Properties

Label 1014.2.i.g.361.2
Level $1014$
Weight $2$
Character 1014.361
Analytic conductor $8.097$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,2,Mod(361,1014)]
 
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, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.361");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.i (of order \(6\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(0.385418 + 0.222521i\) of defining polynomial
Character \(\chi\) \(=\) 1014.361
Dual form 1014.2.i.g.823.2

$q$-expansion

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

Character values

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

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.356896i 0.159609i −0.996811 0.0798043i \(-0.974570\pi\)
0.996811 0.0798043i \(-0.0254296\pi\)
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −3.50647 2.02446i −1.32532 0.765173i −0.340748 0.940155i \(-0.610680\pi\)
−0.984572 + 0.174981i \(0.944013\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.178448 + 0.309081i 0.0564302 + 0.0977400i
\(11\) −0.789689 + 0.455927i −0.238100 + 0.137467i −0.614303 0.789070i \(-0.710563\pi\)
0.376203 + 0.926537i \(0.377229\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 4.04892 1.08212
\(15\) −0.309081 + 0.178448i −0.0798043 + 0.0460751i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.04892 + 1.81678i −0.254400 + 0.440633i −0.964732 0.263233i \(-0.915211\pi\)
0.710333 + 0.703866i \(0.248545\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −4.31966 2.49396i −0.990999 0.572153i −0.0854262 0.996345i \(-0.527225\pi\)
−0.905573 + 0.424191i \(0.860559\pi\)
\(20\) −0.309081 0.178448i −0.0691126 0.0399022i
\(21\) 4.04892i 0.883546i
\(22\) 0.455927 0.789689i 0.0972040 0.168362i
\(23\) 4.24698 + 7.35598i 0.885556 + 1.53383i 0.845075 + 0.534649i \(0.179556\pi\)
0.0404819 + 0.999180i \(0.487111\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 4.87263 0.974525
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −3.50647 + 2.02446i −0.662660 + 0.382587i
\(29\) −4.25786 7.37484i −0.790666 1.36947i −0.925555 0.378612i \(-0.876401\pi\)
0.134890 0.990861i \(-0.456932\pi\)
\(30\) 0.178448 0.309081i 0.0325800 0.0564302i
\(31\) 10.7899i 1.93792i 0.247227 + 0.968958i \(0.420481\pi\)
−0.247227 + 0.968958i \(0.579519\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0.789689 + 0.455927i 0.137467 + 0.0793667i
\(34\) 2.09783i 0.359776i
\(35\) −0.722521 + 1.25144i −0.122128 + 0.211532i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −0.533434 + 0.307979i −0.0876961 + 0.0506314i −0.543207 0.839599i \(-0.682790\pi\)
0.455511 + 0.890230i \(0.349457\pi\)
\(38\) 4.98792 0.809147
\(39\) 0 0
\(40\) 0.356896 0.0564302
\(41\) 6.58515 3.80194i 1.02843 0.593763i 0.111894 0.993720i \(-0.464308\pi\)
0.916534 + 0.399957i \(0.130975\pi\)
\(42\) −2.02446 3.50647i −0.312381 0.541059i
\(43\) −3.13706 + 5.43355i −0.478398 + 0.828609i −0.999693 0.0247671i \(-0.992116\pi\)
0.521296 + 0.853376i \(0.325449\pi\)
\(44\) 0.911854i 0.137467i
\(45\) 0.309081 + 0.178448i 0.0460751 + 0.0266014i
\(46\) −7.35598 4.24698i −1.08458 0.626183i
\(47\) 1.78017i 0.259664i 0.991536 + 0.129832i \(0.0414438\pi\)
−0.991536 + 0.129832i \(0.958556\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 4.69687 + 8.13521i 0.670981 + 1.16217i
\(50\) −4.21982 + 2.43631i −0.596772 + 0.344547i
\(51\) 2.09783 0.293756
\(52\) 0 0
\(53\) 10.4112 1.43009 0.715043 0.699080i \(-0.246407\pi\)
0.715043 + 0.699080i \(0.246407\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0.162718 + 0.281837i 0.0219410 + 0.0380028i
\(56\) 2.02446 3.50647i 0.270530 0.468571i
\(57\) 4.98792i 0.660666i
\(58\) 7.37484 + 4.25786i 0.968364 + 0.559085i
\(59\) 5.23852 + 3.02446i 0.681997 + 0.393751i 0.800607 0.599190i \(-0.204511\pi\)
−0.118610 + 0.992941i \(0.537844\pi\)
\(60\) 0.356896i 0.0460751i
\(61\) 1.55496 2.69327i 0.199092 0.344837i −0.749142 0.662409i \(-0.769534\pi\)
0.948234 + 0.317572i \(0.102867\pi\)
\(62\) −5.39493 9.34429i −0.685157 1.18673i
\(63\) 3.50647 2.02446i 0.441773 0.255058i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −0.911854 −0.112241
\(67\) −11.7604 + 6.78986i −1.43676 + 0.829513i −0.997623 0.0689079i \(-0.978049\pi\)
−0.439136 + 0.898421i \(0.644715\pi\)
\(68\) 1.04892 + 1.81678i 0.127200 + 0.220317i
\(69\) 4.24698 7.35598i 0.511276 0.885556i
\(70\) 1.44504i 0.172716i
\(71\) 9.94360 + 5.74094i 1.18009 + 0.681324i 0.956035 0.293253i \(-0.0947378\pi\)
0.224053 + 0.974577i \(0.428071\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 0.533188i 0.0624049i 0.999513 + 0.0312025i \(0.00993366\pi\)
−0.999513 + 0.0312025i \(0.990066\pi\)
\(74\) 0.307979 0.533434i 0.0358018 0.0620105i
\(75\) −2.43631 4.21982i −0.281321 0.487263i
\(76\) −4.31966 + 2.49396i −0.495499 + 0.286077i
\(77\) 3.69202 0.420745
\(78\) 0 0
\(79\) −11.7071 −1.31715 −0.658575 0.752515i \(-0.728841\pi\)
−0.658575 + 0.752515i \(0.728841\pi\)
\(80\) −0.309081 + 0.178448i −0.0345563 + 0.0199511i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.80194 + 6.58515i −0.419854 + 0.727208i
\(83\) 6.49934i 0.713395i 0.934220 + 0.356697i \(0.116097\pi\)
−0.934220 + 0.356697i \(0.883903\pi\)
\(84\) 3.50647 + 2.02446i 0.382587 + 0.220887i
\(85\) 0.648401 + 0.374354i 0.0703289 + 0.0406044i
\(86\) 6.27413i 0.676556i
\(87\) −4.25786 + 7.37484i −0.456491 + 0.790666i
\(88\) −0.455927 0.789689i −0.0486020 0.0841811i
\(89\) −5.62393 + 3.24698i −0.596136 + 0.344179i −0.767520 0.641025i \(-0.778509\pi\)
0.171384 + 0.985204i \(0.445176\pi\)
\(90\) −0.356896 −0.0376201
\(91\) 0 0
\(92\) 8.49396 0.885556
\(93\) 9.34429 5.39493i 0.968958 0.559428i
\(94\) −0.890084 1.54167i −0.0918051 0.159011i
\(95\) −0.890084 + 1.54167i −0.0913207 + 0.158172i
\(96\) 1.00000i 0.102062i
\(97\) −1.69808 0.980386i −0.172414 0.0995431i 0.411310 0.911496i \(-0.365071\pi\)
−0.583723 + 0.811953i \(0.698405\pi\)
\(98\) −8.13521 4.69687i −0.821780 0.474455i
\(99\) 0.911854i 0.0916448i
\(100\) 2.43631 4.21982i 0.243631 0.421982i
\(101\) 3.49127 + 6.04706i 0.347394 + 0.601705i 0.985786 0.168007i \(-0.0537332\pi\)
−0.638391 + 0.769712i \(0.720400\pi\)
\(102\) −1.81678 + 1.04892i −0.179888 + 0.103858i
\(103\) −4.94869 −0.487609 −0.243804 0.969824i \(-0.578396\pi\)
−0.243804 + 0.969824i \(0.578396\pi\)
\(104\) 0 0
\(105\) 1.44504 0.141022
\(106\) −9.01636 + 5.20560i −0.875746 + 0.505612i
\(107\) 2.13437 + 3.69685i 0.206338 + 0.357388i 0.950558 0.310547i \(-0.100512\pi\)
−0.744220 + 0.667934i \(0.767179\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 6.21983i 0.595752i 0.954605 + 0.297876i \(0.0962782\pi\)
−0.954605 + 0.297876i \(0.903722\pi\)
\(110\) −0.281837 0.162718i −0.0268721 0.0155146i
\(111\) 0.533434 + 0.307979i 0.0506314 + 0.0292320i
\(112\) 4.04892i 0.382587i
\(113\) −6.49396 + 11.2479i −0.610900 + 1.05811i 0.380189 + 0.924909i \(0.375859\pi\)
−0.991089 + 0.133201i \(0.957474\pi\)
\(114\) −2.49396 4.31966i −0.233581 0.404574i
\(115\) 2.62532 1.51573i 0.244812 0.141343i
\(116\) −8.51573 −0.790666
\(117\) 0 0
\(118\) −6.04892 −0.556848
\(119\) 7.35598 4.24698i 0.674322 0.389320i
\(120\) −0.178448 0.309081i −0.0162900 0.0282151i
\(121\) −5.08426 + 8.80620i −0.462206 + 0.800564i
\(122\) 3.10992i 0.281559i
\(123\) −6.58515 3.80194i −0.593763 0.342809i
\(124\) 9.34429 + 5.39493i 0.839142 + 0.484479i
\(125\) 3.52350i 0.315151i
\(126\) −2.02446 + 3.50647i −0.180353 + 0.312381i
\(127\) 4.61141 + 7.98719i 0.409196 + 0.708749i 0.994800 0.101849i \(-0.0324758\pi\)
−0.585604 + 0.810598i \(0.699142\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 6.27413 0.552406
\(130\) 0 0
\(131\) −14.5526 −1.27146 −0.635732 0.771910i \(-0.719302\pi\)
−0.635732 + 0.771910i \(0.719302\pi\)
\(132\) 0.789689 0.455927i 0.0687336 0.0396834i
\(133\) 10.0978 + 17.4900i 0.875593 + 1.51657i
\(134\) 6.78986 11.7604i 0.586554 1.01594i
\(135\) 0.356896i 0.0307167i
\(136\) −1.81678 1.04892i −0.155787 0.0899439i
\(137\) 13.3398 + 7.70171i 1.13969 + 0.658002i 0.946354 0.323131i \(-0.104735\pi\)
0.193338 + 0.981132i \(0.438069\pi\)
\(138\) 8.49396i 0.723054i
\(139\) −1.35690 + 2.35021i −0.115090 + 0.199342i −0.917816 0.397006i \(-0.870049\pi\)
0.802725 + 0.596349i \(0.203382\pi\)
\(140\) 0.722521 + 1.25144i 0.0610642 + 0.105766i
\(141\) 1.54167 0.890084i 0.129832 0.0749586i
\(142\) −11.4819 −0.963538
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −2.63205 + 1.51961i −0.218580 + 0.126197i
\(146\) −0.266594 0.461754i −0.0220635 0.0382151i
\(147\) 4.69687 8.13521i 0.387391 0.670981i
\(148\) 0.615957i 0.0506314i
\(149\) −12.7614 7.36778i −1.04545 0.603592i −0.124079 0.992272i \(-0.539598\pi\)
−0.921373 + 0.388680i \(0.872931\pi\)
\(150\) 4.21982 + 2.43631i 0.344547 + 0.198924i
\(151\) 15.8213i 1.28752i −0.765227 0.643760i \(-0.777373\pi\)
0.765227 0.643760i \(-0.222627\pi\)
\(152\) 2.49396 4.31966i 0.202287 0.350371i
\(153\) −1.04892 1.81678i −0.0847999 0.146878i
\(154\) −3.19738 + 1.84601i −0.257653 + 0.148756i
\(155\) 3.85086 0.309308
\(156\) 0 0
\(157\) −4.27413 −0.341112 −0.170556 0.985348i \(-0.554556\pi\)
−0.170556 + 0.985348i \(0.554556\pi\)
\(158\) 10.1386 5.85354i 0.806586 0.465683i
\(159\) −5.20560 9.01636i −0.412831 0.715043i
\(160\) 0.178448 0.309081i 0.0141075 0.0244350i
\(161\) 34.3913i 2.71042i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 0.275108 + 0.158834i 0.0215481 + 0.0124408i 0.510735 0.859738i \(-0.329373\pi\)
−0.489187 + 0.872179i \(0.662707\pi\)
\(164\) 7.60388i 0.593763i
\(165\) 0.162718 0.281837i 0.0126676 0.0219410i
\(166\) −3.24967 5.62859i −0.252223 0.436863i
\(167\) 10.7051 6.18060i 0.828387 0.478269i −0.0249130 0.999690i \(-0.507931\pi\)
0.853300 + 0.521420i \(0.174598\pi\)
\(168\) −4.04892 −0.312381
\(169\) 0 0
\(170\) −0.748709 −0.0574233
\(171\) 4.31966 2.49396i 0.330333 0.190718i
\(172\) 3.13706 + 5.43355i 0.239199 + 0.414305i
\(173\) −8.53199 + 14.7778i −0.648675 + 1.12354i 0.334764 + 0.942302i \(0.391343\pi\)
−0.983440 + 0.181237i \(0.941990\pi\)
\(174\) 8.51573i 0.645576i
\(175\) −17.0857 9.86443i −1.29156 0.745681i
\(176\) 0.789689 + 0.455927i 0.0595250 + 0.0343668i
\(177\) 6.04892i 0.454664i
\(178\) 3.24698 5.62393i 0.243371 0.421532i
\(179\) −12.4840 21.6230i −0.933100 1.61618i −0.777987 0.628281i \(-0.783759\pi\)
−0.155114 0.987897i \(-0.549574\pi\)
\(180\) 0.309081 0.178448i 0.0230375 0.0133007i
\(181\) −5.26205 −0.391125 −0.195562 0.980691i \(-0.562653\pi\)
−0.195562 + 0.980691i \(0.562653\pi\)
\(182\) 0 0
\(183\) −3.10992 −0.229892
\(184\) −7.35598 + 4.24698i −0.542290 + 0.313091i
\(185\) 0.109916 + 0.190381i 0.00808120 + 0.0139971i
\(186\) −5.39493 + 9.34429i −0.395575 + 0.685157i
\(187\) 1.91292i 0.139886i
\(188\) 1.54167 + 0.890084i 0.112438 + 0.0649160i
\(189\) −3.50647 2.02446i −0.255058 0.147258i
\(190\) 1.78017i 0.129147i
\(191\) −5.26875 + 9.12574i −0.381233 + 0.660316i −0.991239 0.132082i \(-0.957834\pi\)
0.610005 + 0.792397i \(0.291167\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 2.96837 1.71379i 0.213668 0.123361i −0.389347 0.921091i \(-0.627299\pi\)
0.603015 + 0.797730i \(0.293966\pi\)
\(194\) 1.96077 0.140775
\(195\) 0 0
\(196\) 9.39373 0.670981
\(197\) −3.26906 + 1.88740i −0.232911 + 0.134471i −0.611914 0.790924i \(-0.709600\pi\)
0.379003 + 0.925395i \(0.376267\pi\)
\(198\) 0.455927 + 0.789689i 0.0324013 + 0.0561207i
\(199\) 8.97703 15.5487i 0.636365 1.10222i −0.349859 0.936802i \(-0.613771\pi\)
0.986224 0.165414i \(-0.0528961\pi\)
\(200\) 4.87263i 0.344547i
\(201\) 11.7604 + 6.78986i 0.829513 + 0.478920i
\(202\) −6.04706 3.49127i −0.425470 0.245645i
\(203\) 34.4795i 2.41999i
\(204\) 1.04892 1.81678i 0.0734389 0.127200i
\(205\) −1.35690 2.35021i −0.0947697 0.164146i
\(206\) 4.28569 2.47434i 0.298598 0.172396i
\(207\) −8.49396 −0.590371
\(208\) 0 0
\(209\) 4.54825 0.314609
\(210\) −1.25144 + 0.722521i −0.0863578 + 0.0498587i
\(211\) 6.26875 + 10.8578i 0.431559 + 0.747481i 0.997008 0.0773018i \(-0.0246305\pi\)
−0.565449 + 0.824783i \(0.691297\pi\)
\(212\) 5.20560 9.01636i 0.357522 0.619246i
\(213\) 11.4819i 0.786725i
\(214\) −3.69685 2.13437i −0.252711 0.145903i
\(215\) 1.93921 + 1.11960i 0.132253 + 0.0763564i
\(216\) 1.00000i 0.0680414i
\(217\) 21.8436 37.8343i 1.48284 2.56836i
\(218\) −3.10992 5.38653i −0.210630 0.364822i
\(219\) 0.461754 0.266594i 0.0312025 0.0180147i
\(220\) 0.325437 0.0219410
\(221\) 0 0
\(222\) −0.615957 −0.0413403
\(223\) −4.70043 + 2.71379i −0.314764 + 0.181729i −0.649056 0.760740i \(-0.724836\pi\)
0.334292 + 0.942469i \(0.391503\pi\)
\(224\) −2.02446 3.50647i −0.135265 0.234286i
\(225\) −2.43631 + 4.21982i −0.162421 + 0.281321i
\(226\) 12.9879i 0.863943i
\(227\) 14.3559 + 8.28836i 0.952832 + 0.550118i 0.893960 0.448147i \(-0.147916\pi\)
0.0588728 + 0.998265i \(0.481249\pi\)
\(228\) 4.31966 + 2.49396i 0.286077 + 0.165166i
\(229\) 23.8780i 1.57790i −0.614456 0.788951i \(-0.710624\pi\)
0.614456 0.788951i \(-0.289376\pi\)
\(230\) −1.51573 + 2.62532i −0.0999442 + 0.173109i
\(231\) −1.84601 3.19738i −0.121459 0.210372i
\(232\) 7.37484 4.25786i 0.484182 0.279543i
\(233\) −13.9952 −0.916857 −0.458428 0.888731i \(-0.651587\pi\)
−0.458428 + 0.888731i \(0.651587\pi\)
\(234\) 0 0
\(235\) 0.635334 0.0414446
\(236\) 5.23852 3.02446i 0.340998 0.196875i
\(237\) 5.85354 + 10.1386i 0.380229 + 0.658575i
\(238\) −4.24698 + 7.35598i −0.275291 + 0.476818i
\(239\) 13.2862i 0.859413i −0.902969 0.429707i \(-0.858617\pi\)
0.902969 0.429707i \(-0.141383\pi\)
\(240\) 0.309081 + 0.178448i 0.0199511 + 0.0115188i
\(241\) −9.07499 5.23945i −0.584571 0.337502i 0.178377 0.983962i \(-0.442915\pi\)
−0.762948 + 0.646460i \(0.776249\pi\)
\(242\) 10.1685i 0.653657i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −1.55496 2.69327i −0.0995460 0.172419i
\(245\) 2.90342 1.67629i 0.185493 0.107094i
\(246\) 7.60388 0.484805
\(247\) 0 0
\(248\) −10.7899 −0.685157
\(249\) 5.62859 3.24967i 0.356697 0.205939i
\(250\) 1.76175 + 3.05144i 0.111423 + 0.192990i
\(251\) 1.74363 3.02005i 0.110057 0.190624i −0.805736 0.592275i \(-0.798230\pi\)
0.915793 + 0.401651i \(0.131563\pi\)
\(252\) 4.04892i 0.255058i
\(253\) −6.70758 3.87263i −0.421702 0.243470i
\(254\) −7.98719 4.61141i −0.501161 0.289345i
\(255\) 0.748709i 0.0468859i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.26875 + 5.66164i 0.203899 + 0.353163i 0.949781 0.312914i \(-0.101305\pi\)
−0.745882 + 0.666078i \(0.767972\pi\)
\(258\) −5.43355 + 3.13706i −0.338278 + 0.195305i
\(259\) 2.49396 0.154967
\(260\) 0 0
\(261\) 8.51573 0.527110
\(262\) 12.6029 7.27628i 0.778609 0.449530i
\(263\) −4.00969 6.94498i −0.247248 0.428246i 0.715513 0.698599i \(-0.246193\pi\)
−0.962761 + 0.270353i \(0.912860\pi\)
\(264\) −0.455927 + 0.789689i −0.0280604 + 0.0486020i
\(265\) 3.71571i 0.228254i
\(266\) −17.4900 10.0978i −1.07238 0.619138i
\(267\) 5.62393 + 3.24698i 0.344179 + 0.198712i
\(268\) 13.5797i 0.829513i
\(269\) 13.8366 23.9657i 0.843633 1.46122i −0.0431692 0.999068i \(-0.513745\pi\)
0.886803 0.462148i \(-0.152921\pi\)
\(270\) 0.178448 + 0.309081i 0.0108600 + 0.0188101i
\(271\) 12.7556 7.36443i 0.774845 0.447357i −0.0597550 0.998213i \(-0.519032\pi\)
0.834600 + 0.550856i \(0.185699\pi\)
\(272\) 2.09783 0.127200
\(273\) 0 0
\(274\) −15.4034 −0.930555
\(275\) −3.84786 + 2.22156i −0.232035 + 0.133965i
\(276\) −4.24698 7.35598i −0.255638 0.442778i
\(277\) 1.63102 2.82501i 0.0979986 0.169739i −0.812858 0.582463i \(-0.802089\pi\)
0.910856 + 0.412724i \(0.135423\pi\)
\(278\) 2.71379i 0.162762i
\(279\) −9.34429 5.39493i −0.559428 0.322986i
\(280\) −1.25144 0.722521i −0.0747880 0.0431789i
\(281\) 7.72587i 0.460887i 0.973086 + 0.230443i \(0.0740177\pi\)
−0.973086 + 0.230443i \(0.925982\pi\)
\(282\) −0.890084 + 1.54167i −0.0530037 + 0.0918051i
\(283\) −9.89008 17.1301i −0.587904 1.01828i −0.994506 0.104675i \(-0.966620\pi\)
0.406602 0.913605i \(-0.366714\pi\)
\(284\) 9.94360 5.74094i 0.590044 0.340662i
\(285\) 1.78017 0.105448
\(286\) 0 0
\(287\) −30.7875 −1.81733
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 6.29954 + 10.9111i 0.370561 + 0.641831i
\(290\) 1.51961 2.63205i 0.0892348 0.154559i
\(291\) 1.96077i 0.114942i
\(292\) 0.461754 + 0.266594i 0.0270221 + 0.0156012i
\(293\) 11.1820 + 6.45593i 0.653259 + 0.377159i 0.789704 0.613488i \(-0.210234\pi\)
−0.136445 + 0.990648i \(0.543568\pi\)
\(294\) 9.39373i 0.547854i
\(295\) 1.07942 1.86960i 0.0628461 0.108853i
\(296\) −0.307979 0.533434i −0.0179009 0.0310052i
\(297\) −0.789689 + 0.455927i −0.0458224 + 0.0264556i
\(298\) 14.7356 0.853608
\(299\) 0 0
\(300\) −4.87263 −0.281321
\(301\) 22.0000 12.7017i 1.26806 0.732114i
\(302\) 7.91066 + 13.7017i 0.455207 + 0.788442i
\(303\) 3.49127 6.04706i 0.200568 0.347394i
\(304\) 4.98792i 0.286077i
\(305\) −0.961216 0.554958i −0.0550390 0.0317768i
\(306\) 1.81678 + 1.04892i 0.103858 + 0.0599626i
\(307\) 19.9651i 1.13947i 0.821829 + 0.569734i \(0.192954\pi\)
−0.821829 + 0.569734i \(0.807046\pi\)
\(308\) 1.84601 3.19738i 0.105186 0.182188i
\(309\) 2.47434 + 4.28569i 0.140761 + 0.243804i
\(310\) −3.33494 + 1.92543i −0.189412 + 0.109357i
\(311\) −13.4819 −0.764487 −0.382244 0.924062i \(-0.624848\pi\)
−0.382244 + 0.924062i \(0.624848\pi\)
\(312\) 0 0
\(313\) 12.9245 0.730537 0.365269 0.930902i \(-0.380977\pi\)
0.365269 + 0.930902i \(0.380977\pi\)
\(314\) 3.70150 2.13706i 0.208888 0.120601i
\(315\) −0.722521 1.25144i −0.0407094 0.0705108i
\(316\) −5.85354 + 10.1386i −0.329288 + 0.570343i
\(317\) 11.8726i 0.666833i 0.942780 + 0.333417i \(0.108202\pi\)
−0.942780 + 0.333417i \(0.891798\pi\)
\(318\) 9.01636 + 5.20560i 0.505612 + 0.291915i
\(319\) 6.72478 + 3.88255i 0.376515 + 0.217381i
\(320\) 0.356896i 0.0199511i
\(321\) 2.13437 3.69685i 0.119129 0.206338i
\(322\) 17.1957 + 29.7838i 0.958277 + 1.65978i
\(323\) 9.06194 5.23191i 0.504220 0.291111i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −0.317667 −0.0175940
\(327\) 5.38653 3.10992i 0.297876 0.171979i
\(328\) 3.80194 + 6.58515i 0.209927 + 0.363604i
\(329\) 3.60388 6.24210i 0.198688 0.344138i
\(330\) 0.325437i 0.0179147i
\(331\) 8.86742 + 5.11960i 0.487397 + 0.281399i 0.723494 0.690331i \(-0.242535\pi\)
−0.236097 + 0.971730i \(0.575868\pi\)
\(332\) 5.62859 + 3.24967i 0.308909 + 0.178349i
\(333\) 0.615957i 0.0337542i
\(334\) −6.18060 + 10.7051i −0.338188 + 0.585758i
\(335\) 2.42327 + 4.19723i 0.132397 + 0.229319i
\(336\) 3.50647 2.02446i 0.191293 0.110443i
\(337\) −1.44935 −0.0789513 −0.0394757 0.999221i \(-0.512569\pi\)
−0.0394757 + 0.999221i \(0.512569\pi\)
\(338\) 0 0
\(339\) 12.9879 0.705407
\(340\) 0.648401 0.374354i 0.0351645 0.0203022i
\(341\) −4.91939 8.52063i −0.266400 0.461418i
\(342\) −2.49396 + 4.31966i −0.134858 + 0.233581i
\(343\) 9.69202i 0.523320i
\(344\) −5.43355 3.13706i −0.292958 0.169139i
\(345\) −2.62532 1.51573i −0.141343 0.0816041i
\(346\) 17.0640i 0.917365i
\(347\) −3.42058 + 5.92462i −0.183627 + 0.318050i −0.943113 0.332473i \(-0.892117\pi\)
0.759486 + 0.650523i \(0.225450\pi\)
\(348\) 4.25786 + 7.37484i 0.228246 + 0.395333i
\(349\) −29.7368 + 17.1685i −1.59177 + 0.919010i −0.598769 + 0.800922i \(0.704343\pi\)
−0.993003 + 0.118088i \(0.962324\pi\)
\(350\) 19.7289 1.05455
\(351\) 0 0
\(352\) −0.911854 −0.0486020
\(353\) −22.5595 + 13.0248i −1.20072 + 0.693238i −0.960716 0.277533i \(-0.910483\pi\)
−0.240007 + 0.970771i \(0.577150\pi\)
\(354\) 3.02446 + 5.23852i 0.160748 + 0.278424i
\(355\) 2.04892 3.54883i 0.108745 0.188352i
\(356\) 6.49396i 0.344179i
\(357\) −7.35598 4.24698i −0.389320 0.224774i
\(358\) 21.6230 + 12.4840i 1.14281 + 0.659802i
\(359\) 8.49396i 0.448294i 0.974555 + 0.224147i \(0.0719596\pi\)
−0.974555 + 0.224147i \(0.928040\pi\)
\(360\) −0.178448 + 0.309081i −0.00940503 + 0.0162900i
\(361\) 2.93967 + 5.09165i 0.154719 + 0.267982i
\(362\) 4.55706 2.63102i 0.239514 0.138283i
\(363\) 10.1685 0.533709
\(364\) 0 0
\(365\) 0.190293 0.00996037
\(366\) 2.69327 1.55496i 0.140779 0.0812790i
\(367\) −13.7262 23.7744i −0.716500 1.24101i −0.962378 0.271714i \(-0.912410\pi\)
0.245878 0.969301i \(-0.420924\pi\)
\(368\) 4.24698 7.35598i 0.221389 0.383457i
\(369\) 7.60388i 0.395842i
\(370\) −0.190381 0.109916i −0.00989741 0.00571427i
\(371\) −36.5065 21.0770i −1.89532 1.09426i
\(372\) 10.7899i 0.559428i
\(373\) −13.3110 + 23.0553i −0.689216 + 1.19376i 0.282876 + 0.959156i \(0.408711\pi\)
−0.972092 + 0.234600i \(0.924622\pi\)
\(374\) 0.956459 + 1.65664i 0.0494573 + 0.0856626i
\(375\) −3.05144 + 1.76175i −0.157576 + 0.0909764i
\(376\) −1.78017 −0.0918051
\(377\) 0 0
\(378\) 4.04892 0.208254
\(379\) −10.0870 + 5.82371i −0.518132 + 0.299144i −0.736170 0.676797i \(-0.763368\pi\)
0.218038 + 0.975940i \(0.430034\pi\)
\(380\) 0.890084 + 1.54167i 0.0456603 + 0.0790860i
\(381\) 4.61141 7.98719i 0.236250 0.409196i
\(382\) 10.5375i 0.539145i
\(383\) 9.10896 + 5.25906i 0.465446 + 0.268725i 0.714331 0.699807i \(-0.246731\pi\)
−0.248885 + 0.968533i \(0.580064\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 1.31767i 0.0671545i
\(386\) −1.71379 + 2.96837i −0.0872297 + 0.151086i
\(387\) −3.13706 5.43355i −0.159466 0.276203i
\(388\) −1.69808 + 0.980386i −0.0862068 + 0.0497715i
\(389\) 9.25965 0.469483 0.234742 0.972058i \(-0.424576\pi\)
0.234742 + 0.972058i \(0.424576\pi\)
\(390\) 0 0
\(391\) −17.8189 −0.901142
\(392\) −8.13521 + 4.69687i −0.410890 + 0.237228i
\(393\) 7.27628 + 12.6029i 0.367040 + 0.635732i
\(394\) 1.88740 3.26906i 0.0950856 0.164693i
\(395\) 4.17821i 0.210229i
\(396\) −0.789689 0.455927i −0.0396834 0.0229112i
\(397\) −12.5689 7.25667i −0.630816 0.364202i 0.150252 0.988648i \(-0.451991\pi\)
−0.781068 + 0.624446i \(0.785325\pi\)
\(398\) 17.9541i 0.899956i
\(399\) 10.0978 17.4900i 0.505524 0.875593i
\(400\) −2.43631 4.21982i −0.121816 0.210991i
\(401\) −33.6379 + 19.4209i −1.67980 + 0.969832i −0.718013 + 0.696030i \(0.754948\pi\)
−0.961786 + 0.273803i \(0.911718\pi\)
\(402\) −13.5797 −0.677294
\(403\) 0 0
\(404\) 6.98254 0.347394
\(405\) −0.309081 + 0.178448i −0.0153584 + 0.00886715i
\(406\) −17.2397 29.8601i −0.855594 1.48193i
\(407\) 0.280831 0.486414i 0.0139203 0.0241107i
\(408\) 2.09783i 0.103858i
\(409\) 29.3774 + 16.9611i 1.45262 + 0.838671i 0.998630 0.0523356i \(-0.0166665\pi\)
0.453991 + 0.891006i \(0.350000\pi\)
\(410\) 2.35021 + 1.35690i 0.116069 + 0.0670123i
\(411\) 15.4034i 0.759795i
\(412\) −2.47434 + 4.28569i −0.121902 + 0.211141i
\(413\) −12.2458 21.2103i −0.602576 1.04369i
\(414\) 7.35598 4.24698i 0.361527 0.208728i
\(415\) 2.31959 0.113864
\(416\) 0 0
\(417\) 2.71379 0.132895
\(418\) −3.93890 + 2.27413i −0.192658 + 0.111231i
\(419\) −0.477697 0.827396i −0.0233370 0.0404209i 0.854121 0.520074i \(-0.174096\pi\)
−0.877458 + 0.479653i \(0.840762\pi\)
\(420\) 0.722521 1.25144i 0.0352554 0.0610642i
\(421\) 5.68233i 0.276940i −0.990367 0.138470i \(-0.955782\pi\)
0.990367 0.138470i \(-0.0442184\pi\)
\(422\) −10.8578 6.26875i −0.528549 0.305158i
\(423\) −1.54167 0.890084i −0.0749586 0.0432774i
\(424\) 10.4112i 0.505612i
\(425\) −5.11098 + 8.85248i −0.247919 + 0.429408i
\(426\) 5.74094 + 9.94360i 0.278149 + 0.481769i
\(427\) −10.9048 + 6.29590i −0.527721 + 0.304680i
\(428\) 4.26875 0.206338
\(429\) 0 0
\(430\) −2.23921 −0.107984
\(431\) −12.8575 + 7.42327i −0.619323 + 0.357566i −0.776605 0.629987i \(-0.783060\pi\)
0.157282 + 0.987554i \(0.449727\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −13.0749 + 22.6463i −0.628338 + 1.08831i 0.359547 + 0.933127i \(0.382931\pi\)
−0.987885 + 0.155187i \(0.950402\pi\)
\(434\) 43.6872i 2.09705i
\(435\) 2.63205 + 1.51961i 0.126197 + 0.0728599i
\(436\) 5.38653 + 3.10992i 0.257968 + 0.148938i
\(437\) 42.3672i 2.02670i
\(438\) −0.266594 + 0.461754i −0.0127384 + 0.0220635i
\(439\) −11.7751 20.3950i −0.561994 0.973403i −0.997322 0.0731307i \(-0.976701\pi\)
0.435328 0.900272i \(-0.356632\pi\)
\(440\) −0.281837 + 0.162718i −0.0134360 + 0.00775730i
\(441\) −9.39373 −0.447321
\(442\) 0 0
\(443\) 21.9433 1.04256 0.521279 0.853386i \(-0.325455\pi\)
0.521279 + 0.853386i \(0.325455\pi\)
\(444\) 0.533434 0.307979i 0.0253157 0.0146160i
\(445\) 1.15883 + 2.00716i 0.0549340 + 0.0951484i
\(446\) 2.71379 4.70043i 0.128502 0.222572i
\(447\) 14.7356i 0.696968i
\(448\) 3.50647 + 2.02446i 0.165665 + 0.0956467i
\(449\) 9.87565 + 5.70171i 0.466061 + 0.269080i 0.714589 0.699544i \(-0.246614\pi\)
−0.248528 + 0.968625i \(0.579947\pi\)
\(450\) 4.87263i 0.229698i
\(451\) −3.46681 + 6.00469i −0.163246 + 0.282750i
\(452\) 6.49396 + 11.2479i 0.305450 + 0.529055i
\(453\) −13.7017 + 7.91066i −0.643760 + 0.371675i
\(454\) −16.5767 −0.777984
\(455\) 0 0
\(456\) −4.98792 −0.233581
\(457\) 6.64171 3.83459i 0.310686 0.179375i −0.336547 0.941667i \(-0.609259\pi\)
0.647233 + 0.762292i \(0.275926\pi\)
\(458\) 11.9390 + 20.6790i 0.557873 + 0.966264i
\(459\) −1.04892 + 1.81678i −0.0489593 + 0.0847999i
\(460\) 3.03146i 0.141343i
\(461\) 24.6886 + 14.2540i 1.14986 + 0.663874i 0.948854 0.315715i \(-0.102244\pi\)
0.201010 + 0.979589i \(0.435578\pi\)
\(462\) 3.19738 + 1.84601i 0.148756 + 0.0858842i
\(463\) 14.3284i 0.665898i 0.942945 + 0.332949i \(0.108044\pi\)
−0.942945 + 0.332949i \(0.891956\pi\)
\(464\) −4.25786 + 7.37484i −0.197666 + 0.342368i
\(465\) −1.92543 3.33494i −0.0892896 0.154654i
\(466\) 12.1202 6.99761i 0.561458 0.324158i
\(467\) −33.3207 −1.54190 −0.770948 0.636898i \(-0.780217\pi\)
−0.770948 + 0.636898i \(0.780217\pi\)
\(468\) 0 0
\(469\) 54.9831 2.53889
\(470\) −0.550216 + 0.317667i −0.0253796 + 0.0146529i
\(471\) 2.13706 + 3.70150i 0.0984707 + 0.170556i
\(472\) −3.02446 + 5.23852i −0.139212 + 0.241122i
\(473\) 5.72109i 0.263056i
\(474\) −10.1386 5.85354i −0.465683 0.268862i
\(475\) −21.0481 12.1521i −0.965753 0.557578i
\(476\) 8.49396i 0.389320i
\(477\) −5.20560 + 9.01636i −0.238348 + 0.412831i
\(478\) 6.64310 + 11.5062i 0.303849 + 0.526281i
\(479\) 19.1634 11.0640i 0.875597 0.505526i 0.00639300 0.999980i \(-0.497965\pi\)
0.869204 + 0.494453i \(0.164632\pi\)
\(480\) −0.356896 −0.0162900
\(481\) 0 0
\(482\) 10.4789 0.477301
\(483\) −29.7838 + 17.1957i −1.35521 + 0.782430i
\(484\) 5.08426 + 8.80620i 0.231103 + 0.400282i
\(485\) −0.349896 + 0.606037i −0.0158879 + 0.0275187i
\(486\) 1.00000i 0.0453609i
\(487\) 0.109387 + 0.0631549i 0.00495682 + 0.00286182i 0.502476 0.864591i \(-0.332422\pi\)
−0.497520 + 0.867453i \(0.665756\pi\)
\(488\) 2.69327 + 1.55496i 0.121918 + 0.0703896i
\(489\) 0.317667i 0.0143654i
\(490\) −1.67629 + 2.90342i −0.0757272 + 0.131163i
\(491\) 6.97166 + 12.0753i 0.314626 + 0.544949i 0.979358 0.202133i \(-0.0647874\pi\)
−0.664732 + 0.747082i \(0.731454\pi\)
\(492\) −6.58515 + 3.80194i −0.296881 + 0.171405i
\(493\) 17.8646 0.804581
\(494\) 0 0
\(495\) −0.325437 −0.0146273
\(496\) 9.34429 5.39493i 0.419571 0.242239i
\(497\) −23.2446 40.2608i −1.04266 1.80594i
\(498\) −3.24967 + 5.62859i −0.145621 + 0.252223i
\(499\) 28.3913i 1.27097i 0.772113 + 0.635485i \(0.219200\pi\)
−0.772113 + 0.635485i \(0.780800\pi\)
\(500\) −3.05144 1.76175i −0.136465 0.0787878i
\(501\) −10.7051 6.18060i −0.478269 0.276129i
\(502\) 3.48725i 0.155644i
\(503\) −6.28382 + 10.8839i −0.280181 + 0.485289i −0.971429 0.237329i \(-0.923728\pi\)
0.691248 + 0.722618i \(0.257061\pi\)
\(504\) 2.02446 + 3.50647i 0.0901766 + 0.156190i
\(505\) 2.15817 1.24602i 0.0960373 0.0554472i
\(506\) 7.74525 0.344318
\(507\) 0 0
\(508\) 9.22282 0.409196
\(509\) 3.79037 2.18837i 0.168005 0.0969980i −0.413640 0.910441i \(-0.635743\pi\)
0.581645 + 0.813443i \(0.302409\pi\)
\(510\) 0.374354 + 0.648401i 0.0165767 + 0.0287117i
\(511\) 1.07942 1.86960i 0.0477506 0.0827064i
\(512\) 1.00000i 0.0441942i
\(513\) −4.31966 2.49396i −0.190718 0.110111i
\(514\) −5.66164 3.26875i −0.249724 0.144178i
\(515\) 1.76617i 0.0778266i
\(516\) 3.13706 5.43355i 0.138102 0.239199i
\(517\) −0.811626 1.40578i −0.0356953 0.0618261i
\(518\) −2.15983 + 1.24698i −0.0948976 + 0.0547891i
\(519\) 17.0640 0.749026
\(520\) 0 0
\(521\) −23.2707 −1.01951 −0.509753 0.860321i \(-0.670263\pi\)
−0.509753 + 0.860321i \(0.670263\pi\)
\(522\) −7.37484 + 4.25786i −0.322788 + 0.186362i
\(523\) −18.9976 32.9048i −0.830707 1.43883i −0.897478 0.441059i \(-0.854603\pi\)
0.0667707 0.997768i \(-0.478730\pi\)
\(524\) −7.27628 + 12.6029i −0.317866 + 0.550560i
\(525\) 19.7289i 0.861038i
\(526\) 6.94498 + 4.00969i 0.302816 + 0.174831i
\(527\) −19.6028 11.3177i −0.853910 0.493005i
\(528\) 0.911854i 0.0396834i
\(529\) −24.5737 + 42.5628i −1.06842 + 1.85056i
\(530\) 1.85786 + 3.21790i 0.0807001 + 0.139777i
\(531\) −5.23852 + 3.02446i −0.227332 + 0.131250i
\(532\) 20.1957 0.875593
\(533\) 0 0
\(534\) −6.49396 −0.281021
\(535\) 1.31939 0.761750i 0.0570422 0.0329333i
\(536\) −6.78986 11.7604i −0.293277 0.507971i
\(537\) −12.4840 + 21.6230i −0.538726 + 0.933100i
\(538\) 27.6732i 1.19308i
\(539\) −7.41812 4.28286i −0.319521 0.184476i
\(540\) −0.309081 0.178448i −0.0133007 0.00767918i
\(541\) 3.16421i 0.136040i −0.997684 0.0680200i \(-0.978332\pi\)
0.997684 0.0680200i \(-0.0216682\pi\)
\(542\) −7.36443 + 12.7556i −0.316329 + 0.547898i
\(543\) 2.63102 + 4.55706i 0.112908 + 0.195562i
\(544\) −1.81678 + 1.04892i −0.0778937 + 0.0449720i
\(545\) 2.21983 0.0950872
\(546\) 0 0
\(547\) 7.56033 0.323257 0.161628 0.986852i \(-0.448325\pi\)
0.161628 + 0.986852i \(0.448325\pi\)
\(548\) 13.3398 7.70171i 0.569846 0.329001i
\(549\) 1.55496 + 2.69327i 0.0663640 + 0.114946i
\(550\) 2.22156 3.84786i 0.0947277 0.164073i
\(551\) 42.4758i 1.80953i
\(552\) 7.35598 + 4.24698i 0.313091 + 0.180763i
\(553\) 41.0505 + 23.7005i 1.74564 + 1.00785i
\(554\) 3.26205i 0.138591i
\(555\) 0.109916 0.190381i 0.00466569 0.00808120i
\(556\) 1.35690 + 2.35021i 0.0575452 + 0.0996712i
\(557\) 0.359835 0.207751i 0.0152467 0.00880269i −0.492357 0.870393i \(-0.663865\pi\)
0.507604 + 0.861591i \(0.330531\pi\)
\(558\) 10.7899 0.456771
\(559\) 0 0
\(560\) 1.44504 0.0610642
\(561\) −1.65664 + 0.956459i −0.0699432 + 0.0403818i
\(562\) −3.86294 6.69080i −0.162948 0.282234i
\(563\) −14.5233 + 25.1550i −0.612083 + 1.06016i 0.378806 + 0.925476i \(0.376335\pi\)
−0.990889 + 0.134682i \(0.956999\pi\)
\(564\) 1.78017i 0.0749586i
\(565\) 4.01432 + 2.31767i 0.168884 + 0.0975050i
\(566\) 17.1301 + 9.89008i 0.720033 + 0.415711i
\(567\) 4.04892i 0.170039i
\(568\) −5.74094 + 9.94360i −0.240884 + 0.417224i
\(569\) 19.8431 + 34.3692i 0.831865 + 1.44083i 0.896557 + 0.442928i \(0.146060\pi\)
−0.0646918 + 0.997905i \(0.520606\pi\)
\(570\) −1.54167 + 0.890084i −0.0645735 + 0.0372815i
\(571\) 7.09651 0.296980 0.148490 0.988914i \(-0.452559\pi\)
0.148490 + 0.988914i \(0.452559\pi\)
\(572\) 0 0
\(573\) 10.5375 0.440210
\(574\) 26.6627 15.3937i 1.11288 0.642522i
\(575\) 20.6939 + 35.8430i 0.862997 + 1.49475i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 8.78687i 0.365802i −0.983131 0.182901i \(-0.941451\pi\)
0.983131 0.182901i \(-0.0585488\pi\)
\(578\) −10.9111 6.29954i −0.453843 0.262027i
\(579\) −2.96837 1.71379i −0.123361 0.0712228i
\(580\) 3.03923i 0.126197i
\(581\) 13.1576 22.7897i 0.545871 0.945476i
\(582\) −0.980386 1.69808i −0.0406383 0.0703876i
\(583\) −8.22160 + 4.74674i −0.340504 + 0.196590i
\(584\) −0.533188 −0.0220635
\(585\) 0 0
\(586\) −12.9119 −0.533384
\(587\) −31.7889 + 18.3533i −1.31207 + 0.757522i −0.982438 0.186589i \(-0.940257\pi\)
−0.329629 + 0.944111i \(0.606923\pi\)
\(588\) −4.69687 8.13521i −0.193695 0.335490i
\(589\) 26.9095 46.6086i 1.10879 1.92047i
\(590\) 2.15883i 0.0888778i
\(591\) 3.26906 + 1.88740i 0.134471 + 0.0776371i
\(592\) 0.533434 + 0.307979i 0.0219240 + 0.0126578i
\(593\) 10.8310i 0.444776i 0.974958 + 0.222388i \(0.0713852\pi\)
−0.974958 + 0.222388i \(0.928615\pi\)
\(594\) 0.455927 0.789689i 0.0187069 0.0324013i
\(595\) −1.51573 2.62532i −0.0621389 0.107628i
\(596\) −12.7614 + 7.36778i −0.522726 + 0.301796i
\(597\) −17.9541 −0.734811
\(598\) 0 0
\(599\) 23.5254 0.961223 0.480611 0.876934i \(-0.340415\pi\)
0.480611 + 0.876934i \(0.340415\pi\)
\(600\) 4.21982 2.43631i 0.172273 0.0994620i
\(601\) −13.9107 24.0940i −0.567428 0.982813i −0.996819 0.0796950i \(-0.974605\pi\)
0.429392 0.903118i \(-0.358728\pi\)
\(602\) −12.7017 + 22.0000i −0.517683 + 0.896653i
\(603\) 13.5797i 0.553009i
\(604\) −13.7017 7.91066i −0.557513 0.321880i
\(605\) 3.14290 + 1.81455i 0.127777 + 0.0737720i
\(606\) 6.98254i 0.283646i
\(607\) −0.0486218 + 0.0842155i −0.00197350 + 0.00341820i −0.867010 0.498290i \(-0.833962\pi\)
0.865037 + 0.501708i \(0.167295\pi\)
\(608\) −2.49396 4.31966i −0.101143 0.175186i
\(609\) 29.8601 17.2397i 1.20999 0.698590i
\(610\) 1.10992 0.0449392
\(611\) 0 0
\(612\) −2.09783 −0.0847999
\(613\) 6.98454 4.03252i 0.282103 0.162872i −0.352272 0.935898i \(-0.614591\pi\)
0.634375 + 0.773025i \(0.281258\pi\)
\(614\) −9.98254 17.2903i −0.402863 0.697778i
\(615\) −1.35690 + 2.35021i −0.0547153 + 0.0947697i
\(616\) 3.69202i 0.148756i
\(617\) 16.6437 + 9.60925i 0.670051 + 0.386854i 0.796096 0.605171i \(-0.206895\pi\)
−0.126045 + 0.992025i \(0.540228\pi\)
\(618\) −4.28569 2.47434i −0.172396 0.0995327i
\(619\) 12.3827i 0.497703i −0.968542 0.248852i \(-0.919947\pi\)
0.968542 0.248852i \(-0.0800532\pi\)
\(620\) 1.92543 3.33494i 0.0773270 0.133934i
\(621\) 4.24698 + 7.35598i 0.170425 + 0.295185i
\(622\) 11.6756 6.74094i 0.468151 0.270287i
\(623\) 26.2935 1.05343
\(624\) 0 0
\(625\) 23.1056 0.924224
\(626\) −11.1930 + 6.46226i −0.447361 + 0.258284i
\(627\) −2.27413 3.93890i −0.0908199 0.157305i
\(628\) −2.13706 + 3.70150i −0.0852781 + 0.147706i
\(629\) 1.29218i 0.0515224i
\(630\) 1.25144 + 0.722521i 0.0498587 + 0.0287859i
\(631\) −4.10785 2.37167i −0.163531 0.0944145i 0.416001 0.909364i \(-0.363431\pi\)
−0.579532 + 0.814950i \(0.696765\pi\)
\(632\) 11.7071i 0.465683i
\(633\) 6.26875 10.8578i 0.249160 0.431559i
\(634\) −5.93631 10.2820i −0.235761 0.408350i
\(635\) 2.85060 1.64579i 0.113122 0.0653113i
\(636\) −10.4112 −0.412831
\(637\) 0 0
\(638\) −7.76510 −0.307423
\(639\) −9.94360 + 5.74094i −0.393363 + 0.227108i
\(640\) −0.178448 0.309081i −0.00705377 0.0122175i
\(641\) −8.22282 + 14.2423i −0.324782 + 0.562538i −0.981468 0.191625i \(-0.938624\pi\)
0.656686 + 0.754164i \(0.271958\pi\)
\(642\) 4.26875i 0.168474i
\(643\) −1.51143 0.872625i −0.0596050 0.0344130i 0.469901 0.882719i \(-0.344289\pi\)
−0.529506 + 0.848306i \(0.677623\pi\)
\(644\) −29.7838 17.1957i −1.17365 0.677604i
\(645\) 2.23921i 0.0881688i
\(646\) −5.23191 + 9.06194i −0.205847 + 0.356537i
\(647\) 14.3817 + 24.9097i 0.565401 + 0.979303i 0.997012 + 0.0772436i \(0.0246119\pi\)
−0.431611 + 0.902060i \(0.642055\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −5.51573 −0.216511
\(650\) 0 0
\(651\) −43.6872 −1.71224
\(652\) 0.275108 0.158834i 0.0107741 0.00622040i
\(653\) 8.08306 + 14.0003i 0.316315 + 0.547873i 0.979716 0.200391i \(-0.0642211\pi\)
−0.663401 + 0.748264i \(0.730888\pi\)
\(654\) −3.10992 + 5.38653i −0.121607 + 0.210630i
\(655\) 5.19375i 0.202937i
\(656\) −6.58515 3.80194i −0.257107 0.148441i
\(657\) −0.461754 0.266594i −0.0180147 0.0104008i
\(658\) 7.20775i 0.280987i
\(659\) 8.17792 14.1646i 0.318566 0.551773i −0.661623 0.749837i \(-0.730132\pi\)
0.980189 + 0.198064i \(0.0634653\pi\)
\(660\) −0.162718 0.281837i −0.00633381 0.0109705i
\(661\) 28.6792 16.5579i 1.11549 0.644029i 0.175245 0.984525i \(-0.443928\pi\)
0.940246 + 0.340495i \(0.110595\pi\)
\(662\) −10.2392 −0.397958
\(663\) 0 0
\(664\) −6.49934 −0.252223
\(665\) 6.24210 3.60388i 0.242058 0.139752i
\(666\) 0.307979 + 0.533434i 0.0119339 + 0.0206702i
\(667\) 36.1661 62.6416i 1.40036 2.42549i
\(668\) 12.3612i 0.478269i
\(669\) 4.70043 + 2.71379i 0.181729 + 0.104921i
\(670\) −4.19723 2.42327i −0.162153 0.0936191i
\(671\) 2.83579i 0.109474i
\(672\) −2.02446 + 3.50647i −0.0780952 + 0.135265i
\(673\) −17.5770 30.4443i −0.677544 1.17354i −0.975718 0.219030i \(-0.929711\pi\)
0.298174 0.954512i \(-0.403623\pi\)
\(674\) 1.25518 0.724677i 0.0483476 0.0279135i
\(675\) 4.87263 0.187547
\(676\) 0 0
\(677\) 23.7855 0.914153 0.457076 0.889427i \(-0.348897\pi\)
0.457076 + 0.889427i \(0.348897\pi\)
\(678\) −11.2479 + 6.49396i −0.431972 + 0.249399i
\(679\) 3.96950 + 6.87538i 0.152335 + 0.263853i
\(680\) −0.374354 + 0.648401i −0.0143558 + 0.0248650i
\(681\) 16.5767i 0.635222i
\(682\) 8.52063 + 4.91939i 0.326272 + 0.188373i
\(683\) 2.59135 + 1.49612i 0.0991552 + 0.0572473i 0.548758 0.835982i \(-0.315101\pi\)
−0.449602 + 0.893229i \(0.648434\pi\)
\(684\) 4.98792i 0.190718i
\(685\) 2.74871 4.76090i 0.105023 0.181905i
\(686\) 4.84601 + 8.39354i 0.185022 + 0.320467i
\(687\) −20.6790 + 11.9390i −0.788951 + 0.455501i
\(688\) 6.27413 0.239199
\(689\) 0 0
\(690\) 3.03146 0.115406
\(691\) 10.0660 5.81163i 0.382930 0.221085i −0.296162 0.955138i \(-0.595707\pi\)
0.679092 + 0.734053i \(0.262374\pi\)
\(692\) 8.53199 + 14.7778i 0.324338 + 0.561769i
\(693\) −1.84601 + 3.19738i −0.0701241 + 0.121459i
\(694\) 6.84117i 0.259687i
\(695\) 0.838781 + 0.484271i 0.0318168 + 0.0183694i
\(696\) −7.37484 4.25786i −0.279543 0.161394i
\(697\) 15.9517i 0.604213i
\(698\) 17.1685 29.7368i 0.649838 1.12555i
\(699\) 6.99761 + 12.1202i 0.264674 + 0.458428i
\(700\) −17.0857 + 9.86443i −0.645778 + 0.372840i
\(701\) 33.8431 1.27824 0.639118 0.769109i \(-0.279300\pi\)
0.639118 + 0.769109i \(0.279300\pi\)
\(702\) 0 0
\(703\) 3.07234 0.115876
\(704\) 0.789689 0.455927i 0.0297625 0.0171834i
\(705\) −0.317667 0.550216i −0.0119640 0.0207223i
\(706\) 13.0248 22.5595i 0.490193 0.849039i
\(707\) 28.2717i 1.06327i
\(708\) −5.23852 3.02446i −0.196875 0.113666i
\(709\) −22.6820 13.0954i −0.851839 0.491810i 0.00943173 0.999956i \(-0.496998\pi\)
−0.861271 + 0.508146i \(0.830331\pi\)
\(710\) 4.09783i 0.153789i
\(711\) 5.85354 10.1386i 0.219525 0.380229i
\(712\) −3.24698 5.62393i −0.121686 0.210766i
\(713\) −79.3700 + 45.8243i −2.97243 + 1.71613i
\(714\) 8.49396 0.317878
\(715\) 0 0
\(716\) −24.9681 −0.933100
\(717\) −11.5062 + 6.64310i −0.429707 + 0.248091i
\(718\) −4.24698 7.35598i −0.158496 0.274523i
\(719\) −10.8672 + 18.8226i −0.405280 + 0.701966i −0.994354 0.106114i \(-0.966159\pi\)
0.589074 + 0.808079i \(0.299493\pi\)
\(720\) 0.356896i 0.0133007i
\(721\) 17.3524 + 10.0184i 0.646237 + 0.373105i
\(722\) −5.09165 2.93967i −0.189492 0.109403i
\(723\) 10.4789i 0.389714i
\(724\) −2.63102 + 4.55706i −0.0977812 + 0.169362i
\(725\) −20.7470 35.9348i −0.770523 1.33459i
\(726\) −8.80620 + 5.08426i −0.326829 + 0.188695i
\(727\) 2.01400 0.0746951 0.0373476 0.999302i \(-0.488109\pi\)
0.0373476 + 0.999302i \(0.488109\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.164798 + 0.0951463i −0.00609945 + 0.00352152i
\(731\) −6.58104 11.3987i −0.243409 0.421596i
\(732\) −1.55496 + 2.69327i −0.0574729 + 0.0995460i
\(733\) 13.5013i 0.498680i 0.968416 + 0.249340i \(0.0802137\pi\)
−0.968416 + 0.249340i \(0.919786\pi\)
\(734\) 23.7744 + 13.7262i 0.877530 + 0.506642i
\(735\) −2.90342 1.67629i −0.107094 0.0618310i
\(736\) 8.49396i 0.313091i
\(737\) 6.19136 10.7237i 0.228062 0.395014i
\(738\) −3.80194 6.58515i −0.139951 0.242403i
\(739\) 14.3689 8.29590i 0.528569 0.305170i −0.211864 0.977299i \(-0.567954\pi\)
0.740434 + 0.672130i \(0.234620\pi\)
\(740\) 0.219833 0.00808120
\(741\) 0 0
\(742\) 42.1540 1.54752
\(743\) −17.1888 + 9.92394i −0.630594 + 0.364074i −0.780982 0.624553i \(-0.785281\pi\)
0.150388 + 0.988627i \(0.451948\pi\)
\(744\) 5.39493 + 9.34429i 0.197788 + 0.342578i
\(745\) −2.62953 + 4.55448i −0.0963385 + 0.166863i
\(746\) 26.6219i 0.974698i
\(747\) −5.62859 3.24967i −0.205939 0.118899i
\(748\) −1.65664 0.956459i −0.0605726 0.0349716i
\(749\) 17.2838i 0.631537i
\(750\) 1.76175 3.05144i 0.0643300 0.111423i
\(751\) 13.9673 + 24.1922i 0.509676 + 0.882784i 0.999937 + 0.0112087i \(0.00356793\pi\)
−0.490262 + 0.871575i \(0.663099\pi\)
\(752\) 1.54167 0.890084i 0.0562189 0.0324580i
\(753\) −3.48725 −0.127083
\(754\) 0 0
\(755\) −5.64656 −0.205499
\(756\) −3.50647 + 2.02446i −0.127529 + 0.0736288i
\(757\) 0.274127 + 0.474801i 0.00996330 + 0.0172569i 0.870964 0.491347i \(-0.163495\pi\)
−0.861001 + 0.508604i \(0.830162\pi\)
\(758\) 5.82371 10.0870i 0.211527 0.366375i
\(759\) 7.74525i 0.281135i
\(760\) −1.54167 0.890084i −0.0559223 0.0322867i
\(761\) 1.71112 + 0.987918i 0.0620282 + 0.0358120i 0.530693 0.847564i \(-0.321932\pi\)
−0.468665 + 0.883376i \(0.655265\pi\)
\(762\) 9.22282i 0.334107i
\(763\) 12.5918 21.8096i 0.455854 0.789562i
\(764\) 5.26875 + 9.12574i 0.190617 + 0.330158i
\(765\) −0.648401 + 0.374354i −0.0234430 + 0.0135348i
\(766\) −10.5181 −0.380035
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 24.7780 14.3056i 0.893518 0.515873i 0.0184261 0.999830i \(-0.494134\pi\)
0.875091 + 0.483958i \(0.160801\pi\)
\(770\) 0.658834 + 1.14113i 0.0237427 + 0.0411236i
\(771\) 3.26875 5.66164i 0.117721 0.203899i
\(772\) 3.42758i 0.123361i
\(773\) −45.4732 26.2540i −1.63556 0.944290i −0.982336 0.187123i \(-0.940084\pi\)
−0.653222 0.757167i \(-0.726583\pi\)
\(774\) 5.43355 + 3.13706i 0.195305 + 0.112759i
\(775\) 52.5749i 1.88855i
\(776\) 0.980386 1.69808i 0.0351938 0.0609574i
\(777\) −1.24698 2.15983i −0.0447351 0.0774835i
\(778\) −8.01909 + 4.62983i −0.287498 + 0.165987i
\(779\) −37.9275 −1.35889
\(780\) 0 0
\(781\) −10.4698 −0.374639
\(782\) 15.4316 8.90946i 0.551834 0.318602i
\(783\) −4.25786 7.37484i −0.152164 0.263555i
\(784\) 4.69687 8.13521i 0.167745 0.290543i
\(785\) 1.52542i 0.0544445i
\(786\) −12.6029 7.27628i −0.449530 0.259536i
\(787\) 20.4751 + 11.8213i 0.729859 + 0.421384i 0.818371 0.574691i \(-0.194878\pi\)
−0.0885115 + 0.996075i \(0.528211\pi\)
\(788\) 3.77479i 0.134471i
\(789\) −4.00969 + 6.94498i −0.142749 + 0.247248i
\(790\) −2.08911 3.61844i −0.0743270 0.128738i
\(791\) 45.5417 26.2935i 1.61928 0.934889i
\(792\) 0.911854 0.0324013
\(793\) 0 0
\(794\) 14.5133 0.515059
\(795\) −3.21790 + 1.85786i −0.114127 + 0.0658913i
\(796\) −8.97703 15.5487i −0.318183 0.551108i
\(797\) 20.8279 36.0750i 0.737762 1.27784i −0.215739 0.976451i \(-0.569216\pi\)
0.953501 0.301390i \(-0.0974505\pi\)
\(798\) 20.1957i 0.714919i
\(799\) −3.23417 1.86725i −0.114417 0.0660585i
\(800\) 4.21982 + 2.43631i 0.149193 + 0.0861367i
\(801\) 6.49396i 0.229453i
\(802\) 19.4209 33.6379i 0.685775 1.18780i
\(803\) −0.243095 0.421052i −0.00857863 0.0148586i
\(804\) 11.7604 6.78986i 0.414756 0.239460i
\(805\) −12.2741 −0.432606
\(806\) 0 0
\(807\) −27.6732 −0.974144
\(808\) −6.04706 + 3.49127i −0.212735 + 0.122822i
\(809\) 22.1196 + 38.3123i 0.777684 + 1.34699i 0.933274 + 0.359166i \(0.116939\pi\)
−0.155590 + 0.987822i \(0.549728\pi\)
\(810\) 0.178448 0.309081i 0.00627002 0.0108600i
\(811\) 52.3913i 1.83971i −0.392260 0.919854i \(-0.628307\pi\)
0.392260 0.919854i \(-0.371693\pi\)
\(812\) 29.8601 + 17.2397i 1.04788 + 0.604996i
\(813\) −12.7556 7.36443i −0.447357 0.258282i
\(814\) 0.561663i 0.0196863i
\(815\) 0.0566871 0.0981849i 0.00198566 0.00343927i
\(816\) −1.04892 1.81678i −0.0367195 0.0636000i
\(817\) 27.1021 15.6474i 0.948183 0.547434i
\(818\) −33.9221 −1.18606
\(819\) 0 0
\(820\) −2.71379 −0.0947697
\(821\) 22.1941 12.8138i 0.774580 0.447204i −0.0599259 0.998203i \(-0.519086\pi\)
0.834506 + 0.550999i \(0.185753\pi\)
\(822\) 7.70171 + 13.3398i 0.268628 + 0.465277i
\(823\) −20.1277 + 34.8621i −0.701606 + 1.21522i 0.266296 + 0.963891i \(0.414200\pi\)
−0.967902 + 0.251327i \(0.919133\pi\)
\(824\) 4.94869i 0.172396i
\(825\) 3.84786 + 2.22156i 0.133965 + 0.0773448i
\(826\) 21.2103 + 12.2458i 0.738001 + 0.426085i
\(827\) 18.0519i 0.627726i −0.949468 0.313863i \(-0.898377\pi\)
0.949468 0.313863i \(-0.101623\pi\)
\(828\) −4.24698 + 7.35598i −0.147593 + 0.255638i
\(829\) 11.3327 + 19.6289i 0.393602 + 0.681739i 0.992922 0.118771i \(-0.0378955\pi\)
−0.599320 + 0.800510i \(0.704562\pi\)
\(830\) −2.00882 + 1.15979i −0.0697272 + 0.0402570i
\(831\) −3.26205 −0.113159
\(832\) 0 0
\(833\) −19.7065 −0.682790
\(834\) −2.35021 + 1.35690i −0.0813812 + 0.0469855i
\(835\) −2.20583 3.82061i −0.0763360 0.132218i
\(836\) 2.27413 3.93890i 0.0786523 0.136230i
\(837\) 10.7899i 0.372952i
\(838\) 0.827396 + 0.477697i 0.0285819 + 0.0165018i
\(839\) −19.1238 11.0411i −0.660228 0.381183i 0.132136 0.991232i \(-0.457816\pi\)
−0.792364 + 0.610049i \(0.791150\pi\)
\(840\) 1.44504i 0.0498587i
\(841\) −21.7588 + 37.6874i −0.750304 + 1.29957i
\(842\) 2.84117 + 4.92104i 0.0979131 + 0.169590i
\(843\) 6.69080 3.86294i 0.230443 0.133047i
\(844\) 12.5375 0.431559
\(845\) 0 0
\(846\) 1.78017 0.0612034
\(847\) 35.6556 20.5858i 1.22514 0.707335i
\(848\) −5.20560 9.01636i −0.178761 0.309623i
\(849\) −9.89008 + 17.1301i −0.339427 + 0.587904i
\(850\) 10.2220i 0.350610i
\(851\) −4.53097 2.61596i −0.155320 0.0896739i
\(852\) −9.94360 5.74094i −0.340662 0.196681i
\(853\) 28.9831i 0.992364i 0.868219 + 0.496182i \(0.165265\pi\)
−0.868219 + 0.496182i \(0.834735\pi\)
\(854\) 6.29590 10.9048i 0.215441 0.373155i
\(855\) −0.890084 1.54167i −0.0304402 0.0527240i
\(856\) −3.69685 + 2.13437i −0.126356 + 0.0729514i
\(857\) 42.9047 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(858\) 0 0
\(859\) −47.0616 −1.60572 −0.802860 0.596167i \(-0.796690\pi\)
−0.802860 + 0.596167i \(0.796690\pi\)
\(860\) 1.93921 1.11960i 0.0661266 0.0381782i
\(861\) 15.3937 + 26.6627i 0.524617 + 0.908663i
\(862\) 7.42327 12.8575i 0.252838 0.437928i
\(863\) 42.6064i 1.45034i −0.688571 0.725169i \(-0.741762\pi\)
0.688571 0.725169i \(-0.258238\pi\)
\(864\) 0.866025 + 0.500000i 0.0294628 + 0.0170103i
\(865\) 5.27415 + 3.04503i 0.179327 + 0.103534i
\(866\) 26.1497i 0.888604i
\(867\) 6.29954 10.9111i 0.213944 0.370561i
\(868\) −21.8436 37.8343i −0.741421 1.28418i
\(869\) 9.24495 5.33758i 0.313614 0.181065i
\(870\) −3.03923 −0.103040
\(871\) 0 0
\(872\) −6.21983 −0.210630
\(873\) 1.69808 0.980386i 0.0574712 0.0331810i
\(874\) 21.1836 + 36.6911i 0.716546 + 1.24109i
\(875\) −7.13318 + 12.3550i −0.241145 + 0.417676i
\(876\) 0.533188i 0.0180147i
\(877\) −23.7362 13.7041i −0.801515 0.462755i 0.0424859 0.999097i \(-0.486472\pi\)
−0.844000 + 0.536342i \(0.819806\pi\)
\(878\) 20.3950 + 11.7751i 0.688300 + 0.397390i
\(879\) 12.9119i 0.435506i
\(880\) 0.162718 0.281837i 0.00548524 0.00950071i
\(881\) 12.1588 + 21.0597i 0.409642 + 0.709520i 0.994849 0.101363i \(-0.0323205\pi\)
−0.585208 + 0.810883i \(0.698987\pi\)
\(882\) 8.13521 4.69687i 0.273927 0.158152i
\(883\) 32.2306 1.08465 0.542323 0.840170i \(-0.317545\pi\)
0.542323 + 0.840170i \(0.317545\pi\)
\(884\) 0 0
\(885\) −2.15883 −0.0725684
\(886\) −19.0035 + 10.9717i −0.638434 + 0.368600i
\(887\) 17.5821 + 30.4531i 0.590349 + 1.02252i 0.994185 + 0.107684i \(0.0343433\pi\)
−0.403836 + 0.914831i \(0.632323\pi\)
\(888\) −0.307979 + 0.533434i −0.0103351 + 0.0179009i
\(889\) 37.3424i 1.25242i
\(890\) −2.00716 1.15883i −0.0672801 0.0388442i
\(891\) 0.789689 + 0.455927i 0.0264556 + 0.0152741i
\(892\) 5.42758i 0.181729i
\(893\) 4.43967 7.68973i 0.148568 0.257327i
\(894\) −7.36778 12.7614i −0.246415 0.426804i
\(895\) −7.71715 + 4.45550i −0.257956 + 0.148931i
\(896\) −4.04892 −0.135265
\(897\) 0 0
\(898\) −11.4034 −0.380537
\(899\) 79.5734 45.9417i 2.65392 1.53224i
\(900\) 2.43631 + 4.21982i 0.0812104 + 0.140661i
\(901\) −10.9205 + 18.9148i −0.363814 + 0.630144i
\(902\) 6.93362i 0.230864i
\(903\) −22.0000 12.7017i −0.732114 0.422686i
\(904\) −11.2479 6.49396i −0.374099 0.215986i
\(905\) 1.87800i 0.0624269i
\(906\) 7.91066 13.7017i 0.262814 0.455207i
\(907\) −6.56033 11.3628i −0.217832 0.377297i 0.736313 0.676641i \(-0.236565\pi\)
−0.954145 + 0.299345i \(0.903232\pi\)
\(908\) 14.3559 8.28836i 0.476416 0.275059i
\(909\) −6.98254 −0.231596
\(910\) 0 0
\(911\) 45.7453 1.51561 0.757804 0.652482i \(-0.226272\pi\)
0.757804 + 0.652482i \(0.226272\pi\)
\(912\) 4.31966 2.49396i 0.143038 0.0825832i
\(913\) −2.96322 5.13245i −0.0980684 0.169859i
\(914\) −3.83459 + 6.64171i −0.126837 + 0.219688i
\(915\) 1.10992i 0.0366927i
\(916\) −20.6790 11.9390i −0.683252 0.394476i
\(917\) 51.0281 + 29.4611i 1.68510 + 0.972890i
\(918\) 2.09783i 0.0692389i
\(919\) −8.99247 + 15.5754i −0.296634 + 0.513785i −0.975364 0.220603i \(-0.929198\pi\)
0.678730 + 0.734388i \(0.262531\pi\)
\(920\) 1.51573 + 2.62532i 0.0499721 + 0.0865543i
\(921\) 17.2903 9.98254i 0.569734 0.328936i
\(922\) −28.5080 −0.938860
\(923\) 0 0
\(924\) −3.69202 −0.121459
\(925\) −2.59923 + 1.50066i −0.0854620 + 0.0493415i
\(926\) −7.16421 12.4088i −0.235431 0.407778i
\(927\) 2.47434 4.28569i 0.0812681 0.140761i
\(928\) 8.51573i 0.279543i
\(929\) −27.4429 15.8442i −0.900371 0.519830i −0.0230508 0.999734i \(-0.507338\pi\)
−0.877321 + 0.479905i \(0.840671\pi\)
\(930\) 3.33494 + 1.92543i 0.109357 + 0.0631373i
\(931\) 46.8552i 1.53562i
\(932\) −6.99761 + 12.1202i −0.229214 + 0.397011i
\(933\) 6.74094 + 11.6756i 0.220688 + 0.382244i
\(934\) 28.8565 16.6603i 0.944215 0.545143i
\(935\) −0.682713 −0.0223271
\(936\) 0 0
\(937\) −53.0484 −1.73302 −0.866509 0.499162i \(-0.833641\pi\)
−0.866509 + 0.499162i \(0.833641\pi\)
\(938\) −47.6168 + 27.4916i −1.55474 + 0.897631i
\(939\) −6.46226 11.1930i −0.210888 0.365269i
\(940\) 0.317667 0.550216i 0.0103612 0.0179461i
\(941\) 21.9433i 0.715332i 0.933850 + 0.357666i \(0.116427\pi\)
−0.933850 + 0.357666i \(0.883573\pi\)
\(942\) −3.70150 2.13706i −0.120601 0.0696293i
\(943\) 55.9340 + 32.2935i 1.82146 + 1.05162i
\(944\) 6.04892i 0.196875i
\(945\) −0.722521 + 1.25144i −0.0235036 + 0.0407094i
\(946\) 2.86054 + 4.95461i 0.0930043 + 0.161088i
\(947\) −10.5864 + 6.11207i −0.344012 + 0.198616i −0.662045 0.749464i \(-0.730311\pi\)
0.318033 + 0.948080i \(0.396978\pi\)
\(948\) 11.7071 0.380229
\(949\) 0 0
\(950\) 24.3043 0.788534
\(951\) 10.2820 5.93631i 0.333417 0.192498i
\(952\) 4.24698 + 7.35598i 0.137645 + 0.238409i
\(953\) −1.92931 + 3.34167i −0.0624966 + 0.108247i −0.895581 0.444899i \(-0.853240\pi\)
0.833084 + 0.553146i \(0.186573\pi\)
\(954\) 10.4112i 0.337075i
\(955\) 3.25694 + 1.88040i 0.105392 + 0.0608482i
\(956\) −11.5062 6.64310i −0.372137 0.214853i
\(957\) 7.76510i 0.251010i
\(958\) −11.0640 + 19.1634i −0.357461 + 0.619141i
\(959\) −31.1836 54.0116i −1.00697 1.74412i
\(960\) 0.309081 0.178448i 0.00997554 0.00575938i
\(961\) −85.4210 −2.75552
\(962\) 0 0
\(963\) −4.26875 −0.137559
\(964\) −9.07499 + 5.23945i −0.292286 + 0.168751i
\(965\) −0.611645 1.05940i −0.0196896 0.0341033i
\(966\) 17.1957 29.7838i 0.553262 0.958277i
\(967\) 0.613564i 0.0197309i −0.999951 0.00986545i \(-0.996860\pi\)
0.999951 0.00986545i \(-0.00314032\pi\)
\(968\) −8.80620 5.08426i −0.283042 0.163414i
\(969\) −9.06194 5.23191i −0.291111 0.168073i
\(970\) 0.699791i 0.0224689i
\(971\) 6.48845 11.2383i 0.208224 0.360655i −0.742931 0.669368i \(-0.766565\pi\)
0.951155 + 0.308713i \(0.0998983\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) 9.51582 5.49396i 0.305063 0.176128i
\(974\) −0.126310 −0.00404722
\(975\) 0 0
\(976\) −3.10992 −0.0995460
\(977\) −32.0963 + 18.5308i −1.02685 + 0.592853i −0.916081 0.400993i \(-0.868665\pi\)
−0.110770 + 0.993846i \(0.535332\pi\)
\(978\) 0.158834 + 0.275108i 0.00507894 + 0.00879698i
\(979\) 2.96077 5.12821i 0.0946267 0.163898i
\(980\) 3.35258i 0.107094i
\(981\) −5.38653 3.10992i −0.171979 0.0992920i
\(982\) −12.0753 6.97166i −0.385337 0.222474i
\(983\) 14.1193i 0.450337i 0.974320 + 0.225169i \(0.0722933\pi\)
−0.974320 + 0.225169i \(0.927707\pi\)
\(984\) 3.80194 6.58515i 0.121201 0.209927i
\(985\) 0.673604 + 1.16672i 0.0214628 + 0.0371747i
\(986\) −15.4712 + 8.93230i −0.492703 + 0.284462i
\(987\) −7.20775 −0.229425
\(988\) 0 0
\(989\) −53.2922 −1.69459
\(990\) 0.281837 0.162718i 0.00895736 0.00517153i
\(991\) −14.2696 24.7156i −0.453288 0.785118i 0.545300 0.838241i \(-0.316416\pi\)
−0.998588 + 0.0531230i \(0.983082\pi\)
\(992\) −5.39493 + 9.34429i −0.171289 + 0.296681i
\(993\) 10.2392i 0.324932i
\(994\) 40.2608 + 23.2446i 1.27700 + 0.737274i
\(995\) −5.54926 3.20387i −0.175923 0.101569i
\(996\) 6.49934i 0.205939i
\(997\) 9.44265 16.3551i 0.299052 0.517973i −0.676868 0.736105i \(-0.736663\pi\)
0.975919 + 0.218132i \(0.0699964\pi\)
\(998\) −14.1957 24.5876i −0.449356 0.778308i
\(999\) −0.533434 + 0.307979i −0.0168771 + 0.00974401i
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.i.g.361.2 12
13.2 odd 12 1014.2.a.m.1.2 3
13.3 even 3 1014.2.b.g.337.2 6
13.4 even 6 inner 1014.2.i.g.823.2 12
13.5 odd 4 1014.2.e.m.991.2 6
13.6 odd 12 1014.2.e.m.529.2 6
13.7 odd 12 1014.2.e.k.529.2 6
13.8 odd 4 1014.2.e.k.991.2 6
13.9 even 3 inner 1014.2.i.g.823.5 12
13.10 even 6 1014.2.b.g.337.5 6
13.11 odd 12 1014.2.a.o.1.2 yes 3
13.12 even 2 inner 1014.2.i.g.361.5 12
39.2 even 12 3042.2.a.be.1.2 3
39.11 even 12 3042.2.a.bd.1.2 3
39.23 odd 6 3042.2.b.r.1351.2 6
39.29 odd 6 3042.2.b.r.1351.5 6
52.11 even 12 8112.2.a.bz.1.2 3
52.15 even 12 8112.2.a.ce.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1014.2.a.m.1.2 3 13.2 odd 12
1014.2.a.o.1.2 yes 3 13.11 odd 12
1014.2.b.g.337.2 6 13.3 even 3
1014.2.b.g.337.5 6 13.10 even 6
1014.2.e.k.529.2 6 13.7 odd 12
1014.2.e.k.991.2 6 13.8 odd 4
1014.2.e.m.529.2 6 13.6 odd 12
1014.2.e.m.991.2 6 13.5 odd 4
1014.2.i.g.361.2 12 1.1 even 1 trivial
1014.2.i.g.361.5 12 13.12 even 2 inner
1014.2.i.g.823.2 12 13.4 even 6 inner
1014.2.i.g.823.5 12 13.9 even 3 inner
3042.2.a.bd.1.2 3 39.11 even 12
3042.2.a.be.1.2 3 39.2 even 12
3042.2.b.r.1351.2 6 39.23 odd 6
3042.2.b.r.1351.5 6 39.29 odd 6
8112.2.a.bz.1.2 3 52.11 even 12
8112.2.a.ce.1.2 3 52.15 even 12