Properties

Label 441.2.i.d.68.10
Level $441$
Weight $2$
Character 441.68
Analytic conductor $3.521$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(68,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 68.10
Character \(\chi\) \(=\) 441.68
Dual form 441.2.i.d.227.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.981621i q^{2} +(1.73160 + 0.0395255i) q^{3} +1.03642 q^{4} +(0.940599 + 1.62916i) q^{5} +(0.0387990 - 1.69978i) q^{6} -2.98061i q^{8} +(2.99688 + 0.136885i) q^{9} +O(q^{10})\) \(q-0.981621i q^{2} +(1.73160 + 0.0395255i) q^{3} +1.03642 q^{4} +(0.940599 + 1.62916i) q^{5} +(0.0387990 - 1.69978i) q^{6} -2.98061i q^{8} +(2.99688 + 0.136885i) q^{9} +(1.59922 - 0.923312i) q^{10} +(-3.54040 - 2.04405i) q^{11} +(1.79466 + 0.0409650i) q^{12} +(-3.51415 - 2.02890i) q^{13} +(1.56435 + 2.85824i) q^{15} -0.852996 q^{16} +(0.810727 + 1.40422i) q^{17} +(0.134369 - 2.94180i) q^{18} +(7.03722 + 4.06294i) q^{19} +(0.974855 + 1.68850i) q^{20} +(-2.00648 + 3.47533i) q^{22} +(-3.73318 + 2.15535i) q^{23} +(0.117810 - 5.16123i) q^{24} +(0.730548 - 1.26535i) q^{25} +(-1.99161 + 3.44957i) q^{26} +(5.18398 + 0.355482i) q^{27} +(-0.542317 + 0.313107i) q^{29} +(2.80571 - 1.53560i) q^{30} +4.27047i q^{31} -5.12391i q^{32} +(-6.04976 - 3.67941i) q^{33} +(1.37841 - 0.795827i) q^{34} +(3.10602 + 0.141870i) q^{36} +(-3.97076 + 6.87757i) q^{37} +(3.98827 - 6.90789i) q^{38} +(-6.00491 - 3.65214i) q^{39} +(4.85591 - 2.80356i) q^{40} +(-0.912023 + 1.57967i) q^{41} +(-3.53614 - 6.12477i) q^{43} +(-3.66933 - 2.11849i) q^{44} +(2.59585 + 5.01116i) q^{45} +(2.11574 + 3.66457i) q^{46} -7.93736 q^{47} +(-1.47705 - 0.0337151i) q^{48} +(-1.24209 - 0.717122i) q^{50} +(1.34835 + 2.46359i) q^{51} +(-3.64214 - 2.10279i) q^{52} +(-7.24978 + 4.18567i) q^{53} +(0.348949 - 5.08870i) q^{54} -7.69052i q^{55} +(12.0251 + 7.31354i) q^{57} +(0.307352 + 0.532350i) q^{58} -8.17430 q^{59} +(1.62132 + 2.96233i) q^{60} -3.74415i q^{61} +4.19198 q^{62} -6.73573 q^{64} -7.63351i q^{65} +(-3.61179 + 5.93857i) q^{66} +12.5312 q^{67} +(0.840253 + 1.45536i) q^{68} +(-6.54957 + 3.58466i) q^{69} -14.4969i q^{71} +(0.408000 - 8.93253i) q^{72} +(-3.28167 + 1.89468i) q^{73} +(6.75117 + 3.89779i) q^{74} +(1.31503 - 2.16220i) q^{75} +(7.29351 + 4.21091i) q^{76} +(-3.58501 + 5.89455i) q^{78} +8.36133 q^{79} +(-0.802327 - 1.38967i) q^{80} +(8.96253 + 0.820452i) q^{81} +(1.55064 + 0.895261i) q^{82} +(-4.38300 - 7.59159i) q^{83} +(-1.52514 + 2.64162i) q^{85} +(-6.01221 + 3.47115i) q^{86} +(-0.951451 + 0.520740i) q^{87} +(-6.09252 + 10.5526i) q^{88} +(-4.90379 + 8.49362i) q^{89} +(4.91906 - 2.54814i) q^{90} +(-3.86914 + 2.23385i) q^{92} +(-0.168792 + 7.39474i) q^{93} +7.79148i q^{94} +15.2864i q^{95} +(0.202525 - 8.87256i) q^{96} +(-11.4579 + 6.61525i) q^{97} +(-10.3303 - 6.61038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.981621i 0.694111i −0.937845 0.347056i \(-0.887182\pi\)
0.937845 0.347056i \(-0.112818\pi\)
\(3\) 1.73160 + 0.0395255i 0.999740 + 0.0228200i
\(4\) 1.03642 0.518210
\(5\) 0.940599 + 1.62916i 0.420648 + 0.728585i 0.996003 0.0893196i \(-0.0284692\pi\)
−0.575355 + 0.817904i \(0.695136\pi\)
\(6\) 0.0387990 1.69978i 0.0158396 0.693930i
\(7\) 0 0
\(8\) 2.98061i 1.05381i
\(9\) 2.99688 + 0.136885i 0.998958 + 0.0456282i
\(10\) 1.59922 0.923312i 0.505719 0.291977i
\(11\) −3.54040 2.04405i −1.06747 0.616304i −0.139980 0.990154i \(-0.544704\pi\)
−0.927489 + 0.373850i \(0.878037\pi\)
\(12\) 1.79466 + 0.0409650i 0.518075 + 0.0118256i
\(13\) −3.51415 2.02890i −0.974651 0.562715i −0.0739997 0.997258i \(-0.523576\pi\)
−0.900651 + 0.434544i \(0.856910\pi\)
\(14\) 0 0
\(15\) 1.56435 + 2.85824i 0.403913 + 0.737994i
\(16\) −0.852996 −0.213249
\(17\) 0.810727 + 1.40422i 0.196630 + 0.340574i 0.947434 0.319952i \(-0.103667\pi\)
−0.750803 + 0.660526i \(0.770333\pi\)
\(18\) 0.134369 2.94180i 0.0316710 0.693388i
\(19\) 7.03722 + 4.06294i 1.61445 + 0.932103i 0.988322 + 0.152382i \(0.0486945\pi\)
0.626128 + 0.779720i \(0.284639\pi\)
\(20\) 0.974855 + 1.68850i 0.217984 + 0.377560i
\(21\) 0 0
\(22\) −2.00648 + 3.47533i −0.427783 + 0.740943i
\(23\) −3.73318 + 2.15535i −0.778423 + 0.449423i −0.835871 0.548926i \(-0.815037\pi\)
0.0574484 + 0.998348i \(0.481704\pi\)
\(24\) 0.117810 5.16123i 0.0240479 1.05353i
\(25\) 0.730548 1.26535i 0.146110 0.253069i
\(26\) −1.99161 + 3.44957i −0.390587 + 0.676516i
\(27\) 5.18398 + 0.355482i 0.997657 + 0.0684126i
\(28\) 0 0
\(29\) −0.542317 + 0.313107i −0.100706 + 0.0581425i −0.549507 0.835489i \(-0.685184\pi\)
0.448801 + 0.893632i \(0.351851\pi\)
\(30\) 2.80571 1.53560i 0.512250 0.280360i
\(31\) 4.27047i 0.766999i 0.923541 + 0.383499i \(0.125281\pi\)
−0.923541 + 0.383499i \(0.874719\pi\)
\(32\) 5.12391i 0.905788i
\(33\) −6.04976 3.67941i −1.05313 0.640503i
\(34\) 1.37841 0.795827i 0.236396 0.136483i
\(35\) 0 0
\(36\) 3.10602 + 0.141870i 0.517670 + 0.0236450i
\(37\) −3.97076 + 6.87757i −0.652790 + 1.13066i 0.329653 + 0.944102i \(0.393068\pi\)
−0.982443 + 0.186563i \(0.940265\pi\)
\(38\) 3.98827 6.90789i 0.646983 1.12061i
\(39\) −6.00491 3.65214i −0.961556 0.584810i
\(40\) 4.85591 2.80356i 0.767787 0.443282i
\(41\) −0.912023 + 1.57967i −0.142434 + 0.246703i −0.928413 0.371551i \(-0.878826\pi\)
0.785979 + 0.618254i \(0.212160\pi\)
\(42\) 0 0
\(43\) −3.53614 6.12477i −0.539256 0.934019i −0.998944 0.0459387i \(-0.985372\pi\)
0.459688 0.888080i \(-0.347961\pi\)
\(44\) −3.66933 2.11849i −0.553173 0.319375i
\(45\) 2.59585 + 5.01116i 0.386966 + 0.747019i
\(46\) 2.11574 + 3.66457i 0.311949 + 0.540312i
\(47\) −7.93736 −1.15778 −0.578891 0.815405i \(-0.696515\pi\)
−0.578891 + 0.815405i \(0.696515\pi\)
\(48\) −1.47705 0.0337151i −0.213194 0.00486635i
\(49\) 0 0
\(50\) −1.24209 0.717122i −0.175658 0.101416i
\(51\) 1.34835 + 2.46359i 0.188807 + 0.344972i
\(52\) −3.64214 2.10279i −0.505073 0.291604i
\(53\) −7.24978 + 4.18567i −0.995835 + 0.574945i −0.907013 0.421102i \(-0.861643\pi\)
−0.0888214 + 0.996048i \(0.528310\pi\)
\(54\) 0.348949 5.08870i 0.0474859 0.692485i
\(55\) 7.69052i 1.03699i
\(56\) 0 0
\(57\) 12.0251 + 7.31354i 1.59276 + 0.968702i
\(58\) 0.307352 + 0.532350i 0.0403573 + 0.0699009i
\(59\) −8.17430 −1.06420 −0.532101 0.846681i \(-0.678598\pi\)
−0.532101 + 0.846681i \(0.678598\pi\)
\(60\) 1.62132 + 2.96233i 0.209311 + 0.382436i
\(61\) 3.74415i 0.479390i −0.970848 0.239695i \(-0.922953\pi\)
0.970848 0.239695i \(-0.0770474\pi\)
\(62\) 4.19198 0.532382
\(63\) 0 0
\(64\) −6.73573 −0.841966
\(65\) 7.63351i 0.946820i
\(66\) −3.61179 + 5.93857i −0.444580 + 0.730988i
\(67\) 12.5312 1.53093 0.765464 0.643479i \(-0.222510\pi\)
0.765464 + 0.643479i \(0.222510\pi\)
\(68\) 0.840253 + 1.45536i 0.101896 + 0.176489i
\(69\) −6.54957 + 3.58466i −0.788476 + 0.431542i
\(70\) 0 0
\(71\) 14.4969i 1.72047i −0.509898 0.860235i \(-0.670317\pi\)
0.509898 0.860235i \(-0.329683\pi\)
\(72\) 0.408000 8.93253i 0.0480833 1.05271i
\(73\) −3.28167 + 1.89468i −0.384091 + 0.221755i −0.679597 0.733586i \(-0.737845\pi\)
0.295506 + 0.955341i \(0.404512\pi\)
\(74\) 6.75117 + 3.89779i 0.784807 + 0.453109i
\(75\) 1.31503 2.16220i 0.151847 0.249669i
\(76\) 7.29351 + 4.21091i 0.836623 + 0.483025i
\(77\) 0 0
\(78\) −3.58501 + 5.89455i −0.405923 + 0.667426i
\(79\) 8.36133 0.940723 0.470361 0.882474i \(-0.344124\pi\)
0.470361 + 0.882474i \(0.344124\pi\)
\(80\) −0.802327 1.38967i −0.0897029 0.155370i
\(81\) 8.96253 + 0.820452i 0.995836 + 0.0911613i
\(82\) 1.55064 + 0.895261i 0.171239 + 0.0988651i
\(83\) −4.38300 7.59159i −0.481097 0.833285i 0.518668 0.854976i \(-0.326428\pi\)
−0.999765 + 0.0216912i \(0.993095\pi\)
\(84\) 0 0
\(85\) −1.52514 + 2.64162i −0.165424 + 0.286524i
\(86\) −6.01221 + 3.47115i −0.648313 + 0.374304i
\(87\) −0.951451 + 0.520740i −0.102006 + 0.0558292i
\(88\) −6.09252 + 10.5526i −0.649465 + 1.12491i
\(89\) −4.90379 + 8.49362i −0.519801 + 0.900322i 0.479934 + 0.877305i \(0.340661\pi\)
−0.999735 + 0.0230174i \(0.992673\pi\)
\(90\) 4.91906 2.54814i 0.518514 0.268598i
\(91\) 0 0
\(92\) −3.86914 + 2.23385i −0.403386 + 0.232895i
\(93\) −0.168792 + 7.39474i −0.0175029 + 0.766799i
\(94\) 7.79148i 0.803630i
\(95\) 15.2864i 1.56835i
\(96\) 0.202525 8.87256i 0.0206701 0.905552i
\(97\) −11.4579 + 6.61525i −1.16338 + 0.671677i −0.952111 0.305752i \(-0.901092\pi\)
−0.211267 + 0.977428i \(0.567759\pi\)
\(98\) 0 0
\(99\) −10.3303 6.61038i −1.03824 0.664369i
\(100\) 0.757155 1.31143i 0.0757155 0.131143i
\(101\) 0.524900 0.909154i 0.0522295 0.0904642i −0.838729 0.544550i \(-0.816701\pi\)
0.890958 + 0.454085i \(0.150034\pi\)
\(102\) 2.41832 1.32357i 0.239449 0.131053i
\(103\) −1.41937 + 0.819472i −0.139854 + 0.0807449i −0.568295 0.822825i \(-0.692397\pi\)
0.428440 + 0.903570i \(0.359063\pi\)
\(104\) −6.04736 + 10.4743i −0.592992 + 1.02709i
\(105\) 0 0
\(106\) 4.10874 + 7.11654i 0.399076 + 0.691220i
\(107\) 2.97522 + 1.71775i 0.287626 + 0.166061i 0.636871 0.770971i \(-0.280229\pi\)
−0.349245 + 0.937031i \(0.613562\pi\)
\(108\) 5.37278 + 0.368429i 0.516996 + 0.0354521i
\(109\) −1.84529 3.19614i −0.176747 0.306134i 0.764018 0.645195i \(-0.223224\pi\)
−0.940764 + 0.339061i \(0.889891\pi\)
\(110\) −7.54918 −0.719786
\(111\) −7.14761 + 11.7522i −0.678421 + 1.11547i
\(112\) 0 0
\(113\) 15.0858 + 8.70977i 1.41915 + 0.819346i 0.996224 0.0868183i \(-0.0276699\pi\)
0.422925 + 0.906165i \(0.361003\pi\)
\(114\) 7.17913 11.8041i 0.672387 1.10555i
\(115\) −7.02285 4.05465i −0.654885 0.378098i
\(116\) −0.562068 + 0.324510i −0.0521867 + 0.0301300i
\(117\) −10.2538 6.56138i −0.947960 0.606600i
\(118\) 8.02407i 0.738675i
\(119\) 0 0
\(120\) 8.51931 4.66271i 0.777703 0.425646i
\(121\) 2.85627 + 4.94720i 0.259661 + 0.449746i
\(122\) −3.67534 −0.332750
\(123\) −1.64170 + 2.69931i −0.148027 + 0.243388i
\(124\) 4.42600i 0.397466i
\(125\) 12.1546 1.08714
\(126\) 0 0
\(127\) −10.1288 −0.898783 −0.449391 0.893335i \(-0.648359\pi\)
−0.449391 + 0.893335i \(0.648359\pi\)
\(128\) 3.63588i 0.321369i
\(129\) −5.88109 10.7454i −0.517801 0.946082i
\(130\) −7.49322 −0.657199
\(131\) 2.48851 + 4.31022i 0.217422 + 0.376586i 0.954019 0.299746i \(-0.0969019\pi\)
−0.736597 + 0.676332i \(0.763569\pi\)
\(132\) −6.27008 3.81341i −0.545741 0.331915i
\(133\) 0 0
\(134\) 12.3009i 1.06263i
\(135\) 4.29690 + 8.77992i 0.369819 + 0.755655i
\(136\) 4.18544 2.41647i 0.358899 0.207210i
\(137\) −0.728035 0.420331i −0.0622003 0.0359113i 0.468577 0.883422i \(-0.344767\pi\)
−0.530778 + 0.847511i \(0.678100\pi\)
\(138\) 3.51877 + 6.42920i 0.299538 + 0.547290i
\(139\) 5.74392 + 3.31626i 0.487193 + 0.281281i 0.723409 0.690419i \(-0.242574\pi\)
−0.236216 + 0.971701i \(0.575907\pi\)
\(140\) 0 0
\(141\) −13.7443 0.313728i −1.15748 0.0264206i
\(142\) −14.2305 −1.19420
\(143\) 8.29433 + 14.3662i 0.693606 + 1.20136i
\(144\) −2.55632 0.116762i −0.213027 0.00973017i
\(145\) −1.02020 0.589015i −0.0847234 0.0489151i
\(146\) 1.85985 + 3.22136i 0.153923 + 0.266602i
\(147\) 0 0
\(148\) −4.11538 + 7.12804i −0.338282 + 0.585921i
\(149\) 14.7023 8.48838i 1.20446 0.695395i 0.242916 0.970047i \(-0.421896\pi\)
0.961544 + 0.274652i \(0.0885627\pi\)
\(150\) −2.12246 1.29086i −0.173298 0.105398i
\(151\) −0.975709 + 1.68998i −0.0794021 + 0.137528i −0.902992 0.429657i \(-0.858634\pi\)
0.823590 + 0.567186i \(0.191968\pi\)
\(152\) 12.1101 20.9752i 0.982256 1.70132i
\(153\) 2.23743 + 4.31925i 0.180886 + 0.349191i
\(154\) 0 0
\(155\) −6.95730 + 4.01680i −0.558823 + 0.322637i
\(156\) −6.22361 3.78514i −0.498287 0.303054i
\(157\) 9.52118i 0.759873i −0.925013 0.379936i \(-0.875946\pi\)
0.925013 0.379936i \(-0.124054\pi\)
\(158\) 8.20766i 0.652966i
\(159\) −12.7192 + 6.96135i −1.00870 + 0.552071i
\(160\) 8.34769 4.81954i 0.659943 0.381018i
\(161\) 0 0
\(162\) 0.805373 8.79781i 0.0632761 0.691221i
\(163\) −0.555106 + 0.961472i −0.0434793 + 0.0753083i −0.886946 0.461873i \(-0.847178\pi\)
0.843467 + 0.537181i \(0.180511\pi\)
\(164\) −0.945238 + 1.63720i −0.0738107 + 0.127844i
\(165\) 0.303971 13.3169i 0.0236641 1.03672i
\(166\) −7.45206 + 4.30245i −0.578392 + 0.333935i
\(167\) 7.00830 12.1387i 0.542319 0.939324i −0.456452 0.889748i \(-0.650880\pi\)
0.998770 0.0495754i \(-0.0157868\pi\)
\(168\) 0 0
\(169\) 1.73285 + 3.00138i 0.133296 + 0.230875i
\(170\) 2.59307 + 1.49711i 0.198879 + 0.114823i
\(171\) 20.5335 + 13.1394i 1.57024 + 1.00480i
\(172\) −3.66492 6.34783i −0.279448 0.484018i
\(173\) 7.11768 0.541147 0.270574 0.962699i \(-0.412787\pi\)
0.270574 + 0.962699i \(0.412787\pi\)
\(174\) 0.511170 + 0.933965i 0.0387517 + 0.0708037i
\(175\) 0 0
\(176\) 3.01994 + 1.74357i 0.227637 + 0.131426i
\(177\) −14.1546 0.323093i −1.06393 0.0242851i
\(178\) 8.33752 + 4.81367i 0.624924 + 0.360800i
\(179\) 5.19845 3.00133i 0.388550 0.224330i −0.292981 0.956118i \(-0.594647\pi\)
0.681532 + 0.731788i \(0.261314\pi\)
\(180\) 2.69039 + 5.19366i 0.200530 + 0.387113i
\(181\) 1.30283i 0.0968385i −0.998827 0.0484192i \(-0.984582\pi\)
0.998827 0.0484192i \(-0.0154184\pi\)
\(182\) 0 0
\(183\) 0.147989 6.48337i 0.0109397 0.479265i
\(184\) 6.42428 + 11.1272i 0.473604 + 0.820307i
\(185\) −14.9396 −1.09838
\(186\) 7.25884 + 0.165690i 0.532244 + 0.0121490i
\(187\) 6.62866i 0.484736i
\(188\) −8.22643 −0.599974
\(189\) 0 0
\(190\) 15.0054 1.08861
\(191\) 5.73288i 0.414817i 0.978254 + 0.207408i \(0.0665029\pi\)
−0.978254 + 0.207408i \(0.933497\pi\)
\(192\) −11.6636 0.266233i −0.841747 0.0192137i
\(193\) 1.55904 0.112222 0.0561109 0.998425i \(-0.482130\pi\)
0.0561109 + 0.998425i \(0.482130\pi\)
\(194\) 6.49367 + 11.2474i 0.466218 + 0.807514i
\(195\) 0.301718 13.2182i 0.0216065 0.946574i
\(196\) 0 0
\(197\) 19.5504i 1.39291i 0.717602 + 0.696454i \(0.245240\pi\)
−0.717602 + 0.696454i \(0.754760\pi\)
\(198\) −6.48889 + 10.1405i −0.461146 + 0.720652i
\(199\) 0.845590 0.488202i 0.0599423 0.0346077i −0.469729 0.882810i \(-0.655648\pi\)
0.529672 + 0.848203i \(0.322315\pi\)
\(200\) −3.77151 2.17748i −0.266686 0.153971i
\(201\) 21.6990 + 0.495301i 1.53053 + 0.0349358i
\(202\) −0.892445 0.515253i −0.0627922 0.0362531i
\(203\) 0 0
\(204\) 1.39746 + 2.55332i 0.0978417 + 0.178768i
\(205\) −3.43139 −0.239659
\(206\) 0.804411 + 1.39328i 0.0560460 + 0.0970745i
\(207\) −11.4829 + 5.94831i −0.798118 + 0.413436i
\(208\) 2.99756 + 1.73064i 0.207843 + 0.119998i
\(209\) −16.6097 28.7688i −1.14892 1.98998i
\(210\) 0 0
\(211\) 11.9752 20.7417i 0.824408 1.42792i −0.0779625 0.996956i \(-0.524841\pi\)
0.902371 0.430961i \(-0.141825\pi\)
\(212\) −7.51382 + 4.33810i −0.516051 + 0.297942i
\(213\) 0.572998 25.1029i 0.0392612 1.72002i
\(214\) 1.68618 2.92054i 0.115265 0.199644i
\(215\) 6.65218 11.5219i 0.453675 0.785787i
\(216\) 1.05956 15.4514i 0.0720936 1.05134i
\(217\) 0 0
\(218\) −3.13740 + 1.81138i −0.212491 + 0.122682i
\(219\) −5.75744 + 3.15111i −0.389051 + 0.212932i
\(220\) 7.97060i 0.537378i
\(221\) 6.57953i 0.442587i
\(222\) 11.5363 + 7.01625i 0.774263 + 0.470900i
\(223\) 2.68394 1.54957i 0.179730 0.103767i −0.407436 0.913234i \(-0.633577\pi\)
0.587166 + 0.809467i \(0.300244\pi\)
\(224\) 0 0
\(225\) 2.36257 3.69209i 0.157505 0.246139i
\(226\) 8.54970 14.8085i 0.568717 0.985047i
\(227\) 10.8991 18.8779i 0.723401 1.25297i −0.236228 0.971698i \(-0.575911\pi\)
0.959629 0.281269i \(-0.0907554\pi\)
\(228\) 12.4630 + 7.57989i 0.825383 + 0.501991i
\(229\) −11.1810 + 6.45536i −0.738862 + 0.426582i −0.821655 0.569985i \(-0.806949\pi\)
0.0827937 + 0.996567i \(0.473616\pi\)
\(230\) −3.98013 + 6.89378i −0.262442 + 0.454563i
\(231\) 0 0
\(232\) 0.933250 + 1.61644i 0.0612709 + 0.106124i
\(233\) −0.699758 0.404005i −0.0458427 0.0264673i 0.476904 0.878956i \(-0.341759\pi\)
−0.522746 + 0.852488i \(0.675092\pi\)
\(234\) −6.44080 + 10.0653i −0.421048 + 0.657989i
\(235\) −7.46587 12.9313i −0.487020 0.843543i
\(236\) −8.47200 −0.551480
\(237\) 14.4785 + 0.330485i 0.940478 + 0.0214673i
\(238\) 0 0
\(239\) 12.2032 + 7.04552i 0.789360 + 0.455737i 0.839737 0.542993i \(-0.182709\pi\)
−0.0503775 + 0.998730i \(0.516042\pi\)
\(240\) −1.33438 2.43807i −0.0861340 0.157377i
\(241\) 16.0205 + 9.24943i 1.03197 + 0.595808i 0.917549 0.397624i \(-0.130165\pi\)
0.114422 + 0.993432i \(0.463498\pi\)
\(242\) 4.85628 2.80377i 0.312173 0.180233i
\(243\) 15.4871 + 1.77494i 0.993497 + 0.113863i
\(244\) 3.88051i 0.248424i
\(245\) 0 0
\(246\) 2.64970 + 1.61152i 0.168939 + 0.102747i
\(247\) −16.4866 28.5556i −1.04902 1.81695i
\(248\) 12.7286 0.808268
\(249\) −7.28955 13.3188i −0.461956 0.844046i
\(250\) 11.9312i 0.754596i
\(251\) 22.1733 1.39957 0.699783 0.714355i \(-0.253280\pi\)
0.699783 + 0.714355i \(0.253280\pi\)
\(252\) 0 0
\(253\) 17.6226 1.10792
\(254\) 9.94262i 0.623855i
\(255\) −2.74534 + 4.51394i −0.171920 + 0.282674i
\(256\) −17.0405 −1.06503
\(257\) 2.02896 + 3.51427i 0.126563 + 0.219214i 0.922343 0.386372i \(-0.126272\pi\)
−0.795780 + 0.605586i \(0.792939\pi\)
\(258\) −10.5479 + 5.77301i −0.656686 + 0.359412i
\(259\) 0 0
\(260\) 7.91152i 0.490652i
\(261\) −1.66812 + 0.864107i −0.103254 + 0.0534869i
\(262\) 4.23100 2.44277i 0.261392 0.150915i
\(263\) 8.62617 + 4.98032i 0.531913 + 0.307100i 0.741795 0.670627i \(-0.233975\pi\)
−0.209882 + 0.977727i \(0.567308\pi\)
\(264\) −10.9669 + 18.0320i −0.674966 + 1.10979i
\(265\) −13.6383 7.87406i −0.837793 0.483700i
\(266\) 0 0
\(267\) −8.82712 + 14.5137i −0.540211 + 0.888226i
\(268\) 12.9876 0.793341
\(269\) 4.98399 + 8.63253i 0.303880 + 0.526335i 0.977011 0.213188i \(-0.0683846\pi\)
−0.673132 + 0.739523i \(0.735051\pi\)
\(270\) 8.61856 4.21793i 0.524509 0.256695i
\(271\) −16.4822 9.51601i −1.00122 0.578057i −0.0926133 0.995702i \(-0.529522\pi\)
−0.908610 + 0.417646i \(0.862855\pi\)
\(272\) −0.691547 1.19780i −0.0419312 0.0726270i
\(273\) 0 0
\(274\) −0.412606 + 0.714655i −0.0249265 + 0.0431739i
\(275\) −5.17286 + 2.98655i −0.311935 + 0.180096i
\(276\) −6.78810 + 3.71521i −0.408596 + 0.223629i
\(277\) 7.81184 13.5305i 0.469368 0.812969i −0.530019 0.847986i \(-0.677815\pi\)
0.999387 + 0.0350166i \(0.0111484\pi\)
\(278\) 3.25531 5.63836i 0.195240 0.338166i
\(279\) −0.584561 + 12.7981i −0.0349968 + 0.766200i
\(280\) 0 0
\(281\) −20.8780 + 12.0539i −1.24547 + 0.719075i −0.970203 0.242292i \(-0.922101\pi\)
−0.275271 + 0.961367i \(0.588768\pi\)
\(282\) −0.307962 + 13.4917i −0.0183389 + 0.803421i
\(283\) 3.01779i 0.179389i −0.995969 0.0896946i \(-0.971411\pi\)
0.995969 0.0896946i \(-0.0285891\pi\)
\(284\) 15.0249i 0.891564i
\(285\) −0.604202 + 26.4699i −0.0357898 + 1.56794i
\(286\) 14.1022 8.14189i 0.833879 0.481440i
\(287\) 0 0
\(288\) 0.701384 15.3557i 0.0413295 0.904844i
\(289\) 7.18544 12.4456i 0.422673 0.732091i
\(290\) −0.578190 + 1.00145i −0.0339525 + 0.0588074i
\(291\) −20.1021 + 11.0021i −1.17840 + 0.644954i
\(292\) −3.40119 + 1.96368i −0.199040 + 0.114916i
\(293\) −14.9237 + 25.8485i −0.871849 + 1.51009i −0.0117671 + 0.999931i \(0.503746\pi\)
−0.860082 + 0.510156i \(0.829588\pi\)
\(294\) 0 0
\(295\) −7.68873 13.3173i −0.447655 0.775362i
\(296\) 20.4994 + 11.8353i 1.19150 + 0.687914i
\(297\) −17.6267 11.8549i −1.02281 0.687888i
\(298\) −8.33238 14.4321i −0.482682 0.836029i
\(299\) 17.4920 1.01159
\(300\) 1.36292 2.24095i 0.0786884 0.129381i
\(301\) 0 0
\(302\) 1.65892 + 0.957777i 0.0954600 + 0.0551139i
\(303\) 0.944852 1.55354i 0.0542803 0.0892487i
\(304\) −6.00272 3.46567i −0.344280 0.198770i
\(305\) 6.09984 3.52175i 0.349276 0.201655i
\(306\) 4.23987 2.19631i 0.242377 0.125555i
\(307\) 2.68853i 0.153442i 0.997053 + 0.0767212i \(0.0244451\pi\)
−0.997053 + 0.0767212i \(0.975555\pi\)
\(308\) 0 0
\(309\) −2.49016 + 1.36290i −0.141661 + 0.0775324i
\(310\) 3.94297 + 6.82943i 0.223946 + 0.387886i
\(311\) 11.0753 0.628020 0.314010 0.949420i \(-0.398327\pi\)
0.314010 + 0.949420i \(0.398327\pi\)
\(312\) −10.8856 + 17.8983i −0.616276 + 1.01329i
\(313\) 16.7397i 0.946186i 0.881013 + 0.473093i \(0.156863\pi\)
−0.881013 + 0.473093i \(0.843137\pi\)
\(314\) −9.34619 −0.527436
\(315\) 0 0
\(316\) 8.66584 0.487492
\(317\) 2.94187i 0.165232i −0.996581 0.0826160i \(-0.973672\pi\)
0.996581 0.0826160i \(-0.0263275\pi\)
\(318\) 6.83341 + 12.4854i 0.383198 + 0.700147i
\(319\) 2.56002 0.143334
\(320\) −6.33562 10.9736i −0.354172 0.613444i
\(321\) 5.08400 + 3.09205i 0.283761 + 0.172581i
\(322\) 0 0
\(323\) 13.1758i 0.733118i
\(324\) 9.28893 + 0.850332i 0.516052 + 0.0472407i
\(325\) −5.13452 + 2.96442i −0.284812 + 0.164436i
\(326\) 0.943801 + 0.544904i 0.0522723 + 0.0301794i
\(327\) −3.06898 5.60737i −0.169715 0.310088i
\(328\) 4.70839 + 2.71839i 0.259977 + 0.150098i
\(329\) 0 0
\(330\) −13.0722 0.298385i −0.719598 0.0164255i
\(331\) 4.88153 0.268313 0.134157 0.990960i \(-0.457167\pi\)
0.134157 + 0.990960i \(0.457167\pi\)
\(332\) −4.54263 7.86807i −0.249309 0.431816i
\(333\) −12.8413 + 20.0677i −0.703700 + 1.09970i
\(334\) −11.9156 6.87950i −0.651995 0.376429i
\(335\) 11.7868 + 20.4154i 0.643982 + 1.11541i
\(336\) 0 0
\(337\) 6.51421 11.2830i 0.354852 0.614621i −0.632241 0.774772i \(-0.717865\pi\)
0.987093 + 0.160151i \(0.0511980\pi\)
\(338\) 2.94622 1.70100i 0.160253 0.0925221i
\(339\) 25.7783 + 15.6781i 1.40008 + 0.851518i
\(340\) −1.58068 + 2.73782i −0.0857245 + 0.148479i
\(341\) 8.72904 15.1191i 0.472704 0.818748i
\(342\) 12.8979 20.1561i 0.697440 1.08992i
\(343\) 0 0
\(344\) −18.2556 + 10.5399i −0.984275 + 0.568272i
\(345\) −12.0005 7.29861i −0.646086 0.392944i
\(346\) 6.98687i 0.375617i
\(347\) 2.15180i 0.115515i 0.998331 + 0.0577573i \(0.0183949\pi\)
−0.998331 + 0.0577573i \(0.981605\pi\)
\(348\) −0.986102 + 0.539705i −0.0528606 + 0.0289312i
\(349\) −25.2919 + 14.6023i −1.35384 + 0.781642i −0.988785 0.149343i \(-0.952284\pi\)
−0.365058 + 0.930985i \(0.618951\pi\)
\(350\) 0 0
\(351\) −17.4961 11.7670i −0.933870 0.628075i
\(352\) −10.4735 + 18.1407i −0.558240 + 0.966901i
\(353\) −5.41764 + 9.38362i −0.288352 + 0.499440i −0.973416 0.229042i \(-0.926441\pi\)
0.685065 + 0.728482i \(0.259774\pi\)
\(354\) −0.317155 + 13.8945i −0.0168566 + 0.738483i
\(355\) 23.6179 13.6358i 1.25351 0.723713i
\(356\) −5.08239 + 8.80295i −0.269366 + 0.466556i
\(357\) 0 0
\(358\) −2.94617 5.10291i −0.155710 0.269697i
\(359\) 18.1425 + 10.4746i 0.957527 + 0.552829i 0.895411 0.445240i \(-0.146882\pi\)
0.0621161 + 0.998069i \(0.480215\pi\)
\(360\) 14.9363 7.73723i 0.787213 0.407788i
\(361\) 23.5150 + 40.7292i 1.23763 + 2.14364i
\(362\) −1.27888 −0.0672167
\(363\) 4.75037 + 8.67947i 0.249330 + 0.455554i
\(364\) 0 0
\(365\) −6.17348 3.56426i −0.323135 0.186562i
\(366\) −6.36422 0.145270i −0.332663 0.00759336i
\(367\) −4.97835 2.87425i −0.259868 0.150035i 0.364407 0.931240i \(-0.381272\pi\)
−0.624274 + 0.781205i \(0.714605\pi\)
\(368\) 3.18439 1.83851i 0.165998 0.0958389i
\(369\) −2.94945 + 4.60923i −0.153542 + 0.239947i
\(370\) 14.6650i 0.762398i
\(371\) 0 0
\(372\) −0.174940 + 7.66405i −0.00907019 + 0.397363i
\(373\) −14.4467 25.0224i −0.748023 1.29561i −0.948769 0.315970i \(-0.897670\pi\)
0.200747 0.979643i \(-0.435663\pi\)
\(374\) −6.50684 −0.336461
\(375\) 21.0469 + 0.480416i 1.08686 + 0.0248086i
\(376\) 23.6582i 1.22008i
\(377\) 2.54104 0.130870
\(378\) 0 0
\(379\) −0.411434 −0.0211339 −0.0105670 0.999944i \(-0.503364\pi\)
−0.0105670 + 0.999944i \(0.503364\pi\)
\(380\) 15.8431i 0.812734i
\(381\) −17.5390 0.400344i −0.898549 0.0205103i
\(382\) 5.62752 0.287929
\(383\) −12.4007 21.4787i −0.633648 1.09751i −0.986800 0.161944i \(-0.948223\pi\)
0.353152 0.935566i \(-0.385110\pi\)
\(384\) 0.143710 6.29589i 0.00733366 0.321286i
\(385\) 0 0
\(386\) 1.53038i 0.0778944i
\(387\) −9.75898 18.8392i −0.496077 0.957652i
\(388\) −11.8752 + 6.85617i −0.602874 + 0.348069i
\(389\) −3.82694 2.20948i −0.194033 0.112025i 0.399836 0.916587i \(-0.369067\pi\)
−0.593869 + 0.804561i \(0.702400\pi\)
\(390\) −12.9753 0.296173i −0.657028 0.0149973i
\(391\) −6.05319 3.49481i −0.306123 0.176740i
\(392\) 0 0
\(393\) 4.13873 + 7.56193i 0.208772 + 0.381449i
\(394\) 19.1911 0.966833
\(395\) 7.86465 + 13.6220i 0.395714 + 0.685396i
\(396\) −10.7066 6.85113i −0.538024 0.344282i
\(397\) −19.2780 11.1301i −0.967533 0.558605i −0.0690495 0.997613i \(-0.521997\pi\)
−0.898483 + 0.439008i \(0.855330\pi\)
\(398\) −0.479229 0.830049i −0.0240216 0.0416066i
\(399\) 0 0
\(400\) −0.623155 + 1.07934i −0.0311578 + 0.0539668i
\(401\) 5.31899 3.07092i 0.265617 0.153354i −0.361277 0.932459i \(-0.617659\pi\)
0.626894 + 0.779104i \(0.284326\pi\)
\(402\) 0.486198 21.3002i 0.0242493 1.06236i
\(403\) 8.66434 15.0071i 0.431602 0.747556i
\(404\) 0.544017 0.942265i 0.0270658 0.0468794i
\(405\) 7.09349 + 15.3731i 0.352478 + 0.763898i
\(406\) 0 0
\(407\) 28.1162 16.2329i 1.39367 0.804633i
\(408\) 7.34302 4.01892i 0.363534 0.198966i
\(409\) 0.884369i 0.0437293i 0.999761 + 0.0218646i \(0.00696028\pi\)
−0.999761 + 0.0218646i \(0.993040\pi\)
\(410\) 3.36833i 0.166350i
\(411\) −1.24405 0.756622i −0.0613646 0.0373214i
\(412\) −1.47106 + 0.849316i −0.0724739 + 0.0418428i
\(413\) 0 0
\(414\) 5.83899 + 11.2719i 0.286971 + 0.553983i
\(415\) 8.24530 14.2813i 0.404746 0.701040i
\(416\) −10.3959 + 18.0062i −0.509700 + 0.882827i
\(417\) 9.81510 + 5.96946i 0.480648 + 0.292326i
\(418\) −28.2401 + 16.3044i −1.38127 + 0.797476i
\(419\) 7.59365 13.1526i 0.370974 0.642546i −0.618742 0.785595i \(-0.712357\pi\)
0.989716 + 0.143049i \(0.0456905\pi\)
\(420\) 0 0
\(421\) 13.3318 + 23.0914i 0.649753 + 1.12541i 0.983182 + 0.182630i \(0.0584611\pi\)
−0.333428 + 0.942775i \(0.608206\pi\)
\(422\) −20.3605 11.7551i −0.991133 0.572231i
\(423\) −23.7873 1.08650i −1.15658 0.0528275i
\(424\) 12.4759 + 21.6088i 0.605881 + 1.04942i
\(425\) 2.36910 0.114918
\(426\) −24.6415 0.562467i −1.19389 0.0272516i
\(427\) 0 0
\(428\) 3.08358 + 1.78031i 0.149050 + 0.0860543i
\(429\) 13.7946 + 25.2043i 0.666011 + 1.21688i
\(430\) −11.3102 6.52992i −0.545424 0.314901i
\(431\) 4.06785 2.34857i 0.195941 0.113127i −0.398820 0.917029i \(-0.630580\pi\)
0.594761 + 0.803903i \(0.297247\pi\)
\(432\) −4.42191 0.303225i −0.212749 0.0145889i
\(433\) 8.97714i 0.431414i −0.976458 0.215707i \(-0.930794\pi\)
0.976458 0.215707i \(-0.0692056\pi\)
\(434\) 0 0
\(435\) −1.74331 1.06026i −0.0835851 0.0508357i
\(436\) −1.91250 3.31254i −0.0915919 0.158642i
\(437\) −35.0283 −1.67563
\(438\) 3.09320 + 5.65162i 0.147799 + 0.270045i
\(439\) 16.5136i 0.788151i −0.919078 0.394075i \(-0.871065\pi\)
0.919078 0.394075i \(-0.128935\pi\)
\(440\) −22.9225 −1.09279
\(441\) 0 0
\(442\) −6.45861 −0.307205
\(443\) 1.06368i 0.0505368i 0.999681 + 0.0252684i \(0.00804404\pi\)
−0.999681 + 0.0252684i \(0.991956\pi\)
\(444\) −7.40792 + 12.1803i −0.351565 + 0.578049i
\(445\) −18.4500 −0.874614
\(446\) −1.52110 2.63461i −0.0720260 0.124753i
\(447\) 25.7940 14.1174i 1.22002 0.667728i
\(448\) 0 0
\(449\) 15.9081i 0.750749i −0.926873 0.375374i \(-0.877514\pi\)
0.926873 0.375374i \(-0.122486\pi\)
\(450\) −3.62423 2.31915i −0.170848 0.109326i
\(451\) 6.45785 3.72844i 0.304088 0.175565i
\(452\) 15.6352 + 9.02697i 0.735417 + 0.424593i
\(453\) −1.75634 + 2.88780i −0.0825198 + 0.135681i
\(454\) −18.5309 10.6988i −0.869698 0.502121i
\(455\) 0 0
\(456\) 21.7988 35.8421i 1.02082 1.67846i
\(457\) −32.7925 −1.53397 −0.766985 0.641666i \(-0.778244\pi\)
−0.766985 + 0.641666i \(0.778244\pi\)
\(458\) 6.33672 + 10.9755i 0.296095 + 0.512852i
\(459\) 3.70362 + 7.56765i 0.172870 + 0.353228i
\(460\) −7.27862 4.20231i −0.339368 0.195934i
\(461\) 9.23690 + 15.9988i 0.430205 + 0.745138i 0.996891 0.0787967i \(-0.0251078\pi\)
−0.566685 + 0.823934i \(0.691774\pi\)
\(462\) 0 0
\(463\) −0.201921 + 0.349738i −0.00938408 + 0.0162537i −0.870679 0.491851i \(-0.836320\pi\)
0.861295 + 0.508105i \(0.169654\pi\)
\(464\) 0.462594 0.267079i 0.0214754 0.0123988i
\(465\) −12.2060 + 6.68049i −0.566041 + 0.309801i
\(466\) −0.396580 + 0.686897i −0.0183712 + 0.0318199i
\(467\) −7.51283 + 13.0126i −0.347652 + 0.602151i −0.985832 0.167736i \(-0.946354\pi\)
0.638180 + 0.769887i \(0.279688\pi\)
\(468\) −10.6272 6.80035i −0.491242 0.314346i
\(469\) 0 0
\(470\) −12.6936 + 7.32866i −0.585512 + 0.338046i
\(471\) 0.376329 16.4869i 0.0173403 0.759675i
\(472\) 24.3644i 1.12146i
\(473\) 28.9122i 1.32938i
\(474\) 0.324412 14.2124i 0.0149007 0.652796i
\(475\) 10.2821 5.93635i 0.471773 0.272379i
\(476\) 0 0
\(477\) −22.2997 + 11.5515i −1.02103 + 0.528908i
\(478\) 6.91604 11.9789i 0.316332 0.547903i
\(479\) 15.5400 26.9161i 0.710041 1.22983i −0.254800 0.966994i \(-0.582010\pi\)
0.964841 0.262833i \(-0.0846569\pi\)
\(480\) 14.6454 8.01557i 0.668466 0.365859i
\(481\) 27.9077 16.1125i 1.27248 0.734669i
\(482\) 9.07944 15.7261i 0.413557 0.716302i
\(483\) 0 0
\(484\) 2.96029 + 5.12738i 0.134559 + 0.233063i
\(485\) −21.5547 12.4446i −0.978747 0.565080i
\(486\) 1.74232 15.2024i 0.0790333 0.689597i
\(487\) −6.74782 11.6876i −0.305773 0.529614i 0.671660 0.740859i \(-0.265582\pi\)
−0.977433 + 0.211245i \(0.932248\pi\)
\(488\) −11.1599 −0.505184
\(489\) −0.999224 + 1.64294i −0.0451865 + 0.0742965i
\(490\) 0 0
\(491\) −7.07098 4.08243i −0.319109 0.184238i 0.331886 0.943319i \(-0.392315\pi\)
−0.650995 + 0.759082i \(0.725648\pi\)
\(492\) −1.70149 + 2.79762i −0.0767089 + 0.126126i
\(493\) −0.879342 0.507688i −0.0396036 0.0228651i
\(494\) −28.0308 + 16.1836i −1.26116 + 0.728134i
\(495\) 1.05271 23.0475i 0.0473159 1.03591i
\(496\) 3.64269i 0.163562i
\(497\) 0 0
\(498\) −13.0740 + 7.15558i −0.585862 + 0.320649i
\(499\) 14.0097 + 24.2655i 0.627159 + 1.08627i 0.988119 + 0.153690i \(0.0491158\pi\)
−0.360960 + 0.932581i \(0.617551\pi\)
\(500\) 12.5973 0.563367
\(501\) 12.6154 20.7424i 0.563613 0.926703i
\(502\) 21.7658i 0.971455i
\(503\) 5.89656 0.262915 0.131457 0.991322i \(-0.458034\pi\)
0.131457 + 0.991322i \(0.458034\pi\)
\(504\) 0 0
\(505\) 1.97488 0.0878811
\(506\) 17.2987i 0.769022i
\(507\) 2.88196 + 5.26567i 0.127993 + 0.233857i
\(508\) −10.4977 −0.465758
\(509\) 7.01957 + 12.1582i 0.311137 + 0.538905i 0.978609 0.205730i \(-0.0659569\pi\)
−0.667472 + 0.744635i \(0.732624\pi\)
\(510\) 4.43098 + 2.69488i 0.196207 + 0.119331i
\(511\) 0 0
\(512\) 9.45558i 0.417882i
\(513\) 35.0365 + 23.5638i 1.54690 + 1.04037i
\(514\) 3.44968 1.99168i 0.152159 0.0878490i
\(515\) −2.67011 1.54159i −0.117659 0.0679305i
\(516\) −6.09528 11.1368i −0.268330 0.490269i
\(517\) 28.1014 + 16.2243i 1.23590 + 0.713546i
\(518\) 0 0
\(519\) 12.3250 + 0.281330i 0.541007 + 0.0123490i
\(520\) −22.7526 −0.997765
\(521\) −19.2229 33.2950i −0.842170 1.45868i −0.888057 0.459734i \(-0.847945\pi\)
0.0458870 0.998947i \(-0.485389\pi\)
\(522\) 0.848226 + 1.63746i 0.0371258 + 0.0716696i
\(523\) 9.08734 + 5.24658i 0.397362 + 0.229417i 0.685345 0.728219i \(-0.259651\pi\)
−0.287983 + 0.957635i \(0.592985\pi\)
\(524\) 2.57914 + 4.46720i 0.112670 + 0.195150i
\(525\) 0 0
\(526\) 4.88879 8.46764i 0.213161 0.369207i
\(527\) −5.99668 + 3.46219i −0.261220 + 0.150815i
\(528\) 5.16042 + 3.13852i 0.224578 + 0.136587i
\(529\) −2.20889 + 3.82591i −0.0960388 + 0.166344i
\(530\) −7.72935 + 13.3876i −0.335741 + 0.581521i
\(531\) −24.4974 1.11894i −1.06309 0.0485576i
\(532\) 0 0
\(533\) 6.40998 3.70080i 0.277647 0.160300i
\(534\) 14.2470 + 8.66489i 0.616527 + 0.374967i
\(535\) 6.46284i 0.279413i
\(536\) 37.3506i 1.61330i
\(537\) 9.12026 4.99163i 0.393568 0.215405i
\(538\) 8.47388 4.89240i 0.365335 0.210926i
\(539\) 0 0
\(540\) 4.45339 + 9.09968i 0.191644 + 0.391588i
\(541\) −22.5783 + 39.1067i −0.970715 + 1.68133i −0.277311 + 0.960780i \(0.589443\pi\)
−0.693405 + 0.720548i \(0.743890\pi\)
\(542\) −9.34112 + 16.1793i −0.401236 + 0.694960i
\(543\) 0.0514949 2.25598i 0.00220986 0.0968133i
\(544\) 7.19510 4.15409i 0.308487 0.178105i
\(545\) 3.47136 6.01257i 0.148697 0.257550i
\(546\) 0 0
\(547\) −4.05733 7.02751i −0.173479 0.300475i 0.766155 0.642656i \(-0.222168\pi\)
−0.939634 + 0.342181i \(0.888834\pi\)
\(548\) −0.754550 0.435640i −0.0322328 0.0186096i
\(549\) 0.512517 11.2208i 0.0218737 0.478890i
\(550\) 2.93166 + 5.07779i 0.125007 + 0.216518i
\(551\) −5.08854 −0.216779
\(552\) 10.6845 + 19.5217i 0.454762 + 0.830901i
\(553\) 0 0
\(554\) −13.2818 7.66827i −0.564291 0.325794i
\(555\) −25.8694 0.590494i −1.09809 0.0250651i
\(556\) 5.95311 + 3.43703i 0.252468 + 0.145763i
\(557\) 14.0925 8.13633i 0.597120 0.344747i −0.170788 0.985308i \(-0.554631\pi\)
0.767908 + 0.640561i \(0.221298\pi\)
\(558\) 12.5629 + 0.573818i 0.531828 + 0.0242916i
\(559\) 28.6978i 1.21379i
\(560\) 0 0
\(561\) 0.262001 11.4782i 0.0110617 0.484610i
\(562\) 11.8324 + 20.4942i 0.499118 + 0.864498i
\(563\) 10.2719 0.432908 0.216454 0.976293i \(-0.430551\pi\)
0.216454 + 0.976293i \(0.430551\pi\)
\(564\) −14.2449 0.325154i −0.599818 0.0136914i
\(565\) 32.7696i 1.37863i
\(566\) −2.96233 −0.124516
\(567\) 0 0
\(568\) −43.2098 −1.81304
\(569\) 20.6157i 0.864256i −0.901812 0.432128i \(-0.857763\pi\)
0.901812 0.432128i \(-0.142237\pi\)
\(570\) 25.9834 + 0.593097i 1.08833 + 0.0248421i
\(571\) 4.25655 0.178131 0.0890656 0.996026i \(-0.471612\pi\)
0.0890656 + 0.996026i \(0.471612\pi\)
\(572\) 8.59640 + 14.8894i 0.359434 + 0.622557i
\(573\) −0.226595 + 9.92706i −0.00946614 + 0.414709i
\(574\) 0 0
\(575\) 6.29836i 0.262660i
\(576\) −20.1861 0.922018i −0.841090 0.0384174i
\(577\) 14.6609 8.46446i 0.610340 0.352380i −0.162758 0.986666i \(-0.552039\pi\)
0.773099 + 0.634286i \(0.218706\pi\)
\(578\) −12.2168 7.05338i −0.508153 0.293382i
\(579\) 2.69963 + 0.0616216i 0.112193 + 0.00256091i
\(580\) −1.05736 0.610467i −0.0439045 0.0253483i
\(581\) 0 0
\(582\) 10.7999 + 19.7326i 0.447669 + 0.817943i
\(583\) 34.2228 1.41736
\(584\) 5.64730 + 9.78141i 0.233687 + 0.404758i
\(585\) 1.04491 22.8767i 0.0432017 0.945834i
\(586\) 25.3735 + 14.6494i 1.04817 + 0.605160i
\(587\) −12.0558 20.8812i −0.497594 0.861858i 0.502402 0.864634i \(-0.332450\pi\)
−0.999996 + 0.00277589i \(0.999116\pi\)
\(588\) 0 0
\(589\) −17.3507 + 30.0522i −0.714922 + 1.23828i
\(590\) −13.0725 + 7.54743i −0.538187 + 0.310723i
\(591\) −0.772738 + 33.8534i −0.0317862 + 1.39254i
\(592\) 3.38705 5.86654i 0.139207 0.241113i
\(593\) −19.2908 + 33.4126i −0.792178 + 1.37209i 0.132437 + 0.991191i \(0.457720\pi\)
−0.924616 + 0.380902i \(0.875614\pi\)
\(594\) −11.6370 + 17.3028i −0.477471 + 0.709941i
\(595\) 0 0
\(596\) 15.2378 8.79752i 0.624163 0.360360i
\(597\) 1.48352 0.811947i 0.0607164 0.0332308i
\(598\) 17.1705i 0.702154i
\(599\) 33.8236i 1.38199i 0.722857 + 0.690997i \(0.242828\pi\)
−0.722857 + 0.690997i \(0.757172\pi\)
\(600\) −6.44468 3.91960i −0.263103 0.160017i
\(601\) 27.4855 15.8688i 1.12116 0.647300i 0.179461 0.983765i \(-0.442565\pi\)
0.941696 + 0.336465i \(0.109231\pi\)
\(602\) 0 0
\(603\) 37.5544 + 1.71533i 1.52933 + 0.0698534i
\(604\) −1.01124 + 1.75153i −0.0411469 + 0.0712686i
\(605\) −5.37320 + 9.30666i −0.218452 + 0.378370i
\(606\) −1.52499 0.927487i −0.0619486 0.0376766i
\(607\) −0.169355 + 0.0977772i −0.00687391 + 0.00396865i −0.503433 0.864034i \(-0.667930\pi\)
0.496559 + 0.868003i \(0.334597\pi\)
\(608\) 20.8181 36.0581i 0.844287 1.46235i
\(609\) 0 0
\(610\) −3.45702 5.98774i −0.139971 0.242436i
\(611\) 27.8931 + 16.1041i 1.12843 + 0.651502i
\(612\) 2.31892 + 4.47656i 0.0937367 + 0.180954i
\(613\) −1.46664 2.54029i −0.0592370 0.102602i 0.834886 0.550423i \(-0.185533\pi\)
−0.894123 + 0.447821i \(0.852200\pi\)
\(614\) 2.63912 0.106506
\(615\) −5.94180 0.135627i −0.239596 0.00546902i
\(616\) 0 0
\(617\) −7.86982 4.54365i −0.316827 0.182920i 0.333150 0.942874i \(-0.391888\pi\)
−0.649977 + 0.759953i \(0.725222\pi\)
\(618\) 1.33785 + 2.44440i 0.0538161 + 0.0983282i
\(619\) 24.8586 + 14.3521i 0.999152 + 0.576861i 0.907997 0.418976i \(-0.137611\pi\)
0.0911550 + 0.995837i \(0.470944\pi\)
\(620\) −7.21068 + 4.16309i −0.289588 + 0.167194i
\(621\) −20.1189 + 9.84623i −0.807345 + 0.395116i
\(622\) 10.8717i 0.435916i
\(623\) 0 0
\(624\) 5.12217 + 3.11526i 0.205051 + 0.124710i
\(625\) 7.77986 + 13.4751i 0.311194 + 0.539004i
\(626\) 16.4321 0.656758
\(627\) −27.6243 50.4726i −1.10321 2.01568i
\(628\) 9.86793i 0.393773i
\(629\) −12.8768 −0.513433
\(630\) 0 0
\(631\) −20.7691 −0.826805 −0.413403 0.910548i \(-0.635660\pi\)
−0.413403 + 0.910548i \(0.635660\pi\)
\(632\) 24.9219i 0.991340i
\(633\) 21.5561 35.4430i 0.856779 1.40873i
\(634\) −2.88781 −0.114689
\(635\) −9.52711 16.5014i −0.378072 0.654839i
\(636\) −13.1824 + 7.21487i −0.522716 + 0.286088i
\(637\) 0 0
\(638\) 2.51297i 0.0994895i
\(639\) 1.98441 43.4455i 0.0785019 1.71868i
\(640\) 5.92345 3.41990i 0.234145 0.135184i
\(641\) −39.7733 22.9632i −1.57095 0.906990i −0.996052 0.0887664i \(-0.971708\pi\)
−0.574900 0.818224i \(-0.694959\pi\)
\(642\) 3.03522 4.99057i 0.119791 0.196962i
\(643\) −9.15428 5.28523i −0.361010 0.208429i 0.308514 0.951220i \(-0.400168\pi\)
−0.669524 + 0.742791i \(0.733502\pi\)
\(644\) 0 0
\(645\) 11.9743 19.6884i 0.471488 0.775230i
\(646\) 12.9336 0.508866
\(647\) −19.2562 33.3526i −0.757038 1.31123i −0.944355 0.328928i \(-0.893313\pi\)
0.187317 0.982299i \(-0.440021\pi\)
\(648\) 2.44545 26.7138i 0.0960664 1.04942i
\(649\) 28.9402 + 16.7087i 1.13600 + 0.655872i
\(650\) 2.90993 + 5.04015i 0.114137 + 0.197691i
\(651\) 0 0
\(652\) −0.575323 + 0.996488i −0.0225314 + 0.0390255i
\(653\) 11.0867 6.40089i 0.433855 0.250486i −0.267133 0.963660i \(-0.586076\pi\)
0.700988 + 0.713173i \(0.252743\pi\)
\(654\) −5.50431 + 3.01257i −0.215236 + 0.117801i
\(655\) −4.68137 + 8.10837i −0.182916 + 0.316820i
\(656\) 0.777952 1.34745i 0.0303739 0.0526092i
\(657\) −10.0941 + 5.22890i −0.393809 + 0.203999i
\(658\) 0 0
\(659\) 41.5777 24.0049i 1.61964 0.935097i 0.632622 0.774461i \(-0.281979\pi\)
0.987014 0.160636i \(-0.0513546\pi\)
\(660\) 0.315042 13.8019i 0.0122630 0.537238i
\(661\) 10.8312i 0.421285i −0.977563 0.210643i \(-0.932444\pi\)
0.977563 0.210643i \(-0.0675557\pi\)
\(662\) 4.79182i 0.186239i
\(663\) 0.260059 11.3931i 0.0100998 0.442472i
\(664\) −22.6276 + 13.0640i −0.878121 + 0.506983i
\(665\) 0 0
\(666\) 19.6989 + 12.6053i 0.763315 + 0.488446i
\(667\) 1.34971 2.33777i 0.0522611 0.0905188i
\(668\) 7.26354 12.5808i 0.281035 0.486767i
\(669\) 4.70876 2.57716i 0.182051 0.0996387i
\(670\) 20.0402 11.5702i 0.774219 0.446995i
\(671\) −7.65323 + 13.2558i −0.295450 + 0.511734i
\(672\) 0 0
\(673\) −6.19553 10.7310i −0.238820 0.413649i 0.721556 0.692356i \(-0.243427\pi\)
−0.960376 + 0.278707i \(0.910094\pi\)
\(674\) −11.0756 6.39449i −0.426616 0.246307i
\(675\) 4.23696 6.29983i 0.163081 0.242481i
\(676\) 1.79595 + 3.11068i 0.0690752 + 0.119642i
\(677\) 28.9895 1.11416 0.557078 0.830460i \(-0.311922\pi\)
0.557078 + 0.830460i \(0.311922\pi\)
\(678\) 15.3900 25.3045i 0.591048 0.971813i
\(679\) 0 0
\(680\) 7.87364 + 4.54585i 0.301940 + 0.174325i
\(681\) 19.6191 32.2581i 0.751805 1.23613i
\(682\) −14.8413 8.56862i −0.568302 0.328109i
\(683\) −0.132048 + 0.0762380i −0.00505268 + 0.00291717i −0.502524 0.864563i \(-0.667595\pi\)
0.497472 + 0.867480i \(0.334262\pi\)
\(684\) 21.2813 + 13.6179i 0.813712 + 0.520695i
\(685\) 1.58145i 0.0604242i
\(686\) 0 0
\(687\) −19.6162 + 10.7362i −0.748404 + 0.409610i
\(688\) 3.01631 + 5.22441i 0.114996 + 0.199179i
\(689\) 33.9691 1.29412
\(690\) −7.16447 + 11.7800i −0.272747 + 0.448455i
\(691\) 43.2353i 1.64475i 0.568948 + 0.822373i \(0.307350\pi\)
−0.568948 + 0.822373i \(0.692650\pi\)
\(692\) 7.37691 0.280428
\(693\) 0 0
\(694\) 2.11225 0.0801799
\(695\) 12.4771i 0.473282i
\(696\) 1.55213 + 2.83591i 0.0588332 + 0.107495i
\(697\) −2.95761 −0.112027
\(698\) 14.3339 + 24.8271i 0.542546 + 0.939718i
\(699\) −1.19573 0.727234i −0.0452267 0.0275065i
\(700\) 0 0
\(701\) 11.5821i 0.437451i 0.975786 + 0.218726i \(0.0701900\pi\)
−0.975786 + 0.218726i \(0.929810\pi\)
\(702\) −11.5507 + 17.1745i −0.435954 + 0.648210i
\(703\) −55.8863 + 32.2660i −2.10779 + 1.21693i
\(704\) 23.8472 + 13.7682i 0.898774 + 0.518907i
\(705\) −12.4168 22.6869i −0.467643 0.854437i
\(706\) 9.21116 + 5.31807i 0.346667 + 0.200148i
\(707\) 0 0
\(708\) −14.6701 0.334860i −0.551337 0.0125848i
\(709\) −37.8948 −1.42317 −0.711584 0.702601i \(-0.752022\pi\)
−0.711584 + 0.702601i \(0.752022\pi\)
\(710\) −13.3852 23.1838i −0.502337 0.870073i
\(711\) 25.0579 + 1.14454i 0.939743 + 0.0429235i
\(712\) 25.3162 + 14.6163i 0.948765 + 0.547770i
\(713\) −9.20437 15.9424i −0.344707 0.597049i
\(714\) 0 0
\(715\) −15.6033 + 27.0256i −0.583529 + 1.01070i
\(716\) 5.38777 3.11063i 0.201351 0.116250i
\(717\) 20.8526 + 12.6824i 0.778754 + 0.473631i
\(718\) 10.2821 17.8091i 0.383724 0.664630i
\(719\) −23.3158 + 40.3842i −0.869534 + 1.50608i −0.00706058 + 0.999975i \(0.502247\pi\)
−0.862474 + 0.506102i \(0.831086\pi\)
\(720\) −2.21425 4.27450i −0.0825202 0.159301i
\(721\) 0 0
\(722\) 39.9806 23.0828i 1.48792 0.859054i
\(723\) 27.3755 + 16.6495i 1.01811 + 0.619203i
\(724\) 1.35028i 0.0501826i
\(725\) 0.914958i 0.0339807i
\(726\) 8.51995 4.66307i 0.316205 0.173063i
\(727\) 3.72659 2.15155i 0.138212 0.0797965i −0.429300 0.903162i \(-0.641240\pi\)
0.567511 + 0.823366i \(0.307906\pi\)
\(728\) 0 0
\(729\) 26.7473 + 3.68562i 0.990639 + 0.136505i
\(730\) −3.49875 + 6.06002i −0.129495 + 0.224291i
\(731\) 5.73369 9.93104i 0.212068 0.367313i
\(732\) 0.153379 6.71949i 0.00566905 0.248360i
\(733\) 12.1337 7.00539i 0.448168 0.258750i −0.258888 0.965907i \(-0.583356\pi\)
0.707056 + 0.707157i \(0.250023\pi\)
\(734\) −2.82143 + 4.88685i −0.104141 + 0.180377i
\(735\) 0 0
\(736\) 11.0438 + 19.1285i 0.407081 + 0.705086i
\(737\) −44.3653 25.6143i −1.63422 0.943516i
\(738\) 4.52452 + 2.89525i 0.166550 + 0.106575i
\(739\) −18.9313 32.7901i −0.696401 1.20620i −0.969706 0.244274i \(-0.921450\pi\)
0.273305 0.961927i \(-0.411883\pi\)
\(740\) −15.4837 −0.569191
\(741\) −27.4195 50.0985i −1.00728 1.84041i
\(742\) 0 0
\(743\) −24.0489 13.8847i −0.882269 0.509378i −0.0108634 0.999941i \(-0.503458\pi\)
−0.871406 + 0.490563i \(0.836791\pi\)
\(744\) 22.0409 + 0.503105i 0.808058 + 0.0184447i
\(745\) 27.6579 + 15.9683i 1.01331 + 0.585034i
\(746\) −24.5626 + 14.1812i −0.899300 + 0.519211i
\(747\) −12.0961 23.3510i −0.442575 0.854369i
\(748\) 6.87007i 0.251195i
\(749\) 0 0
\(750\) 0.471587 20.6601i 0.0172199 0.754400i
\(751\) 8.67540 + 15.0262i 0.316570 + 0.548315i 0.979770 0.200127i \(-0.0641355\pi\)
−0.663200 + 0.748442i \(0.730802\pi\)
\(752\) 6.77054 0.246896
\(753\) 38.3953 + 0.876410i 1.39920 + 0.0319382i
\(754\) 2.49434i 0.0908387i
\(755\) −3.67100 −0.133601
\(756\) 0 0
\(757\) 18.8111 0.683701 0.341850 0.939754i \(-0.388946\pi\)
0.341850 + 0.939754i \(0.388946\pi\)
\(758\) 0.403872i 0.0146693i
\(759\) 30.5153 + 0.696541i 1.10763 + 0.0252828i
\(760\) 45.5628 1.65274
\(761\) −4.22520 7.31825i −0.153163 0.265286i 0.779225 0.626744i \(-0.215613\pi\)
−0.932389 + 0.361457i \(0.882279\pi\)
\(762\) −0.392986 + 17.2166i −0.0142364 + 0.623693i
\(763\) 0 0
\(764\) 5.94167i 0.214962i
\(765\) −4.93224 + 7.70783i −0.178326 + 0.278677i
\(766\) −21.0840 + 12.1728i −0.761794 + 0.439822i
\(767\) 28.7257 + 16.5848i 1.03723 + 0.598843i
\(768\) −29.5074 0.673534i −1.06476 0.0243041i
\(769\) −19.8100 11.4373i −0.714366 0.412440i 0.0983092 0.995156i \(-0.468657\pi\)
−0.812676 + 0.582716i \(0.801990\pi\)
\(770\) 0 0
\(771\) 3.37445 + 6.16550i 0.121528 + 0.222045i
\(772\) 1.61581 0.0581544
\(773\) 18.8374 + 32.6273i 0.677533 + 1.17352i 0.975722 + 0.219015i \(0.0702843\pi\)
−0.298189 + 0.954507i \(0.596382\pi\)
\(774\) −18.4930 + 9.57963i −0.664717 + 0.344333i
\(775\) 5.40363 + 3.11978i 0.194104 + 0.112066i
\(776\) 19.7175 + 34.1517i 0.707817 + 1.22598i
\(777\) 0 0
\(778\) −2.16888 + 3.75660i −0.0777579 + 0.134681i
\(779\) −12.8362 + 7.41099i −0.459905 + 0.265526i
\(780\) 0.312706 13.6996i 0.0111967 0.490524i
\(781\) −29.6324 + 51.3249i −1.06033 + 1.83655i
\(782\) −3.43058 + 5.94194i −0.122677 + 0.212483i
\(783\) −2.92266 + 1.43035i −0.104447 + 0.0511167i
\(784\) 0 0
\(785\) 15.5116 8.95561i 0.553632 0.319639i
\(786\) 7.42296 4.06267i 0.264768 0.144911i
\(787\) 23.4661i 0.836475i −0.908338 0.418237i \(-0.862648\pi\)
0.908338 0.418237i \(-0.137352\pi\)
\(788\) 20.2624i 0.721818i
\(789\) 14.7402 + 8.96488i 0.524766 + 0.319158i
\(790\) 13.3716 7.72011i 0.475741 0.274669i
\(791\) 0 0
\(792\) −19.7030 + 30.7907i −0.700116 + 1.09410i
\(793\) −7.59650 + 13.1575i −0.269760 + 0.467237i
\(794\) −10.9256 + 18.9237i −0.387734 + 0.671575i
\(795\) −23.3048 14.1738i −0.826536 0.502692i
\(796\) 0.876386 0.505981i 0.0310627 0.0179340i
\(797\) 22.8856 39.6390i 0.810648 1.40408i −0.101763 0.994809i \(-0.532448\pi\)
0.912411 0.409275i \(-0.134218\pi\)
\(798\) 0 0
\(799\) −6.43503 11.1458i −0.227655 0.394310i
\(800\) −6.48352 3.74326i −0.229227 0.132344i
\(801\) −15.8587 + 24.7831i −0.560340 + 0.875667i
\(802\) −3.01448 5.22123i −0.106445 0.184368i
\(803\) 15.4912 0.546674
\(804\) 22.4893 + 0.513339i 0.793135 + 0.0181041i
\(805\) 0 0
\(806\) −14.7313 8.50510i −0.518887 0.299579i
\(807\) 8.28908 + 15.1451i 0.291789 + 0.533132i
\(808\) −2.70984 1.56453i −0.0953317 0.0550398i
\(809\) 11.4669 6.62041i 0.403154 0.232761i −0.284690 0.958620i \(-0.591891\pi\)
0.687844 + 0.725858i \(0.258557\pi\)
\(810\) 15.0906 6.96312i 0.530230 0.244659i
\(811\) 56.0437i 1.96796i −0.178275 0.983981i \(-0.557052\pi\)
0.178275 0.983981i \(-0.442948\pi\)
\(812\) 0 0
\(813\) −28.1645 17.1294i −0.987771 0.600754i
\(814\) −15.9345 27.5994i −0.558505 0.967359i
\(815\) −2.08853 −0.0731579
\(816\) −1.15014 2.10144i −0.0402629 0.0735650i
\(817\) 57.4685i 2.01057i
\(818\) 0.868116 0.0303530
\(819\) 0 0
\(820\) −3.55636 −0.124193
\(821\) 56.3224i 1.96567i 0.184499 + 0.982833i \(0.440934\pi\)
−0.184499 + 0.982833i \(0.559066\pi\)
\(822\) −0.742716 + 1.22119i −0.0259052 + 0.0425938i
\(823\) 17.0436 0.594103 0.297051 0.954862i \(-0.403997\pi\)
0.297051 + 0.954862i \(0.403997\pi\)
\(824\) 2.44253 + 4.23058i 0.0850895 + 0.147379i
\(825\) −9.07537 + 4.96705i −0.315964 + 0.172931i
\(826\) 0 0
\(827\) 45.7715i 1.59163i −0.605539 0.795816i \(-0.707042\pi\)
0.605539 0.795816i \(-0.292958\pi\)
\(828\) −11.9011 + 6.16495i −0.413593 + 0.214247i
\(829\) 30.5567 17.6419i 1.06128 0.612730i 0.135493 0.990778i \(-0.456738\pi\)
0.925786 + 0.378049i \(0.123405\pi\)
\(830\) −14.0188 8.09376i −0.486600 0.280938i
\(831\) 14.0618 23.1207i 0.487798 0.802047i
\(832\) 23.6704 + 13.6661i 0.820623 + 0.473787i
\(833\) 0 0
\(834\) 5.85975 9.63472i 0.202907 0.333623i
\(835\) 26.3680 0.912502
\(836\) −17.2146 29.8166i −0.595380 1.03123i
\(837\) −1.51808 + 22.1380i −0.0524724 + 0.765202i
\(838\) −12.9109 7.45409i −0.445998 0.257497i
\(839\) 22.3195 + 38.6585i 0.770555 + 1.33464i 0.937259 + 0.348634i \(0.113354\pi\)
−0.166704 + 0.986007i \(0.553312\pi\)
\(840\) 0 0
\(841\) −14.3039 + 24.7751i −0.493239 + 0.854315i
\(842\) 22.6670 13.0868i 0.781157 0.451001i
\(843\) −36.6287 + 20.0473i −1.26156 + 0.690466i
\(844\) 12.4114 21.4971i 0.427216 0.739960i
\(845\) −3.25982 + 5.64618i −0.112141 + 0.194235i
\(846\) −1.06653 + 23.3501i −0.0366682 + 0.802793i
\(847\) 0 0
\(848\) 6.18404 3.57036i 0.212361 0.122607i
\(849\) 0.119280 5.22561i 0.00409367 0.179342i
\(850\) 2.32556i 0.0797661i
\(851\) 34.2336i 1.17351i
\(852\) 0.593866 26.0171i 0.0203455 0.891332i
\(853\) −47.7652 + 27.5772i −1.63545 + 0.944227i −0.653077 + 0.757292i \(0.726522\pi\)
−0.982372 + 0.186935i \(0.940145\pi\)
\(854\) 0 0
\(855\) −2.09247 + 45.8114i −0.0715610 + 1.56672i
\(856\) 5.11994 8.86800i 0.174996 0.303102i
\(857\) −19.0771 + 33.0425i −0.651660 + 1.12871i 0.331059 + 0.943610i \(0.392594\pi\)
−0.982720 + 0.185099i \(0.940739\pi\)
\(858\) 24.7411 13.5411i 0.844648 0.462286i
\(859\) −35.0465 + 20.2341i −1.19577 + 0.690378i −0.959609 0.281336i \(-0.909222\pi\)
−0.236160 + 0.971714i \(0.575889\pi\)
\(860\) 6.89444 11.9415i 0.235099 0.407203i
\(861\) 0 0
\(862\) −2.30541 3.99309i −0.0785226 0.136005i
\(863\) −31.3519 18.1011i −1.06723 0.616167i −0.139808 0.990179i \(-0.544649\pi\)
−0.927424 + 0.374012i \(0.877982\pi\)
\(864\) 1.82146 26.5622i 0.0619673 0.903666i
\(865\) 6.69488 + 11.5959i 0.227633 + 0.394272i
\(866\) −8.81216 −0.299449
\(867\) 12.9342 21.2667i 0.439269 0.722255i
\(868\) 0 0
\(869\) −29.6024 17.0910i −1.00419 0.579771i
\(870\) −1.04078 + 1.71127i −0.0352856 + 0.0580173i
\(871\) −44.0365 25.4245i −1.49212 0.861475i
\(872\) −9.52645 + 5.50010i −0.322606 + 0.186257i
\(873\) −35.2436 + 18.2567i −1.19281 + 0.617894i
\(874\) 34.3846i 1.16307i
\(875\) 0 0
\(876\) −5.96712 + 3.26587i −0.201610 + 0.110344i
\(877\) 5.53439 + 9.58584i 0.186883 + 0.323691i 0.944209 0.329346i \(-0.106828\pi\)
−0.757326 + 0.653036i \(0.773495\pi\)
\(878\) −16.2101 −0.547064
\(879\) −26.8635 + 44.1694i −0.906082 + 1.48980i
\(880\) 6.55998i 0.221137i
\(881\) −8.87036 −0.298850 −0.149425 0.988773i \(-0.547742\pi\)
−0.149425 + 0.988773i \(0.547742\pi\)
\(882\) 0 0
\(883\) −14.1903 −0.477540 −0.238770 0.971076i \(-0.576744\pi\)
−0.238770 + 0.971076i \(0.576744\pi\)
\(884\) 6.81915i 0.229353i
\(885\) −12.7874 23.3641i −0.429845 0.785375i
\(886\) 1.04413 0.0350782
\(887\) −19.5180 33.8062i −0.655350 1.13510i −0.981806 0.189887i \(-0.939188\pi\)
0.326456 0.945213i \(-0.394146\pi\)
\(888\) 35.0289 + 21.3043i 1.17549 + 0.714925i
\(889\) 0 0
\(890\) 18.1109i 0.607080i
\(891\) −30.0538 21.2246i −1.00684 0.711050i
\(892\) 2.78169 1.60601i 0.0931378 0.0537732i
\(893\) −55.8570 32.2490i −1.86918 1.07917i
\(894\) −13.8579 25.3200i −0.463478 0.846826i
\(895\) 9.77931 + 5.64609i 0.326886 + 0.188728i
\(896\) 0 0
\(897\) 30.2891 + 0.691378i 1.01132 + 0.0230844i
\(898\) −15.6157 −0.521103
\(899\) −1.33711 2.31595i −0.0445952 0.0772411i
\(900\) 2.44861 3.82655i 0.0816204 0.127552i
\(901\) −11.7552 6.78687i −0.391622 0.226103i
\(902\) −3.65992 6.33916i −0.121862 0.211071i
\(903\) 0 0
\(904\) 25.9605 44.9648i 0.863432 1.49551i
\(905\) 2.12252 1.22544i 0.0705550 0.0407350i
\(906\) 2.83473 + 1.72406i 0.0941775 + 0.0572779i
\(907\) −4.93487 + 8.54745i −0.163860 + 0.283813i −0.936250 0.351335i \(-0.885728\pi\)
0.772390 + 0.635148i \(0.219061\pi\)
\(908\) 11.2961 19.5654i 0.374873 0.649300i
\(909\) 1.69751 2.65277i 0.0563028 0.0879868i
\(910\) 0 0
\(911\) −46.6335 + 26.9239i −1.54504 + 0.892028i −0.546529 + 0.837440i \(0.684051\pi\)
−0.998509 + 0.0545881i \(0.982615\pi\)
\(912\) −10.2573 6.23842i −0.339654 0.206575i
\(913\) 35.8363i 1.18601i
\(914\) 32.1898i 1.06475i
\(915\) 10.7017 5.85715i 0.353787 0.193632i
\(916\) −11.5882 + 6.69046i −0.382885 + 0.221059i
\(917\) 0 0
\(918\) 7.42857 3.63555i 0.245179 0.119991i
\(919\) −11.0899 + 19.2084i −0.365824 + 0.633625i −0.988908 0.148530i \(-0.952546\pi\)
0.623084 + 0.782155i \(0.285879\pi\)
\(920\) −12.0853 + 20.9324i −0.398442 + 0.690122i
\(921\) −0.106265 + 4.65545i −0.00350156 + 0.153402i
\(922\) 15.7047 9.06714i 0.517208 0.298610i
\(923\) −29.4128 + 50.9444i −0.968133 + 1.67686i
\(924\) 0 0
\(925\) 5.80167 + 10.0488i 0.190758 + 0.330402i
\(926\) 0.343310 + 0.198210i 0.0112819 + 0.00651359i
\(927\) −4.36584 + 2.26157i −0.143393 + 0.0742796i
\(928\) 1.60433 + 2.77878i 0.0526647 + 0.0912180i
\(929\) −54.9907 −1.80419 −0.902093 0.431541i \(-0.857970\pi\)
−0.902093 + 0.431541i \(0.857970\pi\)
\(930\) 6.55772 + 11.9817i 0.215036 + 0.392895i
\(931\) 0 0
\(932\) −0.725243 0.418719i −0.0237561 0.0137156i
\(933\) 19.1779 + 0.437754i 0.627856 + 0.0143314i
\(934\) 12.7734 + 7.37475i 0.417960 + 0.241309i
\(935\) 10.7992 6.23491i 0.353171 0.203903i
\(936\) −19.5570 + 30.5625i −0.639239 + 0.998966i
\(937\) 29.3132i 0.957622i 0.877918 + 0.478811i \(0.158932\pi\)
−0.877918 + 0.478811i \(0.841068\pi\)
\(938\) 0 0
\(939\) −0.661646 + 28.9865i −0.0215920 + 0.945940i
\(940\) −7.73777 13.4022i −0.252378 0.437132i
\(941\) −15.1752 −0.494696 −0.247348 0.968927i \(-0.579559\pi\)
−0.247348 + 0.968927i \(0.579559\pi\)
\(942\) −16.1839 0.369413i −0.527299 0.0120361i
\(943\) 7.86293i 0.256052i
\(944\) 6.97265 0.226940
\(945\) 0 0
\(946\) 28.3808 0.922739
\(947\) 2.62670i 0.0853561i 0.999089 + 0.0426781i \(0.0135890\pi\)
−0.999089 + 0.0426781i \(0.986411\pi\)
\(948\) 15.0058 + 0.342521i 0.487365 + 0.0111246i
\(949\) 15.3764 0.499139
\(950\) −5.82725 10.0931i −0.189061 0.327463i
\(951\) 0.116279 5.09415i 0.00377060 0.165189i
\(952\) 0 0
\(953\) 40.5520i 1.31361i 0.754061 + 0.656805i \(0.228092\pi\)
−0.754061 + 0.656805i \(0.771908\pi\)
\(954\) 11.3392 + 21.8898i 0.367121 + 0.708709i
\(955\) −9.33981 + 5.39234i −0.302229 + 0.174492i
\(956\) 12.6476 + 7.30212i 0.409054 + 0.236167i
\(957\) 4.43293 + 0.101186i 0.143296 + 0.00327088i
\(958\) −26.4214 15.2544i −0.853637 0.492847i
\(959\) 0 0
\(960\) −10.5370 19.2523i −0.340081 0.621366i
\(961\) 12.7631 0.411713
\(962\) −15.8164 27.3948i −0.509942 0.883245i
\(963\) 8.68124 + 5.55513i 0.279749 + 0.179012i
\(964\) 16.6039 + 9.58629i 0.534777 + 0.308754i
\(965\) 1.46643 + 2.53993i 0.0472059 + 0.0817631i
\(966\) 0 0
\(967\) 6.47468 11.2145i 0.208212 0.360633i −0.742939 0.669359i \(-0.766569\pi\)
0.951151 + 0.308725i \(0.0999023\pi\)
\(968\) 14.7457 8.51343i 0.473945 0.273632i
\(969\) −0.520778 + 22.8151i −0.0167298 + 0.732927i
\(970\) −12.2159 + 21.1585i −0.392228 + 0.679359i
\(971\) −8.26077 + 14.3081i −0.265101 + 0.459168i −0.967590 0.252526i \(-0.918739\pi\)
0.702489 + 0.711694i \(0.252072\pi\)
\(972\) 16.0511 + 1.83958i 0.514839 + 0.0590047i
\(973\) 0 0
\(974\) −11.4728 + 6.62381i −0.367611 + 0.212240i
\(975\) −9.00810 + 4.93024i −0.288490 + 0.157894i
\(976\) 3.19375i 0.102229i
\(977\) 6.35928i 0.203451i −0.994812 0.101726i \(-0.967564\pi\)
0.994812 0.101726i \(-0.0324364\pi\)
\(978\) 1.61275 + 0.980860i 0.0515700 + 0.0313644i
\(979\) 34.7227 20.0472i 1.10974 0.640711i
\(980\) 0 0
\(981\) −5.09261 9.83102i −0.162594 0.313880i
\(982\) −4.00740 + 6.94103i −0.127881 + 0.221497i
\(983\) 1.11487 1.93102i 0.0355590 0.0615899i −0.847698 0.530479i \(-0.822012\pi\)
0.883257 + 0.468889i \(0.155346\pi\)
\(984\) 8.04560 + 4.89326i 0.256484 + 0.155992i
\(985\) −31.8508 + 18.3891i −1.01485 + 0.585924i
\(986\) −0.498358 + 0.863181i −0.0158709 + 0.0274893i
\(987\) 0 0
\(988\) −17.0870 29.5956i −0.543610 0.941561i
\(989\) 26.4021 + 15.2433i 0.839538 + 0.484708i
\(990\) −22.6239 1.03337i −0.719036 0.0328425i
\(991\) 24.7285 + 42.8310i 0.785527 + 1.36057i 0.928684 + 0.370872i \(0.120941\pi\)
−0.143157 + 0.989700i \(0.545726\pi\)
\(992\) 21.8815 0.694738
\(993\) 8.45286 + 0.192945i 0.268243 + 0.00612292i
\(994\) 0 0
\(995\) 1.59072 + 0.918403i 0.0504293 + 0.0291153i
\(996\) −7.55503 13.8039i −0.239390 0.437393i
\(997\) 7.28219 + 4.20437i 0.230629 + 0.133154i 0.610862 0.791737i \(-0.290823\pi\)
−0.380233 + 0.924891i \(0.624156\pi\)
\(998\) 23.8195 13.7522i 0.753993 0.435318i
\(999\) −23.0292 + 34.2416i −0.728612 + 1.08336i
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 441.2.i.d.68.10 48
3.2 odd 2 1323.2.i.d.1097.8 48
7.2 even 3 441.2.o.e.293.9 yes 48
7.3 odd 6 441.2.s.d.374.16 48
7.4 even 3 441.2.s.d.374.15 48
7.5 odd 6 441.2.o.e.293.10 yes 48
7.6 odd 2 inner 441.2.i.d.68.9 48
9.2 odd 6 441.2.s.d.362.16 48
9.7 even 3 1323.2.s.d.656.9 48
21.2 odd 6 1323.2.o.e.881.16 48
21.5 even 6 1323.2.o.e.881.15 48
21.11 odd 6 1323.2.s.d.962.10 48
21.17 even 6 1323.2.s.d.962.9 48
21.20 even 2 1323.2.i.d.1097.18 48
63.2 odd 6 441.2.o.e.146.10 yes 48
63.11 odd 6 inner 441.2.i.d.227.15 48
63.16 even 3 1323.2.o.e.440.15 48
63.20 even 6 441.2.s.d.362.15 48
63.25 even 3 1323.2.i.d.521.18 48
63.34 odd 6 1323.2.s.d.656.10 48
63.38 even 6 inner 441.2.i.d.227.16 48
63.47 even 6 441.2.o.e.146.9 48
63.52 odd 6 1323.2.i.d.521.8 48
63.61 odd 6 1323.2.o.e.440.16 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.i.d.68.9 48 7.6 odd 2 inner
441.2.i.d.68.10 48 1.1 even 1 trivial
441.2.i.d.227.15 48 63.11 odd 6 inner
441.2.i.d.227.16 48 63.38 even 6 inner
441.2.o.e.146.9 48 63.47 even 6
441.2.o.e.146.10 yes 48 63.2 odd 6
441.2.o.e.293.9 yes 48 7.2 even 3
441.2.o.e.293.10 yes 48 7.5 odd 6
441.2.s.d.362.15 48 63.20 even 6
441.2.s.d.362.16 48 9.2 odd 6
441.2.s.d.374.15 48 7.4 even 3
441.2.s.d.374.16 48 7.3 odd 6
1323.2.i.d.521.8 48 63.52 odd 6
1323.2.i.d.521.18 48 63.25 even 3
1323.2.i.d.1097.8 48 3.2 odd 2
1323.2.i.d.1097.18 48 21.20 even 2
1323.2.o.e.440.15 48 63.16 even 3
1323.2.o.e.440.16 48 63.61 odd 6
1323.2.o.e.881.15 48 21.5 even 6
1323.2.o.e.881.16 48 21.2 odd 6
1323.2.s.d.656.9 48 9.7 even 3
1323.2.s.d.656.10 48 63.34 odd 6
1323.2.s.d.962.9 48 21.17 even 6
1323.2.s.d.962.10 48 21.11 odd 6