.1386i 0.380229 0.658575i
\(238\) 4.24698 + 7.35598i 0.275291 + 0.476818i
\(239\) −13.2862 −0.859413 −0.429707 0.902969i \(-0.641383\pi\)
−0.429707 + 0.902969i \(0.641383\pi\)
\(240\) 0.178448 + 0.309081i 0.0115188 + 0.0199511i
\(241\) 5.23945 + 9.07499i 0.337502 + 0.584571i 0.983962 0.178377i \(-0.0570845\pi\)
−0.646460 + 0.762948i \(0.723751\pi\)
\(242\) 10.1685 0.653657
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 1.55496 2.69327i 0.0995460 0.172419i
\(245\) 1.67629 2.90342i 0.107094 0.185493i
\(246\) −7.60388 −0.484805
\(247\) 0 0
\(248\) −10.7899 −0.685157
\(249\) −3.24967 + 5.62859i −0.205939 + 0.356697i
\(250\) 1.76175 3.05144i 0.111423 0.192990i
\(251\) −1.74363 3.02005i −0.110057 0.190624i 0.805736 0.592275i \(-0.201770\pi\)
−0.915793 + 0.401651i \(0.868437\pi\)
\(252\) −4.04892 −0.255058
\(253\) −3.87263 6.70758i −0.243470 0.421702i
\(254\) 4.61141 + 7.98719i 0.289345 + 0.501161i
\(255\) 0.748709 0.0468859
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.26875 + 5.66164i −0.203899 + 0.353163i −0.949781 0.312914i \(-0.898695\pi\)
0.745882 + 0.666078i \(0.232028\pi\)
\(258\) −3.13706 + 5.43355i −0.195305 + 0.338278i
\(259\) −2.49396 −0.154967
\(260\) 0 0
\(261\) 8.51573 0.527110
\(262\) −7.27628 + 12.6029i −0.449530 + 0.778609i
\(263\) −4.00969 + 6.94498i −0.247248 + 0.428246i −0.962761 0.270353i \(-0.912860\pi\)
0.715513 + 0.698599i \(0.246193\pi\)
\(264\) 0.455927 + 0.789689i 0.0280604 + 0.0486020i
\(265\) −3.71571 −0.228254
\(266\) −10.0978 17.4900i −0.619138 1.07238i
\(267\) −3.24698 5.62393i −0.198712 0.344179i
\(268\) −13.5797 −0.829513
\(269\) 13.8366 + 23.9657i 0.843633 + 1.46122i 0.886803 + 0.462148i \(0.152921\pi\)
−0.0431692 + 0.999068i \(0.513745\pi\)
\(270\) −0.178448 + 0.309081i −0.0108600 + 0.0188101i
\(271\) 7.36443 12.7556i 0.447357 0.774845i −0.550856 0.834600i \(-0.685699\pi\)
0.998213 + 0.0597550i \(0.0190319\pi\)
\(272\) −2.09783 −0.127200
\(273\) 0 0
\(274\) −15.4034 −0.930555
\(275\) 2.22156 3.84786i 0.133965 0.232035i
\(276\) −4.24698 + 7.35598i −0.255638 + 0.442778i
\(277\) −1.63102 2.82501i −0.0979986 0.169739i 0.812858 0.582463i \(-0.197911\pi\)
−0.910856 + 0.412724i \(0.864577\pi\)
\(278\) −2.71379 −0.162762
\(279\) −5.39493 9.34429i −0.322986 0.559428i
\(280\) 0.722521 + 1.25144i 0.0431789 + 0.0747880i
\(281\) −7.72587 −0.460887 −0.230443 0.973086i \(-0.574018\pi\)
−0.230443 + 0.973086i \(0.574018\pi\)
\(282\) −0.890084 1.54167i −0.0530037 0.0918051i
\(283\) 9.89008 17.1301i 0.587904 1.01828i −0.406602 0.913605i \(-0.633286\pi\)
0.994506 0.104675i \(-0.0333802\pi\)
\(284\) 5.74094 9.94360i 0.340662 0.590044i
\(285\) −1.78017 −0.105448
\(286\) 0 0
\(287\) −30.7875 −1.81733
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 6.29954 10.9111i 0.370561 0.641831i
\(290\) −1.51961 2.63205i −0.0892348 0.154559i
\(291\) 1.96077 0.114942
\(292\) 0.266594 + 0.461754i 0.0156012 + 0.0270221i
\(293\) −6.45593 11.1820i −0.377159 0.653259i 0.613488 0.789704i \(-0.289766\pi\)
−0.990648 + 0.136445i \(0.956432\pi\)
\(294\) −9.39373 −0.547854
\(295\) 1.07942 + 1.86960i 0.0628461 + 0.108853i
\(296\) 0.307979 0.533434i 0.0179009 0.0310052i
\(297\) −0.455927 + 0.789689i −0.0264556 + 0.0458224i
\(298\) −14.7356 −0.853608
\(299\) 0 0
\(300\) −4.87263 −0.281321
\(301\) −12.7017 + 22.0000i −0.732114 + 1.26806i
\(302\) 7.91066 13.7017i 0.455207 0.788442i
\(303\) −3.49127 6.04706i −0.200568 0.347394i
\(304\) 4.98792 0.286077
\(305\) −0.554958 0.961216i −0.0317768 0.0550390i
\(306\) −1.04892 1.81678i −0.0599626 0.103858i
\(307\) −19.9651 −1.13947 −0.569734 0.821829i \(-0.692954\pi\)
−0.569734 + 0.821829i \(0.692954\pi\)
\(308\) 1.84601 + 3.19738i 0.105186 + 0.182188i
\(309\) −2.47434 + 4.28569i −0.140761 + 0.243804i
\(310\) −1.92543 + 3.33494i −0.109357 + 0.189412i
\(311\) 13.4819 0.764487 0.382244 0.924062i \(-0.375152\pi\)
0.382244 + 0.924062i \(0.375152\pi\)
\(312\) 0 0
\(313\) 12.9245 0.730537 0.365269 0.930902i \(-0.380977\pi\)
0.365269 + 0.930902i \(0.380977\pi\)
\(314\) −2.13706 + 3.70150i −0.120601 + 0.208888i
\(315\) −0.722521 + 1.25144i −0.0407094 + 0.0705108i
\(316\) 5.85354 + 10.1386i 0.329288 + 0.570343i
\(317\) 11.8726 0.666833 0.333417 0.942780i \(-0.391798\pi\)
0.333417 + 0.942780i \(0.391798\pi\)
\(318\) 5.20560 + 9.01636i 0.291915 + 0.505612i
\(319\) −3.88255 6.72478i −0.217381 0.376515i
\(320\) −0.356896 −0.0199511
\(321\) 2.13437 + 3.69685i 0.119129 + 0.206338i
\(322\) −17.1957 + 29.7838i −0.958277 + 1.65978i
\(323\) 5.23191 9.06194i 0.291111 0.504220i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −0.317667 −0.0175940
\(327\) −3.10992 + 5.38653i −0.171979 + 0.297876i
\(328\) 3.80194 6.58515i 0.209927 0.363604i
\(329\) −3.60388 6.24210i −0.198688 0.344138i
\(330\) 0.325437 0.0179147
\(331\) 5.11960 + 8.86742i 0.281399 + 0.487397i 0.971730 0.236097i \(-0.0758682\pi\)
−0.690331 + 0.723494i \(0.742535\pi\)
\(332\) −3.24967 5.62859i −0.178349 0.308909i
\(333\) 0.615957 0.0337542
\(334\) −6.18060 10.7051i −0.338188 0.585758i
\(335\) −2.42327 + 4.19723i −0.132397 + 0.229319i
\(336\) 2.02446 3.50647i 0.110443 0.191293i
\(337\) 1.44935 0.0789513 0.0394757 0.999221i \(-0.487431\pi\)
0.0394757 + 0.999221i \(0.487431\pi\)
\(338\) 0 0
\(339\) 12.9879 0.705407
\(340\) −0.374354 + 0.648401i −0.0203022 + 0.0351645i
\(341\) −4.91939 + 8.52063i −0.266400 + 0.461418i
\(342\) 2.49396 + 4.31966i 0.134858 + 0.233581i
\(343\) −9.69202 −0.523320
\(344\) −3.13706 5.43355i −0.169139 0.292958i
\(345\) 1.51573 + 2.62532i 0.0816041 + 0.141343i
\(346\) 17.0640 0.917365
\(347\) −3.42058 5.92462i −0.183627 0.318050i 0.759486 0.650523i \(-0.225450\pi\)
−0.943113 + 0.332473i \(0.892117\pi\)
\(348\) −4.25786 + 7.37484i −0.228246 + 0.395333i
\(349\) −17.1685 + 29.7368i −0.919010 + 1.59177i −0.118088 + 0.993003i \(0.537676\pi\)
−0.800922 + 0.598769i \(0.795657\pi\)
\(350\) −19.7289 −1.05455
\(351\) 0 0
\(352\) −0.911854 −0.0486020
\(353\) 13.0248 22.5595i 0.693238 1.20072i −0.277533 0.960716i \(-0.589517\pi\)
0.970771 0.240007i \(-0.0771497\pi\)
\(354\) 3.02446 5.23852i 0.160748 0.278424i
\(355\) −2.04892 3.54883i −0.108745 0.188352i
\(356\) 6.49396 0.344179
\(357\) −4.24698 7.35598i −0.224774 0.389320i
\(358\) −12.4840 21.6230i −0.659802 1.14281i
\(359\) −8.49396 −0.448294 −0.224147 0.974555i \(-0.571960\pi\)
−0.224147 + 0.974555i \(0.571960\pi\)
\(360\) −0.178448 0.309081i −0.00940503 0.0162900i
\(361\) −2.93967 + 5.09165i −0.154719 + 0.267982i
\(362\) 2.63102 4.55706i 0.138283 0.239514i
\(363\) −10.1685 −0.533709
\(364\) 0 0
\(365\) 0.190293 0.00996037
\(366\) −1.55496 + 2.69327i −0.0812790 + 0.140779i
\(367\) −13.7262 + 23.7744i −0.716500 + 1.24101i 0.245878 + 0.969301i \(0.420924\pi\)
−0.962378 + 0.271714i \(0.912410\pi\)
\(368\) −4.24698 7.35598i −0.221389 0.383457i
\(369\) 7.60388 0.395842
\(370\) −0.109916 0.190381i −0.00571427 0.00989741i
\(371\) 21.0770 + 36.5065i 1.09426 + 1.89532i
\(372\) 10.7899 0.559428
\(373\) −13.3110 23.0553i −0.689216 1.19376i −0.972092 0.234600i \(-0.924622\pi\)
0.282876 0.959156i \(-0.408711\pi\)
\(374\) −0.956459 + 1.65664i −0.0494573 + 0.0856626i
\(375\) −1.76175 + 3.05144i −0.0909764 + 0.157576i
\(376\) 1.78017 0.0918051
\(377\) 0 0
\(378\) 4.04892 0.208254
\(379\) 5.82371 10.0870i 0.299144 0.518132i −0.676797 0.736170i \(-0.736632\pi\)
0.975940 + 0.218038i \(0.0699656\pi\)
\(380\) 0.890084 1.54167i 0.0456603 0.0790860i
\(381\) −4.61141 7.98719i −0.236250 0.409196i
\(382\) −10.5375 −0.539145
\(383\) 5.25906 + 9.10896i 0.268725 + 0.465446i 0.968533 0.248885i \(-0.0800642\pi\)
−0.699807 + 0.714331i \(0.746731\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 1.31767 0.0671545
\(386\) −1.71379 2.96837i −0.0872297 0.151086i
\(387\) 3.13706 5.43355i 0.159466 0.276203i
\(388\) −0.980386 + 1.69808i −0.0497715 + 0.0862068i
\(389\) −9.25965 −0.469483 −0.234742 0.972058i \(-0.575424\pi\)
−0.234742 + 0.972058i \(0.575424\pi\)
\(390\) 0 0
\(391\) −17.8189 −0.901142
\(392\) 4.69687 8.13521i 0.237228 0.410890i
\(393\) 7.27628 12.6029i 0.367040 0.635732i
\(394\) −1.88740 3.26906i −0.0950856 0.164693i
\(395\) 4.17821 0.210229
\(396\) −0.455927 0.789689i −0.0229112 0.0396834i
\(397\) 7.25667 + 12.5689i 0.364202 + 0.630816i 0.988648 0.150252i \(-0.0480085\pi\)
−0.624446 + 0.781068i \(0.714675\pi\)
\(398\) −17.9541 −0.899956
\(399\) 10.0978 + 17.4900i 0.505524 + 0.875593i
\(400\) 2.43631 4.21982i 0.121816 0.210991i
\(401\) −19.4209 + 33.6379i −0.969832 + 1.67980i −0.273803 + 0.961786i \(0.588282\pi\)
−0.696030 + 0.718013i \(0.745052\pi\)
\(402\) 13.5797 0.677294
\(403\) 0 0
\(404\) 6.98254 0.347394
\(405\) 0.178448 0.309081i 0.00886715 0.0153584i
\(406\) −17.2397 + 29.8601i −0.855594 + 1.48193i
\(407\) −0.280831 0.486414i −0.0139203 0.0241107i
\(408\) 2.09783 0.103858
\(409\) 16.9611 + 29.3774i 0.838671 + 1.45262i 0.891006 + 0.453991i \(0.150000\pi\)
−0.0523356 + 0.998630i \(0.516667\pi\)
\(410\) −1.35690 2.35021i −0.0670123 0.116069i
\(411\) 15.4034 0.759795
\(412\) −2.47434 4.28569i −0.121902 0.211141i
\(413\) 12.2458 21.2103i 0.602576 1.04369i
\(414\) 4.24698 7.35598i 0.208728 0.361527i
\(415\) −2.31959 −0.113864
\(416\) 0 0
\(417\) 2.71379 0.132895
\(418\) 2.27413 3.93890i 0.111231 0.192658i
\(419\) −0.477697 + 0.827396i −0.0233370 + 0.0404209i −0.877458 0.479653i \(-0.840762\pi\)
0.854121 + 0.520074i \(0.174096\pi\)
\(420\) −0.722521 1.25144i −0.0352554 0.0610642i
\(421\) −5.68233 −0.276940 −0.138470 0.990367i \(-0.544218\pi\)
−0.138470 + 0.990367i \(0.544218\pi\)
\(422\) −6.26875 10.8578i −0.305158 0.528549i
\(423\) 0.890084 + 1.54167i 0.0432774 + 0.0749586i
\(424\) −10.4112 −0.505612
\(425\) −5.11098 8.85248i −0.247919 0.429408i
\(426\) −5.74094 + 9.94360i −0.278149 + 0.481769i
\(427\) −6.29590 + 10.9048i −0.304680 + 0.527721i
\(428\) −4.26875 −0.206338
\(429\) 0 0
\(430\) −2.23921 −0.107984
\(431\) 7.42327 12.8575i 0.357566 0.619323i −0.629987 0.776605i \(-0.716940\pi\)
0.987554 + 0.157282i \(0.0502732\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 13.0749 + 22.6463i 0.628338 + 1.08831i 0.987885 + 0.155187i \(0.0495979\pi\)
−0.359547 + 0.933127i \(0.617069\pi\)
\(434\) 43.6872 2.09705
\(435\) 1.51961 + 2.63205i 0.0728599 + 0.126197i
\(436\) −3.10992 5.38653i −0.148938 0.257968i
\(437\) 42.3672 2.02670
\(438\) −0.266594 0.461754i −0.0127384 0.0220635i
\(439\) 11.7751 20.3950i 0.561994 0.973403i −0.435328 0.900272i \(-0.643368\pi\)
0.997322 0.0731307i \(-0.0232990\pi\)
\(440\) −0.162718 + 0.281837i −0.00775730 + 0.0134360i
\(441\) 9.39373 0.447321
\(442\) 0 0
\(443\) 21.9433 1.04256 0.521279 0.853386i \(-0.325455\pi\)
0.521279 + 0.853386i \(0.325455\pi\)
\(444\) −0.307979 + 0.533434i −0.0146160 + 0.0253157i
\(445\) 1.15883 2.00716i 0.0549340 0.0951484i
\(446\) −2.71379 4.70043i −0.128502 0.222572i
\(447\) 14.7356 0.696968
\(448\) 2.02446 + 3.50647i 0.0956467 + 0.165665i
\(449\) −5.70171 9.87565i −0.269080 0.466061i 0.699544 0.714589i \(-0.253386\pi\)
−0.968625 + 0.248528i \(0.920053\pi\)
\(450\) 4.87263 0.229698
\(451\) −3.46681 6.00469i −0.163246 0.282750i
\(452\) −6.49396 + 11.2479i −0.305450 + 0.529055i
\(453\) −7.91066 + 13.7017i −0.371675 + 0.643760i
\(454\) 16.5767 0.777984
\(455\) 0 0
\(456\) −4.98792 −0.233581
\(457\) −3.83459 + 6.64171i −0.179375 + 0.310686i −0.941667 0.336547i \(-0.890741\pi\)
0.762292 + 0.647233i \(0.224074\pi\)
\(458\) 11.9390 20.6790i 0.557873 0.966264i
\(459\) 1.04892 + 1.81678i 0.0489593 + 0.0847999i
\(460\) −3.03146 −0.141343
\(461\) 14.2540 + 24.6886i 0.663874 + 1.14986i 0.979589 + 0.201010i \(0.0644222\pi\)
−0.315715 + 0.948854i \(0.602244\pi\)
\(462\) −1.84601 3.19738i −0.0858842 0.148756i
\(463\) −14.3284 −0.665898 −0.332949 0.942945i \(-0.608044\pi\)
−0.332949 + 0.942945i \(0.608044\pi\)
\(464\) −4.25786 7.37484i −0.197666 0.342368i
\(465\) 1.92543 3.33494i 0.0892896 0.154654i
\(466\) 6.99761 12.1202i 0.324158 0.561458i
\(467\) 33.3207 1.54190 0.770948 0.636898i \(-0.219783\pi\)
0.770948 + 0.636898i \(0.219783\pi\)
\(468\) 0 0
\(469\) 54.9831 2.53889
\(470\) 0.317667 0.550216i 0.0146529 0.0253796i
\(471\) 2.13706 3.70150i 0.0984707 0.170556i
\(472\) 3.02446 + 5.23852i 0.139212 + 0.241122i
\(473\) −5.72109 −0.263056
\(474\) −5.85354 10.1386i −0.268862 0.465683i
\(475\) 12.1521 + 21.0481i 0.557578 + 0.965753i
\(476\) 8.49396 0.389320
\(477\) −5.20560 9.01636i −0.238348 0.412831i
\(478\) −6.64310 + 11.5062i −0.303849 + 0.526281i
\(479\) 11.0640 19.1634i 0.505526 0.875597i −0.494453 0.869204i \(-0.664632\pi\)
0.999980 0.00639300i \(-0.00203497\pi\)
\(480\) 0.356896 0.0162900
\(481\) 0 0
\(482\) 10.4789 0.477301
\(483\) 17.1957 29.7838i 0.782430 1.35521i
\(484\) 5.08426 8.80620i 0.231103 0.400282i
\(485\) 0.349896 + 0.606037i 0.0158879 + 0.0275187i
\(486\) −1.00000 −0.0453609
\(487\) 0.0631549 + 0.109387i 0.00286182 + 0.00495682i 0.867453 0.497520i \(-0.165756\pi\)
−0.864591 + 0.502476i \(0.832422\pi\)
\(488\) −1.55496 2.69327i −0.0703896 0.121918i
\(489\) 0.317667 0.0143654
\(490\) −1.67629 2.90342i −0.0757272 0.131163i
\(491\) −6.97166 + 12.0753i −0.314626 + 0.544949i −0.979358 0.202133i \(-0.935213\pi\)
0.664732 + 0.747082i \(0.268546\pi\)
\(492\) −3.80194 + 6.58515i −0.171405 + 0.296881i
\(493\) −17.8646 −0.804581
\(494\) 0 0
\(495\) −0.325437 −0.0146273
\(496\) −5.39493 + 9.34429i −0.242239 + 0.419571i
\(497\) −23.2446 + 40.2608i −1.04266 + 1.80594i
\(498\) 3.24967 + 5.62859i 0.145621 + 0.252223i
\(499\) 28.3913 1.27097 0.635485 0.772113i \(-0.280800\pi\)
0.635485 + 0.772113i \(0.280800\pi\)
\(500\) −1.76175 3.05144i −0.0787878 0.136465i
\(501\) 6.18060 + 10.7051i 0.276129 + 0.478269i
\(502\) −3.48725 −0.155644
\(503\) −6.28382 10.8839i −0.280181 0.485289i 0.691248 0.722618i \(-0.257061\pi\)
−0.971429 + 0.237329i \(0.923728\pi\)
\(504\) −2.02446 + 3.50647i −0.0901766 + 0.156190i
\(505\) 1.24602 2.15817i 0.0554472 0.0960373i
\(506\) −7.74525 −0.344318
\(507\) 0 0
\(508\) 9.22282 0.409196
\(509\) −2.18837 + 3.79037i −0.0969980 + 0.168005i −0.910441 0.413640i \(-0.864257\pi\)
0.813443 + 0.581645i \(0.197591\pi\)
\(510\) 0.374354 0.648401i 0.0165767 0.0287117i
\(511\) −1.07942 1.86960i −0.0477506 0.0827064i
\(512\) −1.00000 −0.0441942
\(513\) −2.49396 4.31966i −0.110111 0.190718i
\(514\) 3.26875 + 5.66164i 0.144178 + 0.249724i
\(515\) −1.76617 −0.0778266
\(516\) 3.13706 + 5.43355i 0.138102 + 0.239199i
\(517\) 0.811626 1.40578i 0.0356953 0.0618261i
\(518\) −1.24698 + 2.15983i −0.0547891 + 0.0948976i
\(519\) −17.0640 −0.749026
\(520\) 0 0
\(521\) −23.2707 −1.01951 −0.509753 0.860321i \(-0.670263\pi\)
−0.509753 + 0.860321i \(0.670263\pi\)
\(522\) 4.25786 7.37484i 0.186362 0.322788i
\(523\) −18.9976 + 32.9048i −0.830707 + 1.43883i 0.0667707 + 0.997768i \(0.478730\pi\)
−0.897478 + 0.441059i \(0.854603\pi\)
\(524\) 7.27628 + 12.6029i 0.317866 + 0.550560i
\(525\) 19.7289 0.861038
\(526\) 4.00969 + 6.94498i 0.174831 + 0.302816i
\(527\) 11.3177 + 19.6028i 0.493005 + 0.853910i
\(528\) 0.911854 0.0396834
\(529\) −24.5737 42.5628i −1.06842 1.85056i
\(530\) −1.85786 + 3.21790i −0.0807001 + 0.139777i
\(531\) −3.02446 + 5.23852i −0.131250 + 0.227332i
\(532\) −20.1957 −0.875593
\(533\) 0 0
\(534\) −6.49396 −0.281021
\(535\) −0.761750 + 1.31939i −0.0329333 + 0.0570422i
\(536\) −6.78986 + 11.7604i −0.293277 + 0.507971i
\(537\) 12.4840 + 21.6230i 0.538726 + 0.933100i
\(538\) 27.6732 1.19308
\(539\) −4.28286 7.41812i −0.184476 0.319521i
\(540\) 0.178448 + 0.309081i 0.00767918 + 0.0133007i
\(541\) 3.16421 0.136040 0.0680200 0.997684i \(-0.478332\pi\)
0.0680200 + 0.997684i \(0.478332\pi\)
\(542\) −7.36443 12.7556i −0.316329 0.547898i
\(543\) −2.63102 + 4.55706i −0.112908 + 0.195562i
\(544\) −1.04892 + 1.81678i −0.0449720 + 0.0778937i
\(545\) −2.21983 −0.0950872
\(546\) 0 0
\(547\) 7.56033 0.323257 0.161628 0.986852i \(-0.448325\pi\)
0.161628 + 0.986852i \(0.448325\pi\)
\(548\) −7.70171 + 13.3398i −0.329001 + 0.569846i
\(549\) 1.55496 2.69327i 0.0663640 0.114946i
\(550\) −2.22156 3.84786i −0.0947277 0.164073i
\(551\) 42.4758 1.80953
\(552\) 4.24698 + 7.35598i 0.180763 + 0.313091i
\(553\) −23.7005 41.0505i −1.00785 1.74564i
\(554\) −3.26205 −0.138591
\(555\) 0.109916 + 0.190381i 0.00466569 + 0.00808120i
\(556\) −1.35690 + 2.35021i −0.0575452 + 0.0996712i
\(557\) 0.207751 0.359835i 0.00880269 0.0152467i −0.861591 0.507604i \(-0.830531\pi\)
0.870393 + 0.492357i \(0.163865\pi\)
\(558\) −10.7899 −0.456771
\(559\) 0 0
\(560\) 1.44504 0.0610642
\(561\) 0.956459 1.65664i 0.0403818 0.0699432i
\(562\) −3.86294 + 6.69080i −0.162948 + 0.282234i
\(563\) 14.5233 + 25.1550i 0.612083 + 1.06016i 0.990889 + 0.134682i \(0.0430013\pi\)
−0.378806 + 0.925476i \(0.623665\pi\)
\(564\) −1.78017 −0.0749586
\(565\) 2.31767 + 4.01432i 0.0975050 + 0.168884i
\(566\) −9.89008 17.1301i −0.415711 0.720033i
\(567\) −4.04892 −0.170039
\(568\) −5.74094 9.94360i −0.240884 0.417224i
\(569\) −19.8431 + 34.3692i −0.831865 + 1.44083i 0.0646918 + 0.997905i \(0.479394\pi\)
−0.896557 + 0.442928i \(0.853940\pi\)
\(570\) −0.890084 + 1.54167i −0.0372815 + 0.0645735i
\(571\) −7.09651 −0.296980 −0.148490 0.988914i \(-0.547441\pi\)
−0.148490 + 0.988914i \(0.547441\pi\)
\(572\) 0 0
\(573\) 10.5375 0.440210
\(574\) −15.3937 + 26.6627i −0.642522 + 1.11288i
\(575\) 20.6939 35.8430i 0.862997 1.49475i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −8.78687 −0.365802 −0.182901 0.983131i \(-0.558549\pi\)
−0.182901 + 0.983131i \(0.558549\pi\)
\(578\) −6.29954 10.9111i −0.262027 0.453843i
\(579\) 1.71379 + 2.96837i 0.0712228 + 0.123361i
\(580\) −3.03923 −0.126197
\(581\) 13.1576 + 22.7897i 0.545871 + 0.945476i
\(582\) 0.980386 1.69808i 0.0406383 0.0703876i
\(583\) −4.74674 + 8.22160i −0.196590 + 0.340504i
\(584\) 0.533188 0.0220635
\(585\) 0 0
\(586\) −12.9119 −0.533384
\(587\) 18.3533 31.7889i 0.757522 1.31207i −0.186589 0.982438i \(-0.559743\pi\)
0.944111 0.329629i \(-0.106923\pi\)
\(588\) −4.69687 + 8.13521i −0.193695 + 0.335490i
\(589\) −26.9095 46.6086i −1.10879 1.92047i
\(590\) 2.15883 0.0888778
\(591\) 1.88740 + 3.26906i 0.0776371 + 0.134471i
\(592\) −0.307979 0.533434i −0.0126578 0.0219240i
\(593\) −10.8310 −0.444776 −0.222388 0.974958i \(-0.571385\pi\)
−0.222388 + 0.974958i \(0.571385\pi\)
\(594\) 0.455927 + 0.789689i 0.0187069 + 0.0324013i
\(595\) 1.51573 2.62532i 0.0621389 0.107628i
\(596\) −7.36778 + 12.7614i −0.301796 + 0.522726i
\(597\) 17.9541 0.734811
\(598\) 0 0
\(599\) 23.5254 0.961223 0.480611 0.876934i \(-0.340415\pi\)
0.480611 + 0.876934i \(0.340415\pi\)
\(600\) −2.43631 + 4.21982i −0.0994620 + 0.172273i
\(601\) −13.9107 + 24.0940i −0.567428 + 0.982813i 0.429392 + 0.903118i \(0.358728\pi\)
−0.996819 + 0.0796950i \(0.974605\pi\)
\(602\) 12.7017 + 22.0000i 0.517683 + 0.896653i
\(603\) −13.5797 −0.553009
\(604\) −7.91066 13.7017i −0.321880 0.557513i
\(605\) −1.81455 3.14290i −0.0737720 0.127777i
\(606\) −6.98254 −0.283646
\(607\) −0.0486218 0.0842155i −0.00197350 0.00341820i 0.865037 0.501708i \(-0.167295\pi\)
−0.867010 + 0.498290i \(0.833962\pi\)
\(608\) 2.49396 4.31966i 0.101143 0.175186i
\(609\) 17.2397 29.8601i 0.698590 1.20999i
\(610\) −1.10992 −0.0449392
\(611\) 0 0
\(612\) −2.09783 −0.0847999
\(613\) −4.03252 + 6.98454i −0.162872 + 0.282103i −0.935898 0.352272i \(-0.885409\pi\)
0.773025 + 0.634375i \(0.218742\pi\)
\(614\) −9.98254 + 17.2903i −0.402863 + 0.697778i
\(615\) 1.35690 + 2.35021i 0.0547153 + 0.0947697i
\(616\) 3.69202 0.148756
\(617\) 9.60925 + 16.6437i 0.386854 + 0.670051i 0.992025 0.126045i \(-0.0402284\pi\)
−0.605171 + 0.796096i \(0.706895\pi\)
\(618\) 2.47434 + 4.28569i 0.0995327 + 0.172396i
\(619\) 12.3827 0.497703 0.248852 0.968542i \(-0.419947\pi\)
0.248852 + 0.968542i \(0.419947\pi\)
\(620\) 1.92543 + 3.33494i 0.0773270 + 0.133934i
\(621\) −4.24698 + 7.35598i −0.170425 + 0.295185i
\(622\) 6.74094 11.6756i 0.270287 0.468151i
\(623\) −26.2935 −1.05343
\(624\) 0 0
\(625\) 23.1056 0.924224
\(626\) 6.46226 11.1930i 0.258284 0.447361i
\(627\) −2.27413 + 3.93890i −0.0908199 + 0.157305i
\(628\) 2.13706 + 3.70150i 0.0852781 + 0.147706i
\(629\) −1.29218 −0.0515224
\(630\) 0.722521 + 1.25144i 0.0287859 + 0.0498587i
\(631\) 2.37167 + 4.10785i 0.0944145 + 0.163531i 0.909364 0.416001i \(-0.136569\pi\)
−0.814950 + 0.579532i \(0.803235\pi\)
\(632\) 11.7071 0.465683
\(633\) 6.26875 + 10.8578i 0.249160 + 0.431559i
\(634\) 5.93631 10.2820i 0.235761 0.408350i
\(635\) 1.64579 2.85060i 0.0653113 0.113122i
\(636\) 10.4112 0.412831
\(637\) 0 0
\(638\) −7.76510 −0.307423
\(639\) 5.74094 9.94360i 0.227108 0.393363i
\(640\) −0.178448 + 0.309081i −0.00705377 + 0.0122175i
\(641\) 8.22282 + 14.2423i 0.324782 + 0.562538i 0.981468 0.191625i \(-0.0613758\pi\)
−0.656686 + 0.754164i \(0.728042\pi\)
\(642\) 4.26875 0.168474
\(643\) −0.872625 1.51143i −0.0344130 0.0596050i 0.848306 0.529506i \(-0.177623\pi\)
−0.882719 + 0.469901i \(0.844289\pi\)
\(644\) 17.1957 + 29.7838i 0.677604 + 1.17365i
\(645\) 2.23921 0.0881688
\(646\) −5.23191 9.06194i −0.205847 0.356537i
\(647\) −14.3817 + 24.9097i −0.565401 + 0.979303i 0.431611 + 0.902060i \(0.357945\pi\)
−0.997012 + 0.0772436i \(0.975388\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 5.51573 0.216511
\(650\) 0 0
\(651\) −43.6872 −1.71224
\(652\) −0.158834 + 0.275108i −0.00622040 + 0.0107741i
\(653\) 8.08306 14.0003i 0.316315 0.547873i −0.663401 0.748264i \(-0.730888\pi\)
0.979716 + 0.200391i \(0.0642211\pi\)
\(654\) 3.10992 + 5.38653i 0.121607 + 0.210630i
\(655\) 5.19375 0.202937
\(656\) −3.80194 6.58515i −0.148441 0.257107i
\(657\) 0.266594 + 0.461754i 0.0104008 + 0.0180147i
\(658\) −7.20775 −0.280987
\(659\) 8.17792 + 14.1646i 0.318566 + 0.551773i 0.980189 0.198064i \(-0.0634653\pi\)
−0.661623 + 0.749837i \(0.730132\pi\)
\(660\) 0.162718 0.281837i 0.00633381 0.0109705i
\(661\) 16.5579 28.6792i 0.644029 1.11549i −0.340495 0.940246i \(-0.610595\pi\)
0.984525 0.175245i \(-0.0560719\pi\)
\(662\) 10.2392 0.397958
\(663\) 0 0
\(664\) −6.49934 −0.252223
\(665\) −3.60388 + 6.24210i −0.139752 + 0.242058i
\(666\) 0.307979 0.533434i 0.0119339 0.0206702i
\(667\) −36.1661 62.6416i −1.40036 2.42549i
\(668\) −12.3612 −0.478269
\(669\) 2.71379 + 4.70043i 0.104921 + 0.181729i
\(670\) 2.42327 + 4.19723i 0.0936191 + 0.162153i
\(671\) −2.83579 −0.109474
\(672\) −2.02446 3.50647i −0.0780952 0.135265i
\(673\) 17.5770 30.4443i 0.677544 1.17354i −0.298174 0.954512i \(-0.596377\pi\)
0.975718 0.219030i \(-0.0702892\pi\)
\(674\) 0.724677 1.25518i 0.0279135 0.0483476i
\(675\) −4.87263 −0.187547
\(676\) 0 0
\(677\) 23.7855 0.914153 0.457076 0.889427i \(-0.348897\pi\)
0.457076 + 0.889427i \(0.348897\pi\)
\(678\) 6.49396 11.2479i 0.249399 0.431972i
\(679\) 3.96950 6.87538i 0.152335 0.263853i
\(680\) 0.374354 + 0.648401i 0.0143558 + 0.0248650i
\(681\) −16.5767 −0.635222
\(682\) 4.91939 + 8.52063i 0.188373 + 0.326272i
\(683\) −1.49612 2.59135i −0.0572473 0.0991552i 0.835982 0.548758i \(-0.184899\pi\)
−0.893229 + 0.449602i \(0.851566\pi\)
\(684\) 4.98792 0.190718
\(685\) 2.74871 + 4.76090i 0.105023 + 0.181905i
\(686\) −4.84601 + 8.39354i −0.185022 + 0.320467i
\(687\) −11.9390 + 20.6790i −0.455501 + 0.788951i
\(688\) −6.27413 −0.239199
\(689\) 0 0
\(690\) 3.03146 0.115406
\(691\) −5.81163 + 10.0660i −0.221085 + 0.382930i −0.955138 0.296162i \(-0.904293\pi\)
0.734053 + 0.679092i \(0.237626\pi\)
\(692\) 8.53199 14.7778i 0.324338 0.561769i
\(693\) 1.84601 + 3.19738i 0.0701241 + 0.121459i
\(694\) −6.84117 −0.259687
\(695\) 0.484271 + 0.838781i 0.0183694 + 0.0318168i
\(696\) 4.25786 + 7.37484i 0.161394 + 0.279543i
\(697\) −15.9517 −0.604213
\(698\) 17.1685 + 29.7368i 0.649838 + 1.12555i
\(699\) −6.99761 + 12.1202i −0.264674 + 0.458428i
\(700\) −9.86443 + 17.0857i −0.372840 + 0.645778i
\(701\) −33.8431 −1.27824 −0.639118 0.769109i \(-0.720700\pi\)
−0.639118 + 0.769109i \(0.720700\pi\)
\(702\) 0 0
\(703\) 3.07234 0.115876
\(704\) −0.455927 + 0.789689i −0.0171834 + 0.0297625i
\(705\) −0.317667 + 0.550216i −0.0119640 + 0.0207223i
\(706\) −13.0248 22.5595i −0.490193 0.849039i
\(707\) −28.2717 −1.06327
\(708\) −3.02446 5.23852i −0.113666 0.196875i
\(709\) 13.0954 + 22.6820i 0.491810 + 0.851839i 0.999956 0.00943173i \(-0.00300226\pi\)
−0.508146 + 0.861271i \(0.669669\pi\)
\(710\) −4.09783 −0.153789
\(711\) 5.85354 + 10.1386i 0.219525 + 0.380229i
\(712\) 3.24698 5.62393i 0.121686 0.210766i
\(713\) −45.8243 + 79.3700i −1.71613 + 2.97243i
\(714\) −8.49396 −0.317878
\(715\) 0 0
\(716\) −24.9681 −0.933100
\(717\) 6.64310 11.5062i 0.248091 0.429707i
\(718\) −4.24698 + 7.35598i −0.158496 + 0.274523i
\(719\) 10.8672 + 18.8226i 0.405280 + 0.701966i 0.994354 0.106114i \(-0.0338407\pi\)
−0.589074 + 0.808079i \(0.700507\pi\)
\(720\) −0.356896 −0.0133007
\(721\) 10.0184 + 17.3524i 0.373105 + 0.646237i
\(722\) 2.93967 + 5.09165i 0.109403 + 0.189492i
\(723\) −10.4789 −0.389714
\(724\) −2.63102 4.55706i −0.0977812 0.169362i
\(725\) 20.7470 35.9348i 0.770523 1.33459i
\(726\) −5.08426 + 8.80620i −0.188695 + 0.326829i
\(727\) −2.01400 −0.0746951 −0.0373476 0.999302i \(-0.511891\pi\)
−0.0373476 + 0.999302i \(0.511891\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.0951463 0.164798i 0.00352152 0.00609945i
\(731\) −6.58104 + 11.3987i −0.243409 + 0.421596i
\(732\) 1.55496 + 2.69327i 0.0574729 + 0.0995460i
\(733\) 13.5013 0.498680 0.249340 0.968416i \(-0.419786\pi\)
0.249340 + 0.968416i \(0.419786\pi\)
\(734\) 13.7262 + 23.7744i 0.506642 + 0.877530i
\(735\) 1.67629 + 2.90342i 0.0618310 + 0.107094i
\(736\) −8.49396 −0.313091
\(737\) 6.19136 + 10.7237i 0.228062 + 0.395014i
\(738\) 3.80194 6.58515i 0.139951 0.242403i
\(739\) 8.29590 14.3689i 0.305170 0.528569i −0.672130 0.740434i \(-0.734620\pi\)
0.977299 + 0.211864i \(0.0679535\pi\)
\(740\) −0.219833 −0.00808120
\(741\) 0 0
\(742\) 42.1540 1.54752
\(743\) 9.92394 17.1888i 0.364074 0.630594i −0.624553 0.780982i \(-0.714719\pi\)
0.988627 + 0.150388i \(0.0480522\pi\)
\(744\) 5.39493 9.34429i 0.197788 0.342578i
\(745\) 2.62953 + 4.55448i 0.0963385 + 0.166863i
\(746\) −26.6219 −0.974698
\(747\) −3.24967 5.62859i −0.118899 0.205939i
\(748\) 0.956459 + 1.65664i 0.0349716 + 0.0605726i
\(749\) 17.2838 0.631537
\(750\) 1.76175 + 3.05144i 0.0643300 + 0.111423i
\(751\) −13.9673 + 24.1922i −0.509676 + 0.882784i 0.490262 + 0.871575i \(0.336901\pi\)
−0.999937 + 0.0112087i \(0.996432\pi\)
\(752\) 0.890084 1.54167i 0.0324580 0.0562189i
\(753\) 3.48725 0.127083
\(754\) 0 0
\(755\) −5.64656 −0.205499
\(756\) 2.02446 3.50647i 0.0736288 0.127529i
\(757\) 0.274127 0.474801i 0.00996330 0.0172569i −0.861001 0.508604i \(-0.830162\pi\)
0.870964 + 0.491347i \(0.163495\pi\)
\(758\) −5.82371 10.0870i −0.211527 0.366375i
\(759\) 7.74525 0.281135
\(760\) −0.890084 1.54167i −0.0322867 0.0559223i
\(761\) −0.987918 1.71112i −0.0358120 0.0620282i 0.847564 0.530693i \(-0.178068\pi\)
−0.883376 + 0.468665i \(0.844735\pi\)
\(762\) −9.22282 −0.334107
\(763\) 12.5918 + 21.8096i 0.455854 + 0.789562i
\(764\) −5.26875 + 9.12574i −0.190617 + 0.330158i
\(765\) −0.374354 + 0.648401i −0.0135348 + 0.0234430i
\(766\) 10.5181 0.380035
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −14.3056 + 24.7780i −0.515873 + 0.893518i 0.483958 + 0.875091i \(0.339199\pi\)
−0.999830 + 0.0184261i \(0.994134\pi\)
\(770\) 0.658834 1.14113i 0.0237427 0.0411236i
\(771\) −3.26875 5.66164i −0.117721 0.203899i
\(772\) −3.42758 −0.123361
\(773\) −26.2540 45.4732i −0.944290 1.63556i −0.757167 0.653222i \(-0.773417\pi\)
−0.187123 0.982336i \(-0.559916\pi\)
\(774\) −3.13706 5.43355i −0.112759 0.195305i
\(775\) −52.5749 −1.88855
\(776\) 0.980386 + 1.69808i 0.0351938 + 0.0609574i
\(777\) 1.24698 2.15983i 0.0447351 0.0774835i
\(778\) −4.62983 + 8.01909i −0.165987 + 0.287498i
\(779\) 37.9275 1.35889
\(780\) 0 0
\(781\) −10.4698 −0.374639
\(782\) −8.90946 + 15.4316i −0.318602 + 0.551834i
\(783\) −4.25786 + 7.37484i −0.152164 + 0.263555i
\(784\) −4.69687 8.13521i −0.167745 0.290543i
\(785\) 1.52542 0.0544445
\(786\) −7.27628 12.6029i −0.259536 0.449530i
\(787\) −11.8213 20.4751i −0.421384 0.729859i 0.574691 0.818371i \(-0.305122\pi\)
−0.996075 + 0.0885115i \(0.971789\pi\)
\(788\) −3.77479 −0.134471
\(789\) −4.00969 6.94498i −0.142749 0.247248i
\(790\) 2.08911 3.61844i 0.0743270 0.128738i
\(791\) 26.2935 45.5417i 0.934889 1.61928i
\(792\) −0.911854 −0.0324013
\(793\) 0 0
\(794\) 14.5133 0.515059
\(795\) 1.85786 3.21790i 0.0658913 0.114127i
\(796\) −8.97703 + 15.5487i −0.318183 + 0.551108i
\(797\) −20.8279 36.0750i −0.737762 1.27784i −0.953501 0.301390i \(-0.902549\pi\)
0.215739 0.976451i \(-0.430784\pi\)
\(798\) 20.1957 0.714919
\(799\) −1.86725 3.23417i −0.0660585 0.114417i
\(800\) −2.43631 4.21982i −0.0861367 0.149193i
\(801\) 6.49396 0.229453
\(802\) 19.4209 + 33.6379i 0.685775 + 1.18780i
\(803\) 0.243095 0.421052i 0.00857863 0.0148586i
\(804\) 6.78986 11.7604i 0.239460 0.414756i
\(805\) 12.2741 0.432606
\(806\) 0 0
\(807\) −27.6732 −0.974144
\(808\) 3.49127 6.04706i 0.122822 0.212735i
\(809\) 22.1196 38.3123i 0.777684 1.34699i −0.155590 0.987822i \(-0.549728\pi\)
0.933274 0.359166i \(-0.116939\pi\)
\(810\) −0.178448 0.309081i −0.00627002 0.0108600i
\(811\) −52.3913 −1.83971 −0.919854 0.392260i \(-0.871693\pi\)
−0.919854 + 0.392260i \(0.871693\pi\)
\(812\) 17.2397 + 29.8601i 0.604996 + 1.04788i
\(813\) 7.36443 + 12.7556i 0.258282 + 0.447357i
\(814\) −0.561663 −0.0196863
\(815\) 0.0566871 + 0.0981849i 0.00198566 + 0.00343927i
\(816\) 1.04892 1.81678i 0.0367195 0.0636000i
\(817\) 15.6474 27.1021i 0.547434 0.948183i
\(818\) 33.9221 1.18606
\(819\) 0 0
\(820\) −2.71379 −0.0947697
\(821\) −12.8138 + 22.1941i −0.447204 + 0.774580i −0.998203 0.0599259i \(-0.980914\pi\)
0.550999 + 0.834506i \(0.314247\pi\)
\(822\) 7.70171 13.3398i 0.268628 0.465277i
\(823\) 20.1277 + 34.8621i 0.701606 + 1.21522i 0.967902 + 0.251327i \(0.0808669\pi\)
−0.266296 + 0.963891i \(0.585800\pi\)
\(824\) −4.94869 −0.172396
\(825\) 2.22156 + 3.84786i 0.0773448 + 0.133965i
\(826\) −12.2458 21.2103i −0.426085 0.738001i
\(827\) 18.0519 0.627726 0.313863 0.949468i \(-0.398377\pi\)
0.313863 + 0.949468i \(0.398377\pi\)
\(828\) −4.24698 7.35598i −0.147593 0.255638i
\(829\) −11.3327 + 19.6289i −0.393602 + 0.681739i −0.992922 0.118771i \(-0.962105\pi\)
0.599320 + 0.800510i \(0.295438\pi\)
\(830\) −1.15979 + 2.00882i −0.0402570 + 0.0697272i
\(831\) 3.26205 0.113159
\(832\) 0 0
\(833\) −19.7065 −0.682790
\(834\) 1.35690 2.35021i 0.0469855 0.0813812i
\(835\) −2.20583 + 3.82061i −0.0763360 + 0.132218i
\(836\) −2.27413 3.93890i −0.0786523 0.136230i
\(837\) 10.7899 0.372952
\(838\) 0.477697 + 0.827396i 0.0165018 + 0.0285819i
\(839\) 11.0411 + 19.1238i 0.381183 + 0.660228i 0.991232 0.132136i \(-0.0421835\pi\)
−0.610049 + 0.792364i \(0.708850\pi\)
\(840\) −1.44504 −0.0498587
\(841\) −21.7588 37.6874i −0.750304 1.29957i
\(842\) −2.84117 + 4.92104i −0.0979131 + 0.169590i
\(843\) 3.86294 6.69080i 0.133047 0.230443i
\(844\) −12.5375 −0.431559
\(845\) 0 0
\(846\) 1.78017 0.0612034
\(847\) −20.5858 + 35.6556i −0.707335 + 1.22514i
\(848\) −5.20560 + 9.01636i −0.178761 + 0.309623i
\(849\) 9.89008 + 17.1301i 0.339427 + 0.587904i
\(850\) −10.2220 −0.350610
\(851\) −2.61596 4.53097i −0.0896739 0.155320i
\(852\) 5.74094 + 9.94360i 0.196681 + 0.340662i
\(853\) −28.9831 −0.992364 −0.496182 0.868219i \(-0.665265\pi\)
−0.496182 + 0.868219i \(0.665265\pi\)
\(854\) 6.29590 + 10.9048i 0.215441 + 0.373155i
\(855\) 0.890084 1.54167i 0.0304402 0.0527240i
\(856\) −2.13437 + 3.69685i −0.0729514 + 0.126356i
\(857\) −42.9047 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(858\) 0 0
\(859\) −47.0616 −1.60572 −0.802860 0.596167i \(-0.796690\pi\)
−0.802860 + 0.596167i \(0.796690\pi\)
\(860\) −1.11960 + 1.93921i −0.0381782 + 0.0661266i
\(861\) 15.3937 26.6627i 0.524617 0.908663i
\(862\) −7.42327 12.8575i −0.252838 0.437928i
\(863\) −42.6064 −1.45034 −0.725169 0.688571i \(-0.758238\pi\)
−0.725169 + 0.688571i \(0.758238\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) −3.04503 5.27415i −0.103534 0.179327i
\(866\) 26.1497 0.888604
\(867\) 6.29954 + 10.9111i 0.213944 + 0.370561i
\(868\) 21.8436 37.8343i 0.741421 1.28418i
\(869\) 5.33758 9.24495i 0.181065 0.313614i
\(870\) 3.03923 0.103040
\(871\) 0 0
\(872\) −6.21983 −0.210630
\(873\) −0.980386 + 1.69808i −0.0331810 + 0.0574712i
\(874\) 21.1836 36.6911i 0.716546 1.24109i
\(875\) 7.13318 + 12.3550i 0.241145 + 0.417676i
\(876\) −0.533188 −0.0180147
\(877\) −13.7041 23.7362i −0.462755 0.801515i 0.536342 0.844000i \(-0.319806\pi\)
−0.999097 + 0.0424859i \(0.986472\pi\)
\(878\) −11.7751 20.3950i −0.397390 0.688300i
\(879\) 12.9119 0.435506
\(880\) 0.162718 + 0.281837i 0.00548524 + 0.00950071i
\(881\) −12.1588 + 21.0597i −0.409642 + 0.709520i −0.994849 0.101363i \(-0.967680\pi\)
0.585208 + 0.810883i \(0.301013\pi\)
\(882\) 4.69687 8.13521i 0.158152 0.273927i
\(883\) −32.2306 −1.08465 −0.542323 0.840170i \(-0.682455\pi\)
−0.542323 + 0.840170i \(0.682455\pi\)
\(884\) 0 0
\(885\) −2.15883 −0.0725684
\(886\) 10.9717 19.0035i 0.368600 0.638434i
\(887\) 17.5821 30.4531i 0.590349 1.02252i −0.403836 0.914831i \(-0.632323\pi\)
0.994185 0.107684i \(-0.0343433\pi\)
\(888\) 0.307979 + 0.533434i 0.0103351 + 0.0179009i
\(889\) −37.3424 −1.25242
\(890\) −1.15883 2.00716i −0.0388442 0.0672801i
\(891\) −0.455927 0.789689i −0.0152741 0.0264556i
\(892\) −5.42758 −0.181729
\(893\) 4.43967 + 7.68973i 0.148568 + 0.257327i
\(894\) 7.36778 12.7614i 0.246415 0.426804i
\(895\) −4.45550 + 7.71715i −0.148931 + 0.257956i
\(896\) 4.04892 0.135265
\(897\) 0 0
\(898\) −11.4034 −0.380537
\(899\) −45.9417 + 79.5734i −1.53224 + 2.65392i
\(900\) 2.43631 4.21982i 0.0812104 0.140661i
\(901\) 10.9205 + 18.9148i 0.363814 + 0.630144i
\(902\) −6.93362 −0.230864
\(903\) −12.7017 22.0000i −0.422686 0.732114i
\(904\) 6.49396 + 11.2479i 0.215986 + 0.374099i
\(905\) −1.87800 −0.0624269
\(906\) 7.91066 + 13.7017i 0.262814 + 0.455207i
\(907\) 6.56033 11.3628i 0.217832 0.377297i −0.736313 0.676641i \(-0.763435\pi\)
0.954145 + 0.299345i \(0.0967681\pi\)
\(908\) 8.28836 14.3559i 0.275059 0.476416i
\(909\) 6.98254 0.231596
\(910\) 0 0
\(911\) 45.7453 1.51561 0.757804 0.652482i \(-0.226272\pi\)
0.757804 + 0.652482i \(0.226272\pi\)
\(912\) −2.49396 + 4.31966i −0.0825832 + 0.143038i
\(913\) −2.96322 + 5.13245i −0.0980684 + 0.169859i
\(914\) 3.83459 + 6.64171i 0.126837 + 0.219688i
\(915\) 1.10992 0.0366927
\(916\) −11.9390 20.6790i −0.394476 0.683252i
\(917\) −29.4611 51.0281i −0.972890 1.68510i
\(918\) 2.09783 0.0692389
\(919\) −8.99247 15.5754i −0.296634 0.513785i 0.678730 0.734388i \(-0.262531\pi\)
−0.975364 + 0.220603i \(0.929198\pi\)
\(920\) −1.51573 + 2.62532i −0.0499721 + 0.0865543i
\(921\) 9.98254 17.2903i 0.328936 0.569734i
\(922\) 28.5080 0.938860
\(923\) 0 0
\(924\) −3.69202 −0.121459
\(925\) 1.50066 2.59923i 0.0493415 0.0854620i
\(926\) −7.16421 + 12.4088i −0.235431 + 0.407778i
\(927\) −2.47434 4.28569i −0.0812681 0.140761i
\(928\) −8.51573 −0.279543
\(929\) −15.8442 27.4429i −0.519830 0.900371i −0.999734 0.0230508i \(-0.992662\pi\)
0.479905 0.877321i \(-0.340671\pi\)
\(930\) −1.92543 3.33494i −0.0631373 0.109357i
\(931\) 46.8552 1.53562
\(932\) −6.99761 12.1202i −0.229214 0.397011i
\(933\) −6.74094 + 11.6756i −0.220688 + 0.382244i
\(934\) 16.6603 28.8565i 0.545143 0.944215i
\(935\) 0.682713 0.0223271
\(936\) 0 0
\(937\) −53.0484 −1.73302 −0.866509 0.499162i \(-0.833641\pi\)
−0.866509 + 0.499162i \(0.833641\pi\)
\(938\) 27.4916 47.6168i 0.897631 1.55474i
\(939\) −6.46226 + 11.1930i −0.210888 + 0.365269i
\(940\) −0.317667 0.550216i −0.0103612 0.0179461i
\(941\) 21.9433 0.715332 0.357666 0.933850i \(-0.383573\pi\)
0.357666 + 0.933850i \(0.383573\pi\)
\(942\) −2.13706 3.70150i −0.0696293 0.120601i
\(943\) −32.2935 55.9340i −1.05162 1.82146i
\(944\) 6.04892 0.196875
\(945\) −0.722521 1.25144i −0.0235036 0.0407094i
\(946\) −2.86054 + 4.95461i −0.0930043 + 0.161088i
\(947\) −6.11207 + 10.5864i −0.198616 + 0.344012i −0.948080 0.318033i \(-0.896978\pi\)
0.749464 + 0.662045i \(0.230311\pi\)
\(948\) −11.7071 −0.380229
\(949\) 0 0
\(950\) 24.3043 0.788534
\(951\) −5.93631 + 10.2820i −0.192498 + 0.333417i
\(952\) 4.24698 7.35598i 0.137645 0.238409i
\(953\) 1.92931 + 3.34167i 0.0624966 + 0.108247i 0.895581 0.444899i \(-0.146760\pi\)
−0.833084 + 0.553146i \(0.813427\pi\)
\(954\) −10.4112 −0.337075
\(955\) 1.88040 + 3.25694i 0.0608482 + 0.105392i
\(956\) 6.64310 + 11.5062i 0.214853 + 0.372137i
\(957\) 7.76510 0.251010
\(958\) −11.0640 19.1634i −0.357461 0.619141i
\(959\) 31.1836 54.0116i 1.00697 1.74412i
\(960\) 0.178448 0.309081i 0.00575938 0.00997554i
\(961\) 85.4210 2.75552
\(962\) 0 0
\(963\) −4.26875 −0.137559
\(964\) 5.23945 9.07499i 0.168751 0.292286i
\(965\) −0.611645 + 1.05940i −0.0196896 + 0.0341033i
\(966\) −17.1957 29.7838i −0.553262 0.958277i
\(967\) −0.613564 −0.0197309 −0.00986545 0.999951i \(-0.503140\pi\)
−0.00986545 + 0.999951i \(0.503140\pi\)
\(968\) −5.08426 8.80620i −0.163414 0.283042i
\(969\) 5.23191 + 9.06194i 0.168073 + 0.291111i
\(970\) 0.699791 0.0224689
\(971\) 6.48845 + 11.2383i 0.208224 + 0.360655i 0.951155 0.308713i \(-0.0998983\pi\)
−0.742931 + 0.669368i \(0.766565\pi\)
\(972\) −0.500000 + 0.866025i −0.0160375 + 0.0277778i
\(973\) 5.49396 9.51582i 0.176128 0.305063i
\(974\) 0.126310 0.00404722
\(975\) 0 0
\(976\) −3.10992 −0.0995460
\(977\) 18.5308 32.0963i 0.592853 1.02685i −0.400993 0.916081i \(-0.631335\pi\)
0.993846 0.110770i \(-0.0353317\pi\)
\(978\) 0.158834 0.275108i 0.00507894 0.00879698i
\(979\) −2.96077 5.12821i −0.0946267 0.163898i
\(980\) −3.35258 −0.107094
\(981\) −3.10992 5.38653i −0.0992920 0.171979i
\(982\) 6.97166 + 12.0753i 0.222474 + 0.385337i
\(983\) −14.1193 −0.450337 −0.225169 0.974320i \(-0.572293\pi\)
−0.225169 + 0.974320i \(0.572293\pi\)
\(984\) 3.80194 + 6.58515i 0.121201 + 0.209927i
\(985\) −0.673604 + 1.16672i −0.0214628 + 0.0371747i
\(986\) −8.93230 + 15.4712i −0.284462 + 0.492703i
\(987\) 7.20775 0.229425
\(988\) 0 0
\(989\) −53.2922 −1.69459
\(990\) −0.162718 + 0.281837i −0.00517153 + 0.00895736i
\(991\) −14.2696 + 24.7156i −0.453288 + 0.785118i −0.998588 0.0531230i \(-0.983082\pi\)
0.545300 + 0.838241i \(0.316416\pi\)
\(992\) 5.39493 + 9.34429i 0.171289 + 0.296681i
\(993\) −10.2392 −0.324932
\(994\) 23.2446 + 40.2608i 0.737274 + 1.27700i
\(995\) 3.20387 + 5.54926i 0.101569 + 0.175923i
\(996\) 6.49934 0.205939
\(997\) 9.44265 + 16.3551i 0.299052 + 0.517973i 0.975919 0.218132i \(-0.0699964\pi\)
−0.676868 + 0.736105i \(0.736663\pi\)
\(998\) 14.1957 24.5876i 0.449356 0.778308i
\(999\) −0.307979 + 0.533434i −0.00974401 + 0.0168771i
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 1014.2.e.m.529.2 6
13.2 odd 12 1014.2.i.g.361.5 12
13.3 even 3 inner 1014.2.e.m.991.2 6
13.4 even 6 1014.2.a.o.1.2 yes 3
13.5 odd 4 1014.2.i.g.823.2 12
13.6 odd 12 1014.2.b.g.337.5 6
13.7 odd 12 1014.2.b.g.337.2 6
13.8 odd 4 1014.2.i.g.823.5 12
13.9 even 3 1014.2.a.m.1.2 3
13.10 even 6 1014.2.e.k.991.2 6
13.11 odd 12 1014.2.i.g.361.2 12
13.12 even 2 1014.2.e.k.529.2 6
39.17 odd 6 3042.2.a.bd.1.2 3
39.20 even 12 3042.2.b.r.1351.5 6
39.32 even 12 3042.2.b.r.1351.2 6
39.35 odd 6 3042.2.a.be.1.2 3
52.35 odd 6 8112.2.a.ce.1.2 3
52.43 odd 6 8112.2.a.bz.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1014.2.a.m.1.2 3 13.9 even 3
1014.2.a.o.1.2 yes 3 13.4 even 6
1014.2.b.g.337.2 6 13.7 odd 12
1014.2.b.g.337.5 6 13.6 odd 12
1014.2.e.k.529.2 6 13.12 even 2
1014.2.e.k.991.2 6 13.10 even 6
1014.2.e.m.529.2 6 1.1 even 1 trivial
1014.2.e.m.991.2 6 13.3 even 3 inner
1014.2.i.g.361.2 12 13.11 odd 12
1014.2.i.g.361.5 12 13.2 odd 12
1014.2.i.g.823.2 12 13.5 odd 4
1014.2.i.g.823.5 12 13.8 odd 4
3042.2.a.bd.1.2 3 39.17 odd 6
3042.2.a.be.1.2 3 39.35 odd 6
3042.2.b.r.1351.2 6 39.32 even 12
3042.2.b.r.1351.5 6 39.20 even 12
8112.2.a.bz.1.2 3 52.43 odd 6
8112.2.a.ce.1.2 3 52.35 odd 6