Properties

Label 722.2.e.i.389.1
Level $722$
Weight $2$
Character 722.389
Analytic conductor $5.765$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [722,2,Mod(99,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\), degree \(6\), 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: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 389.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 722.389
Dual form 722.2.e.i.245.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 + 0.984808i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +O(q^{10})\) \(q+(0.173648 + 0.984808i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.766044 - 0.642788i) q^{6} +(2.00000 - 3.46410i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.347296 + 1.96962i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.53209 - 1.28558i) q^{13} +(3.75877 + 1.36808i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-1.04189 - 5.90885i) q^{17} -2.00000 q^{18} +(0.694593 + 3.93923i) q^{21} +(2.29813 - 1.92836i) q^{22} +(5.63816 - 2.05212i) q^{23} +(0.939693 + 0.342020i) q^{24} +(-3.83022 - 3.21394i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-2.50000 - 4.33013i) q^{27} +(-0.694593 + 3.93923i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.766044 + 0.642788i) q^{32} +(2.81908 + 1.02606i) q^{33} +(5.63816 - 2.05212i) q^{34} +(-0.347296 - 1.96962i) q^{36} +10.0000 q^{37} +2.00000 q^{39} +(-6.89440 + 5.78509i) q^{41} +(-3.75877 + 1.36808i) q^{42} +(3.75877 + 1.36808i) q^{43} +(2.29813 + 1.92836i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-0.173648 + 0.984808i) q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.50000 - 4.33013i) q^{50} +(4.59627 + 3.85673i) q^{51} +(1.87939 + 0.684040i) q^{52} +(5.63816 - 2.05212i) q^{53} +(3.83022 - 3.21394i) q^{54} -4.00000 q^{56} +(1.56283 + 8.86327i) q^{59} +(3.75877 - 1.36808i) q^{61} +(1.87939 + 0.684040i) q^{62} +(6.12836 + 5.14230i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.520945 + 2.95442i) q^{66} +(1.21554 - 6.89365i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(-5.63816 - 2.05212i) q^{71} +(1.87939 - 0.684040i) q^{72} +(-0.766044 + 0.642788i) q^{73} +(1.73648 + 9.84808i) q^{74} +5.00000 q^{75} -12.0000 q^{77} +(0.347296 + 1.96962i) q^{78} +(3.06418 - 2.57115i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-6.89440 - 5.78509i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-2.00000 - 3.46410i) q^{84} +(-0.694593 + 3.93923i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-4.59627 - 3.85673i) q^{89} +(-7.51754 + 2.73616i) q^{91} +(-4.59627 + 3.85673i) q^{92} +(0.347296 + 1.96962i) q^{93} -1.00000 q^{96} +(-2.95202 - 16.7417i) q^{97} +(6.89440 - 5.78509i) q^{98} +(5.63816 - 2.05212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 12 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 12 q^{7} - 3 q^{8} - 9 q^{11} + 3 q^{12} - 12 q^{18} + 6 q^{26} - 15 q^{27} + 6 q^{31} + 60 q^{37} + 12 q^{39} + 18 q^{46} - 27 q^{49} + 15 q^{50} - 24 q^{56} - 3 q^{64} + 18 q^{68} - 18 q^{69} + 30 q^{75} - 72 q^{77} - 9 q^{83} - 12 q^{84} - 9 q^{88} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 + 0.984808i 0.122788 + 0.696364i
\(3\) −0.766044 + 0.642788i −0.442276 + 0.371114i −0.836560 0.547875i \(-0.815437\pi\)
0.394284 + 0.918989i \(0.370993\pi\)
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) 0 0 0.342020 0.939693i \(-0.388889\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(6\) −0.766044 0.642788i −0.312736 0.262417i
\(7\) 2.00000 3.46410i 0.755929 1.30931i −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) −0.500000 0.866025i −0.176777 0.306186i
\(9\) −0.347296 + 1.96962i −0.115765 + 0.656539i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −1.53209 1.28558i −0.424925 0.356554i 0.405108 0.914269i \(-0.367234\pi\)
−0.830033 + 0.557714i \(0.811678\pi\)
\(14\) 3.75877 + 1.36808i 1.00457 + 0.365635i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) −1.04189 5.90885i −0.252695 1.43311i −0.801920 0.597431i \(-0.796188\pi\)
0.549225 0.835675i \(-0.314923\pi\)
\(18\) −2.00000 −0.471405
\(19\) 0 0
\(20\) 0 0
\(21\) 0.694593 + 3.93923i 0.151573 + 0.859611i
\(22\) 2.29813 1.92836i 0.489964 0.411128i
\(23\) 5.63816 2.05212i 1.17564 0.427897i 0.320978 0.947087i \(-0.395988\pi\)
0.854659 + 0.519190i \(0.173766\pi\)
\(24\) 0.939693 + 0.342020i 0.191814 + 0.0698146i
\(25\) −3.83022 3.21394i −0.766044 0.642788i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) −2.50000 4.33013i −0.481125 0.833333i
\(28\) −0.694593 + 3.93923i −0.131266 + 0.744445i
\(29\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0.766044 + 0.642788i 0.135419 + 0.113630i
\(33\) 2.81908 + 1.02606i 0.490738 + 0.178614i
\(34\) 5.63816 2.05212i 0.966936 0.351936i
\(35\) 0 0
\(36\) −0.347296 1.96962i −0.0578827 0.328269i
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −6.89440 + 5.78509i −1.07672 + 0.903479i −0.995645 0.0932286i \(-0.970281\pi\)
−0.0810797 + 0.996708i \(0.525837\pi\)
\(42\) −3.75877 + 1.36808i −0.579991 + 0.211099i
\(43\) 3.75877 + 1.36808i 0.573207 + 0.208630i 0.612328 0.790604i \(-0.290233\pi\)
−0.0391204 + 0.999235i \(0.512456\pi\)
\(44\) 2.29813 + 1.92836i 0.346457 + 0.290712i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 0 0 −0.984808 0.173648i \(-0.944444\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(48\) −0.173648 + 0.984808i −0.0250640 + 0.142145i
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) 2.50000 4.33013i 0.353553 0.612372i
\(51\) 4.59627 + 3.85673i 0.643606 + 0.540050i
\(52\) 1.87939 + 0.684040i 0.260624 + 0.0948593i
\(53\) 5.63816 2.05212i 0.774460 0.281880i 0.0755995 0.997138i \(-0.475913\pi\)
0.698861 + 0.715258i \(0.253691\pi\)
\(54\) 3.83022 3.21394i 0.521227 0.437362i
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) 0 0
\(58\) 0 0
\(59\) 1.56283 + 8.86327i 0.203464 + 1.15390i 0.899839 + 0.436222i \(0.143684\pi\)
−0.696376 + 0.717678i \(0.745205\pi\)
\(60\) 0 0
\(61\) 3.75877 1.36808i 0.481261 0.175165i −0.0899856 0.995943i \(-0.528682\pi\)
0.571247 + 0.820778i \(0.306460\pi\)
\(62\) 1.87939 + 0.684040i 0.238682 + 0.0868732i
\(63\) 6.12836 + 5.14230i 0.772100 + 0.647869i
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −0.520945 + 2.95442i −0.0641238 + 0.363664i
\(67\) 1.21554 6.89365i 0.148502 0.842194i −0.815987 0.578070i \(-0.803806\pi\)
0.964489 0.264124i \(-0.0850828\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) 0 0
\(71\) −5.63816 2.05212i −0.669126 0.243542i −0.0149545 0.999888i \(-0.504760\pi\)
−0.654172 + 0.756346i \(0.726983\pi\)
\(72\) 1.87939 0.684040i 0.221488 0.0806149i
\(73\) −0.766044 + 0.642788i −0.0896587 + 0.0752326i −0.686515 0.727115i \(-0.740861\pi\)
0.596857 + 0.802348i \(0.296416\pi\)
\(74\) 1.73648 + 9.84808i 0.201862 + 1.14482i
\(75\) 5.00000 0.577350
\(76\) 0 0
\(77\) −12.0000 −1.36753
\(78\) 0.347296 + 1.96962i 0.0393236 + 0.223015i
\(79\) 3.06418 2.57115i 0.344747 0.289277i −0.453930 0.891038i \(-0.649978\pi\)
0.798677 + 0.601760i \(0.205534\pi\)
\(80\) 0 0
\(81\) −0.939693 0.342020i −0.104410 0.0380022i
\(82\) −6.89440 5.78509i −0.761359 0.638856i
\(83\) −1.50000 + 2.59808i −0.164646 + 0.285176i −0.936530 0.350588i \(-0.885982\pi\)
0.771883 + 0.635764i \(0.219315\pi\)
\(84\) −2.00000 3.46410i −0.218218 0.377964i
\(85\) 0 0
\(86\) −0.694593 + 3.93923i −0.0748999 + 0.424778i
\(87\) 0 0
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) −4.59627 3.85673i −0.487203 0.408812i 0.365819 0.930686i \(-0.380789\pi\)
−0.853023 + 0.521874i \(0.825233\pi\)
\(90\) 0 0
\(91\) −7.51754 + 2.73616i −0.788052 + 0.286828i
\(92\) −4.59627 + 3.85673i −0.479194 + 0.402091i
\(93\) 0.347296 + 1.96962i 0.0360130 + 0.204240i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −2.95202 16.7417i −0.299732 1.69987i −0.647320 0.762218i \(-0.724110\pi\)
0.347588 0.937647i \(-0.387001\pi\)
\(98\) 6.89440 5.78509i 0.696440 0.584382i
\(99\) 5.63816 2.05212i 0.566656 0.206246i
\(100\) 4.69846 + 1.71010i 0.469846 + 0.171010i
\(101\) 0 0 0.642788 0.766044i \(-0.277778\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) 1.00000 + 1.73205i 0.0985329 + 0.170664i 0.911078 0.412235i \(-0.135252\pi\)
−0.812545 + 0.582899i \(0.801918\pi\)
\(104\) −0.347296 + 1.96962i −0.0340552 + 0.193137i
\(105\) 0 0
\(106\) 3.00000 + 5.19615i 0.291386 + 0.504695i
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 3.83022 + 3.21394i 0.368563 + 0.309261i
\(109\) −15.0351 5.47232i −1.44010 0.524153i −0.500292 0.865857i \(-0.666774\pi\)
−0.939808 + 0.341703i \(0.888996\pi\)
\(110\) 0 0
\(111\) −7.66044 + 6.42788i −0.727097 + 0.610107i
\(112\) −0.694593 3.93923i −0.0656328 0.372222i
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.06418 2.57115i 0.283283 0.237703i
\(118\) −8.45723 + 3.07818i −0.778551 + 0.283370i
\(119\) −22.5526 8.20848i −2.06740 0.752470i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 2.00000 + 3.46410i 0.181071 + 0.313625i
\(123\) 1.56283 8.86327i 0.140916 0.799174i
\(124\) −0.347296 + 1.96962i −0.0311881 + 0.176877i
\(125\) 0 0
\(126\) −4.00000 + 6.92820i −0.356348 + 0.617213i
\(127\) −1.53209 1.28558i −0.135951 0.114076i 0.572276 0.820061i \(-0.306060\pi\)
−0.708227 + 0.705984i \(0.750505\pi\)
\(128\) −0.939693 0.342020i −0.0830579 0.0302306i
\(129\) −3.75877 + 1.36808i −0.330941 + 0.120453i
\(130\) 0 0
\(131\) 1.56283 + 8.86327i 0.136545 + 0.774387i 0.973771 + 0.227530i \(0.0730650\pi\)
−0.837226 + 0.546858i \(0.815824\pi\)
\(132\) −3.00000 −0.261116
\(133\) 0 0
\(134\) 7.00000 0.604708
\(135\) 0 0
\(136\) −4.59627 + 3.85673i −0.394127 + 0.330711i
\(137\) −8.45723 + 3.07818i −0.722550 + 0.262987i −0.677008 0.735976i \(-0.736724\pi\)
−0.0455422 + 0.998962i \(0.514502\pi\)
\(138\) −5.63816 2.05212i −0.479952 0.174688i
\(139\) 8.42649 + 7.07066i 0.714725 + 0.599726i 0.925921 0.377718i \(-0.123291\pi\)
−0.211195 + 0.977444i \(0.567736\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.04189 5.90885i 0.0874334 0.495859i
\(143\) −1.04189 + 5.90885i −0.0871271 + 0.494123i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 0 0
\(146\) −0.766044 0.642788i −0.0633983 0.0531975i
\(147\) 8.45723 + 3.07818i 0.697541 + 0.253884i
\(148\) −9.39693 + 3.42020i −0.772423 + 0.281139i
\(149\) 13.7888 11.5702i 1.12962 0.947866i 0.130572 0.991439i \(-0.458319\pi\)
0.999050 + 0.0435730i \(0.0138741\pi\)
\(150\) 0.868241 + 4.92404i 0.0708916 + 0.402046i
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) −2.08378 11.8177i −0.167916 0.952297i
\(155\) 0 0
\(156\) −1.87939 + 0.684040i −0.150471 + 0.0547671i
\(157\) 15.0351 + 5.47232i 1.19993 + 0.436739i 0.863200 0.504862i \(-0.168457\pi\)
0.336730 + 0.941601i \(0.390679\pi\)
\(158\) 3.06418 + 2.57115i 0.243773 + 0.204550i
\(159\) −3.00000 + 5.19615i −0.237915 + 0.412082i
\(160\) 0 0
\(161\) 4.16756 23.6354i 0.328449 1.86273i
\(162\) 0.173648 0.984808i 0.0136431 0.0773738i
\(163\) 9.50000 + 16.4545i 0.744097 + 1.28881i 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) −2.81908 1.02606i −0.218803 0.0796377i
\(167\) −22.5526 + 8.20848i −1.74517 + 0.635192i −0.999515 0.0311360i \(-0.990088\pi\)
−0.745659 + 0.666328i \(0.767865\pi\)
\(168\) 3.06418 2.57115i 0.236406 0.198369i
\(169\) −1.56283 8.86327i −0.120218 0.681790i
\(170\) 0 0
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) −1.04189 5.90885i −0.0792134 0.449241i −0.998456 0.0555496i \(-0.982309\pi\)
0.919243 0.393692i \(-0.128802\pi\)
\(174\) 0 0
\(175\) −18.7939 + 6.84040i −1.42068 + 0.517086i
\(176\) −2.81908 1.02606i −0.212496 0.0773422i
\(177\) −6.89440 5.78509i −0.518215 0.434834i
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 0 0
\(181\) −0.347296 + 1.96962i −0.0258143 + 0.146400i −0.994991 0.0999676i \(-0.968126\pi\)
0.969176 + 0.246368i \(0.0792372\pi\)
\(182\) −4.00000 6.92820i −0.296500 0.513553i
\(183\) −2.00000 + 3.46410i −0.147844 + 0.256074i
\(184\) −4.59627 3.85673i −0.338841 0.284322i
\(185\) 0 0
\(186\) −1.87939 + 0.684040i −0.137803 + 0.0501563i
\(187\) −13.7888 + 11.5702i −1.00834 + 0.846095i
\(188\) 0 0
\(189\) −20.0000 −1.45479
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −0.173648 0.984808i −0.0125320 0.0710724i
\(193\) −1.53209 + 1.28558i −0.110282 + 0.0925377i −0.696261 0.717788i \(-0.745155\pi\)
0.585979 + 0.810326i \(0.300710\pi\)
\(194\) 15.9748 5.81434i 1.14692 0.417445i
\(195\) 0 0
\(196\) 6.89440 + 5.78509i 0.492457 + 0.413221i
\(197\) −9.00000 + 15.5885i −0.641223 + 1.11063i 0.343937 + 0.938993i \(0.388239\pi\)
−0.985160 + 0.171639i \(0.945094\pi\)
\(198\) 3.00000 + 5.19615i 0.213201 + 0.369274i
\(199\) −1.73648 + 9.84808i −0.123096 + 0.698112i 0.859325 + 0.511431i \(0.170884\pi\)
−0.982421 + 0.186681i \(0.940227\pi\)
\(200\) −0.868241 + 4.92404i −0.0613939 + 0.348182i
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 0 0
\(203\) 0 0
\(204\) −5.63816 2.05212i −0.394750 0.143677i
\(205\) 0 0
\(206\) −1.53209 + 1.28558i −0.106746 + 0.0895703i
\(207\) 2.08378 + 11.8177i 0.144833 + 0.821386i
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) −3.47296 19.6962i −0.239089 1.35594i −0.833830 0.552022i \(-0.813856\pi\)
0.594741 0.803917i \(-0.297255\pi\)
\(212\) −4.59627 + 3.85673i −0.315673 + 0.264881i
\(213\) 5.63816 2.05212i 0.386320 0.140609i
\(214\) 0 0
\(215\) 0 0
\(216\) −2.50000 + 4.33013i −0.170103 + 0.294628i
\(217\) −4.00000 6.92820i −0.271538 0.470317i
\(218\) 2.77837 15.7569i 0.188175 1.06719i
\(219\) 0.173648 0.984808i 0.0117341 0.0665471i
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) −7.66044 6.42788i −0.514135 0.431411i
\(223\) 13.1557 + 4.78828i 0.880971 + 0.320647i 0.742601 0.669734i \(-0.233592\pi\)
0.138369 + 0.990381i \(0.455814\pi\)
\(224\) 3.75877 1.36808i 0.251143 0.0914087i
\(225\) 7.66044 6.42788i 0.510696 0.428525i
\(226\) −2.60472 14.7721i −0.173264 0.982627i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) −16.0000 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(230\) 0 0
\(231\) 9.19253 7.71345i 0.604824 0.507508i
\(232\) 0 0
\(233\) −2.81908 1.02606i −0.184684 0.0672195i 0.248023 0.968754i \(-0.420219\pi\)
−0.432707 + 0.901535i \(0.642441\pi\)
\(234\) 3.06418 + 2.57115i 0.200312 + 0.168081i
\(235\) 0 0
\(236\) −4.50000 7.79423i −0.292925 0.507361i
\(237\) −0.694593 + 3.93923i −0.0451186 + 0.255881i
\(238\) 4.16756 23.6354i 0.270143 1.53205i
\(239\) 6.00000 + 10.3923i 0.388108 + 0.672222i 0.992195 0.124696i \(-0.0397955\pi\)
−0.604087 + 0.796918i \(0.706462\pi\)
\(240\) 0 0
\(241\) −3.83022 3.21394i −0.246726 0.207028i 0.511035 0.859560i \(-0.329262\pi\)
−0.757761 + 0.652532i \(0.773707\pi\)
\(242\) 1.87939 + 0.684040i 0.120811 + 0.0439718i
\(243\) 15.0351 5.47232i 0.964501 0.351050i
\(244\) −3.06418 + 2.57115i −0.196164 + 0.164601i
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) 0 0
\(248\) −2.00000 −0.127000
\(249\) −0.520945 2.95442i −0.0330135 0.187229i
\(250\) 0 0
\(251\) 2.81908 1.02606i 0.177939 0.0647644i −0.251514 0.967854i \(-0.580929\pi\)
0.429453 + 0.903089i \(0.358706\pi\)
\(252\) −7.51754 2.73616i −0.473561 0.172362i
\(253\) −13.7888 11.5702i −0.866894 0.727411i
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −0.520945 + 2.95442i −0.0324956 + 0.184292i −0.996735 0.0807404i \(-0.974272\pi\)
0.964240 + 0.265032i \(0.0853826\pi\)
\(258\) −2.00000 3.46410i −0.124515 0.215666i
\(259\) 20.0000 34.6410i 1.24274 2.15249i
\(260\) 0 0
\(261\) 0 0
\(262\) −8.45723 + 3.07818i −0.522490 + 0.190171i
\(263\) −9.19253 + 7.71345i −0.566836 + 0.475632i −0.880594 0.473871i \(-0.842856\pi\)
0.313758 + 0.949503i \(0.398412\pi\)
\(264\) −0.520945 2.95442i −0.0320619 0.181832i
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 1.21554 + 6.89365i 0.0742508 + 0.421097i
\(269\) −9.19253 + 7.71345i −0.560479 + 0.470297i −0.878471 0.477796i \(-0.841436\pi\)
0.317992 + 0.948093i \(0.396991\pi\)
\(270\) 0 0
\(271\) 15.0351 + 5.47232i 0.913316 + 0.332420i 0.755576 0.655061i \(-0.227357\pi\)
0.157740 + 0.987481i \(0.449579\pi\)
\(272\) −4.59627 3.85673i −0.278690 0.233848i
\(273\) 4.00000 6.92820i 0.242091 0.419314i
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) −2.60472 + 14.7721i −0.157071 + 0.890792i
\(276\) 1.04189 5.90885i 0.0627144 0.355671i
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −5.50000 + 9.52628i −0.329868 + 0.571348i
\(279\) 3.06418 + 2.57115i 0.183448 + 0.153931i
\(280\) 0 0
\(281\) 25.3717 9.23454i 1.51355 0.550887i 0.554021 0.832502i \(-0.313093\pi\)
0.959527 + 0.281616i \(0.0908703\pi\)
\(282\) 0 0
\(283\) 0.868241 + 4.92404i 0.0516116 + 0.292704i 0.999678 0.0253681i \(-0.00807579\pi\)
−0.948067 + 0.318072i \(0.896965\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 6.25133 + 35.4531i 0.369005 + 2.09273i
\(288\) −1.53209 + 1.28558i −0.0902792 + 0.0757532i
\(289\) −17.8542 + 6.49838i −1.05024 + 0.382258i
\(290\) 0 0
\(291\) 13.0228 + 10.9274i 0.763407 + 0.640575i
\(292\) 0.500000 0.866025i 0.0292603 0.0506803i
\(293\) 12.0000 + 20.7846i 0.701047 + 1.21425i 0.968099 + 0.250568i \(0.0806172\pi\)
−0.267052 + 0.963682i \(0.586049\pi\)
\(294\) −1.56283 + 8.86327i −0.0911463 + 0.516916i
\(295\) 0 0
\(296\) −5.00000 8.66025i −0.290619 0.503367i
\(297\) −7.50000 + 12.9904i −0.435194 + 0.753778i
\(298\) 13.7888 + 11.5702i 0.798764 + 0.670242i
\(299\) −11.2763 4.10424i −0.652126 0.237354i
\(300\) −4.69846 + 1.71010i −0.271266 + 0.0987327i
\(301\) 12.2567 10.2846i 0.706465 0.592795i
\(302\) 1.73648 + 9.84808i 0.0999233 + 0.566693i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 2.08378 + 11.8177i 0.119122 + 0.675573i
\(307\) 5.36231 4.49951i 0.306043 0.256801i −0.476811 0.879006i \(-0.658207\pi\)
0.782854 + 0.622205i \(0.213763\pi\)
\(308\) 11.2763 4.10424i 0.642527 0.233861i
\(309\) −1.87939 0.684040i −0.106914 0.0389137i
\(310\) 0 0
\(311\) 15.0000 25.9808i 0.850572 1.47323i −0.0301210 0.999546i \(-0.509589\pi\)
0.880693 0.473688i \(-0.157077\pi\)
\(312\) −1.00000 1.73205i −0.0566139 0.0980581i
\(313\) −3.29932 + 18.7113i −0.186488 + 1.05763i 0.737540 + 0.675304i \(0.235987\pi\)
−0.924028 + 0.382324i \(0.875124\pi\)
\(314\) −2.77837 + 15.7569i −0.156793 + 0.889215i
\(315\) 0 0
\(316\) −2.00000 + 3.46410i −0.112509 + 0.194871i
\(317\) 13.7888 + 11.5702i 0.774456 + 0.649846i 0.941846 0.336045i \(-0.109089\pi\)
−0.167390 + 0.985891i \(0.553534\pi\)
\(318\) −5.63816 2.05212i −0.316172 0.115077i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 24.0000 1.33747
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 1.73648 + 9.84808i 0.0963227 + 0.546273i
\(326\) −14.5548 + 12.2130i −0.806118 + 0.676414i
\(327\) 15.0351 5.47232i 0.831442 0.302620i
\(328\) 8.45723 + 3.07818i 0.466973 + 0.169964i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.50000 + 4.33013i 0.137412 + 0.238005i 0.926516 0.376254i \(-0.122788\pi\)
−0.789104 + 0.614260i \(0.789455\pi\)
\(332\) 0.520945 2.95442i 0.0285905 0.162145i
\(333\) −3.47296 + 19.6962i −0.190317 + 1.07934i
\(334\) −12.0000 20.7846i −0.656611 1.13728i
\(335\) 0 0
\(336\) 3.06418 + 2.57115i 0.167165 + 0.140268i
\(337\) 10.3366 + 3.76222i 0.563072 + 0.204941i 0.607845 0.794056i \(-0.292034\pi\)
−0.0447732 + 0.998997i \(0.514257\pi\)
\(338\) 8.45723 3.07818i 0.460013 0.167431i
\(339\) 11.4907 9.64181i 0.624087 0.523671i
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) −0.694593 3.93923i −0.0374499 0.212389i
\(345\) 0 0
\(346\) 5.63816 2.05212i 0.303109 0.110323i
\(347\) 8.45723 + 3.07818i 0.454008 + 0.165245i 0.558894 0.829239i \(-0.311226\pi\)
−0.104886 + 0.994484i \(0.533448\pi\)
\(348\) 0 0
\(349\) 2.00000 3.46410i 0.107058 0.185429i −0.807519 0.589841i \(-0.799190\pi\)
0.914577 + 0.404412i \(0.132524\pi\)
\(350\) −10.0000 17.3205i −0.534522 0.925820i
\(351\) −1.73648 + 9.84808i −0.0926865 + 0.525651i
\(352\) 0.520945 2.95442i 0.0277664 0.157471i
\(353\) −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 4.50000 7.79423i 0.239172 0.414259i
\(355\) 0 0
\(356\) 5.63816 + 2.05212i 0.298822 + 0.108762i
\(357\) 22.5526 8.20848i 1.19361 0.434439i
\(358\) −6.89440 + 5.78509i −0.364380 + 0.305751i
\(359\) −1.04189 5.90885i −0.0549888 0.311857i 0.944891 0.327386i \(-0.106168\pi\)
−0.999879 + 0.0155292i \(0.995057\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −2.00000 −0.105118
\(363\) 0.347296 + 1.96962i 0.0182283 + 0.103378i
\(364\) 6.12836 5.14230i 0.321213 0.269530i
\(365\) 0 0
\(366\) −3.75877 1.36808i −0.196474 0.0715107i
\(367\) −16.8530 14.1413i −0.879718 0.738171i 0.0864029 0.996260i \(-0.472463\pi\)
−0.966121 + 0.258089i \(0.916907\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) −9.00000 15.5885i −0.468521 0.811503i
\(370\) 0 0
\(371\) 4.16756 23.6354i 0.216369 1.22709i
\(372\) −1.00000 1.73205i −0.0518476 0.0898027i
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) −13.7888 11.5702i −0.713002 0.598280i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −3.47296 19.6962i −0.178630 1.01306i
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 2.08378 + 11.8177i 0.106615 + 0.604646i
\(383\) 27.5776 23.1404i 1.40915 1.18242i 0.452288 0.891872i \(-0.350608\pi\)
0.956861 0.290545i \(-0.0938366\pi\)
\(384\) 0.939693 0.342020i 0.0479535 0.0174536i
\(385\) 0 0
\(386\) −1.53209 1.28558i −0.0779813 0.0654341i
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 8.50000 + 14.7224i 0.431522 + 0.747418i
\(389\) −6.25133 + 35.4531i −0.316955 + 1.79754i 0.244085 + 0.969754i \(0.421512\pi\)
−0.561040 + 0.827789i \(0.689599\pi\)
\(390\) 0 0
\(391\) −18.0000 31.1769i −0.910299 1.57668i
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) −6.89440 5.78509i −0.347776 0.291819i
\(394\) −16.9145 6.15636i −0.852139 0.310153i
\(395\) 0 0
\(396\) −4.59627 + 3.85673i −0.230971 + 0.193808i
\(397\) −1.73648 9.84808i −0.0871515 0.494261i −0.996872 0.0790387i \(-0.974815\pi\)
0.909720 0.415222i \(-0.136296\pi\)
\(398\) −10.0000 −0.501255
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 4.68850 + 26.5898i 0.234133 + 1.32783i 0.844433 + 0.535662i \(0.179938\pi\)
−0.610300 + 0.792170i \(0.708951\pi\)
\(402\) −5.36231 + 4.49951i −0.267448 + 0.224415i
\(403\) −3.75877 + 1.36808i −0.187238 + 0.0681489i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15.0000 25.9808i −0.743522 1.28782i
\(408\) 1.04189 5.90885i 0.0515812 0.292531i
\(409\) −0.868241 + 4.92404i −0.0429317 + 0.243478i −0.998720 0.0505773i \(-0.983894\pi\)
0.955788 + 0.294055i \(0.0950050\pi\)
\(410\) 0 0
\(411\) 4.50000 7.79423i 0.221969 0.384461i
\(412\) −1.53209 1.28558i −0.0754806 0.0633357i
\(413\) 33.8289 + 12.3127i 1.66461 + 0.605870i
\(414\) −11.2763 + 4.10424i −0.554200 + 0.201712i
\(415\) 0 0
\(416\) −0.347296 1.96962i −0.0170276 0.0965683i
\(417\) −11.0000 −0.538672
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 7.66044 6.42788i 0.373347 0.313276i −0.436737 0.899589i \(-0.643866\pi\)
0.810084 + 0.586314i \(0.199421\pi\)
\(422\) 18.7939 6.84040i 0.914870 0.332986i
\(423\) 0 0
\(424\) −4.59627 3.85673i −0.223214 0.187299i
\(425\) −15.0000 + 25.9808i −0.727607 + 1.26025i
\(426\) 3.00000 + 5.19615i 0.145350 + 0.251754i
\(427\) 2.77837 15.7569i 0.134455 0.762531i
\(428\) 0 0
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 0 0
\(431\) 22.9813 + 19.2836i 1.10697 + 0.928860i 0.997874 0.0651713i \(-0.0207594\pi\)
0.109098 + 0.994031i \(0.465204\pi\)
\(432\) −4.69846 1.71010i −0.226055 0.0822773i
\(433\) 24.4320 8.89252i 1.17413 0.427347i 0.320003 0.947416i \(-0.396316\pi\)
0.854124 + 0.520069i \(0.174094\pi\)
\(434\) 6.12836 5.14230i 0.294170 0.246838i
\(435\) 0 0
\(436\) 16.0000 0.766261
\(437\) 0 0
\(438\) 1.00000 0.0477818
\(439\) −2.43107 13.7873i −0.116029 0.658032i −0.986236 0.165346i \(-0.947126\pi\)
0.870207 0.492687i \(-0.163985\pi\)
\(440\) 0 0
\(441\) 16.9145 6.15636i 0.805451 0.293160i
\(442\) −11.2763 4.10424i −0.536359 0.195219i
\(443\) 6.89440 + 5.78509i 0.327563 + 0.274858i 0.791706 0.610902i \(-0.209193\pi\)
−0.464143 + 0.885760i \(0.653638\pi\)
\(444\) 5.00000 8.66025i 0.237289 0.410997i
\(445\) 0 0
\(446\) −2.43107 + 13.7873i −0.115115 + 0.652848i
\(447\) −3.12567 + 17.7265i −0.147839 + 0.838437i
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) 4.50000 7.79423i 0.212368 0.367832i −0.740087 0.672511i \(-0.765216\pi\)
0.952455 + 0.304679i \(0.0985491\pi\)
\(450\) 7.66044 + 6.42788i 0.361117 + 0.303013i
\(451\) 25.3717 + 9.23454i 1.19471 + 0.434838i
\(452\) 14.0954 5.13030i 0.662991 0.241309i
\(453\) −7.66044 + 6.42788i −0.359919 + 0.302008i
\(454\) −0.520945 2.95442i −0.0244491 0.138658i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) −2.77837 15.7569i −0.129825 0.736273i
\(459\) −22.9813 + 19.2836i −1.07268 + 0.900083i
\(460\) 0 0
\(461\) −5.63816 2.05212i −0.262595 0.0955768i 0.207368 0.978263i \(-0.433510\pi\)
−0.469963 + 0.882686i \(0.655733\pi\)
\(462\) 9.19253 + 7.71345i 0.427675 + 0.358862i
\(463\) 17.0000 29.4449i 0.790057 1.36842i −0.135874 0.990726i \(-0.543384\pi\)
0.925931 0.377693i \(-0.123282\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.520945 2.95442i 0.0241323 0.136861i
\(467\) 13.5000 + 23.3827i 0.624705 + 1.08202i 0.988598 + 0.150581i \(0.0481143\pi\)
−0.363892 + 0.931441i \(0.618552\pi\)
\(468\) −2.00000 + 3.46410i −0.0924500 + 0.160128i
\(469\) −21.4492 17.9981i −0.990434 0.831073i
\(470\) 0 0
\(471\) −15.0351 + 5.47232i −0.692780 + 0.252151i
\(472\) 6.89440 5.78509i 0.317340 0.266280i
\(473\) −2.08378 11.8177i −0.0958122 0.543378i
\(474\) −4.00000 −0.183726
\(475\) 0 0
\(476\) 24.0000 1.10004
\(477\) 2.08378 + 11.8177i 0.0954096 + 0.541095i
\(478\) −9.19253 + 7.71345i −0.420457 + 0.352805i
\(479\) −33.8289 + 12.3127i −1.54568 + 0.562583i −0.967400 0.253253i \(-0.918499\pi\)
−0.578283 + 0.815836i \(0.696277\pi\)
\(480\) 0 0
\(481\) −15.3209 12.8558i −0.698572 0.586172i
\(482\) 2.50000 4.33013i 0.113872 0.197232i
\(483\) 12.0000 + 20.7846i 0.546019 + 0.945732i
\(484\) −0.347296 + 1.96962i −0.0157862 + 0.0895280i
\(485\) 0 0
\(486\) 8.00000 + 13.8564i 0.362887 + 0.628539i
\(487\) 1.00000 1.73205i 0.0453143 0.0784867i −0.842479 0.538730i \(-0.818904\pi\)
0.887793 + 0.460243i \(0.152238\pi\)
\(488\) −3.06418 2.57115i −0.138709 0.116391i
\(489\) −17.8542 6.49838i −0.807393 0.293867i
\(490\) 0 0
\(491\) 0 0 −0.642788 0.766044i \(-0.722222\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(492\) 1.56283 + 8.86327i 0.0704580 + 0.399587i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.347296 1.96962i −0.0155941 0.0884383i
\(497\) −18.3851 + 15.4269i −0.824683 + 0.691991i
\(498\) 2.81908 1.02606i 0.126326 0.0459789i
\(499\) 23.4923 + 8.55050i 1.05166 + 0.382773i 0.809289 0.587410i \(-0.199853\pi\)
0.242371 + 0.970184i \(0.422075\pi\)
\(500\) 0 0
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) 1.50000 + 2.59808i 0.0669483 + 0.115958i
\(503\) 1.04189 5.90885i 0.0464555 0.263462i −0.952730 0.303819i \(-0.901738\pi\)
0.999185 + 0.0403564i \(0.0128493\pi\)
\(504\) 1.38919 7.87846i 0.0618792 0.350935i
\(505\) 0 0
\(506\) 9.00000 15.5885i 0.400099 0.692991i
\(507\) 6.89440 + 5.78509i 0.306191 + 0.256925i
\(508\) 1.87939 + 0.684040i 0.0833842 + 0.0303494i
\(509\) −22.5526 + 8.20848i −0.999627 + 0.363835i −0.789441 0.613827i \(-0.789629\pi\)
−0.210187 + 0.977661i \(0.567407\pi\)
\(510\) 0 0
\(511\) 0.694593 + 3.93923i 0.0307270 + 0.174261i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.00000 −0.132324
\(515\) 0 0
\(516\) 3.06418 2.57115i 0.134893 0.113189i
\(517\) 0 0
\(518\) 37.5877 + 13.6808i 1.65151 + 0.601100i
\(519\) 4.59627 + 3.85673i 0.201754 + 0.169291i
\(520\) 0 0
\(521\) 4.50000 + 7.79423i 0.197149 + 0.341471i 0.947603 0.319451i \(-0.103499\pi\)
−0.750454 + 0.660922i \(0.770165\pi\)
\(522\) 0 0
\(523\) 4.86215 27.5746i 0.212607 1.20575i −0.672404 0.740184i \(-0.734738\pi\)
0.885011 0.465570i \(-0.154151\pi\)
\(524\) −4.50000 7.79423i −0.196583 0.340492i
\(525\) 10.0000 17.3205i 0.436436 0.755929i
\(526\) −9.19253 7.71345i −0.400813 0.336322i
\(527\) −11.2763 4.10424i −0.491204 0.178784i
\(528\) 2.81908 1.02606i 0.122685 0.0446535i
\(529\) 9.95858 8.35624i 0.432982 0.363315i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 18.0000 0.779667
\(534\) 1.04189 + 5.90885i 0.0450869 + 0.255701i
\(535\) 0 0
\(536\) −6.57785 + 2.39414i −0.284120 + 0.103411i
\(537\) −8.45723 3.07818i −0.364957 0.132833i
\(538\) −9.19253 7.71345i −0.396318 0.332550i
\(539\) −13.5000 + 23.3827i −0.581486 + 1.00716i
\(540\) 0 0
\(541\) 7.64052 43.3315i 0.328492 1.86297i −0.155416 0.987849i \(-0.549672\pi\)
0.483907 0.875119i \(-0.339217\pi\)
\(542\) −2.77837 + 15.7569i −0.119341 + 0.676818i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 0 0
\(546\) 7.51754 + 2.73616i 0.321721 + 0.117097i
\(547\) −3.75877 + 1.36808i −0.160713 + 0.0584949i −0.421124 0.907003i \(-0.638364\pi\)
0.260411 + 0.965498i \(0.416142\pi\)
\(548\) 6.89440 5.78509i 0.294514 0.247127i
\(549\) 1.38919 + 7.87846i 0.0592890 + 0.336245i
\(550\) −15.0000 −0.639602
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) −2.77837 15.7569i −0.118148 0.670053i
\(554\) 6.12836 5.14230i 0.260369 0.218475i
\(555\) 0 0
\(556\) −10.3366 3.76222i −0.438370 0.159554i
\(557\) 18.3851 + 15.4269i 0.779000 + 0.653659i 0.942997 0.332802i \(-0.107994\pi\)
−0.163996 + 0.986461i \(0.552439\pi\)
\(558\) −2.00000 + 3.46410i −0.0846668 + 0.146647i
\(559\) −4.00000 6.92820i −0.169182 0.293032i
\(560\) 0 0
\(561\) 3.12567 17.7265i 0.131966 0.748415i
\(562\) 13.5000 + 23.3827i 0.569463 + 0.986339i
\(563\) −10.5000 + 18.1865i −0.442522 + 0.766471i −0.997876 0.0651433i \(-0.979250\pi\)
0.555354 + 0.831614i \(0.312583\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −4.69846 + 1.71010i −0.197491 + 0.0718809i
\(567\) −3.06418 + 2.57115i −0.128683 + 0.107978i
\(568\) 1.04189 + 5.90885i 0.0437167 + 0.247930i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) −1.04189 5.90885i −0.0435636 0.247061i
\(573\) −9.19253 + 7.71345i −0.384024 + 0.322234i
\(574\) −33.8289 + 12.3127i −1.41199 + 0.513923i
\(575\) −28.1908 10.2606i −1.17564 0.427897i
\(576\) −1.53209 1.28558i −0.0638370 0.0535656i
\(577\) −5.50000 + 9.52628i −0.228968 + 0.396584i −0.957503 0.288425i \(-0.906868\pi\)
0.728535 + 0.685009i \(0.240202\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0.347296 1.96962i 0.0144331 0.0818544i
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) −8.50000 + 14.7224i −0.352336 + 0.610264i
\(583\) −13.7888 11.5702i −0.571074 0.479188i
\(584\) 0.939693 + 0.342020i 0.0388848 + 0.0141529i
\(585\) 0 0
\(586\) −18.3851 + 15.4269i −0.759480 + 0.637279i
\(587\) −2.08378 11.8177i −0.0860067 0.487768i −0.997135 0.0756451i \(-0.975898\pi\)
0.911128 0.412123i \(-0.135213\pi\)
\(588\) −9.00000 −0.371154
\(589\) 0 0
\(590\) 0 0
\(591\) −3.12567 17.7265i −0.128573 0.729172i
\(592\) 7.66044 6.42788i 0.314842 0.264184i
\(593\) 19.7335 7.18242i 0.810360 0.294947i 0.0965872 0.995325i \(-0.469207\pi\)
0.713772 + 0.700378i \(0.246985\pi\)
\(594\) −14.0954 5.13030i −0.578341 0.210499i
\(595\) 0 0
\(596\) −9.00000 + 15.5885i −0.368654 + 0.638528i
\(597\) −5.00000 8.66025i −0.204636 0.354441i
\(598\) 2.08378 11.8177i 0.0852120 0.483261i
\(599\) 1.04189 5.90885i 0.0425704 0.241429i −0.956096 0.293053i \(-0.905329\pi\)
0.998667 + 0.0516242i \(0.0164398\pi\)
\(600\) −2.50000 4.33013i −0.102062 0.176777i
\(601\) −6.50000 + 11.2583i −0.265141 + 0.459237i −0.967600 0.252486i \(-0.918752\pi\)
0.702460 + 0.711723i \(0.252085\pi\)
\(602\) 12.2567 + 10.2846i 0.499546 + 0.419169i
\(603\) 13.1557 + 4.78828i 0.535741 + 0.194994i
\(604\) −9.39693 + 3.42020i −0.382356 + 0.139166i
\(605\) 0 0
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −11.2763 + 4.10424i −0.455818 + 0.165904i
\(613\) −1.87939 0.684040i −0.0759077 0.0276281i 0.303787 0.952740i \(-0.401749\pi\)
−0.379695 + 0.925112i \(0.623971\pi\)
\(614\) 5.36231 + 4.49951i 0.216405 + 0.181586i
\(615\) 0 0
\(616\) 6.00000 + 10.3923i 0.241747 + 0.418718i
\(617\) 0.520945 2.95442i 0.0209724 0.118941i −0.972524 0.232802i \(-0.925211\pi\)
0.993497 + 0.113861i \(0.0363218\pi\)
\(618\) 0.347296 1.96962i 0.0139703 0.0792296i
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 0 0
\(621\) −22.9813 19.2836i −0.922209 0.773825i
\(622\) 28.1908 + 10.2606i 1.13035 + 0.411413i
\(623\) −22.5526 + 8.20848i −0.903552 + 0.328866i
\(624\) 1.53209 1.28558i 0.0613326 0.0514642i
\(625\) 4.34120 + 24.6202i 0.173648 + 0.984808i
\(626\) −19.0000 −0.759393
\(627\) 0 0
\(628\) −16.0000 −0.638470
\(629\) −10.4189 59.0885i −0.415428 2.35601i
\(630\) 0 0
\(631\) 26.3114 9.57656i 1.04744 0.381237i 0.239744 0.970836i \(-0.422936\pi\)
0.807696 + 0.589599i \(0.200714\pi\)
\(632\) −3.75877 1.36808i −0.149516 0.0544193i
\(633\) 15.3209 + 12.8558i 0.608951 + 0.510970i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 0 0
\(636\) 1.04189 5.90885i 0.0413136 0.234301i
\(637\) −3.12567 + 17.7265i −0.123843 + 0.702351i
\(638\) 0 0
\(639\) 6.00000 10.3923i 0.237356 0.411113i
\(640\) 0 0
\(641\) −36.6480 13.3388i −1.44751 0.526850i −0.505615 0.862759i \(-0.668734\pi\)
−0.941894 + 0.335909i \(0.890957\pi\)
\(642\) 0 0
\(643\) −32.9399 + 27.6399i −1.29902 + 1.09001i −0.308710 + 0.951156i \(0.599897\pi\)
−0.990313 + 0.138854i \(0.955658\pi\)
\(644\) 4.16756 + 23.6354i 0.164225 + 0.931365i
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 0.173648 + 0.984808i 0.00682154 + 0.0386869i
\(649\) 20.6832 17.3553i 0.811887 0.681254i
\(650\) −9.39693 + 3.42020i −0.368578 + 0.134151i
\(651\) 7.51754 + 2.73616i 0.294636 + 0.107239i
\(652\) −14.5548 12.2130i −0.570012 0.478297i
\(653\) 6.00000 10.3923i 0.234798 0.406682i −0.724416 0.689363i \(-0.757890\pi\)
0.959214 + 0.282681i \(0.0912238\pi\)
\(654\) 8.00000 + 13.8564i 0.312825 + 0.541828i
\(655\) 0 0
\(656\) −1.56283 + 8.86327i −0.0610184 + 0.346053i
\(657\) −1.00000 1.73205i −0.0390137 0.0675737i
\(658\) 0 0
\(659\) −27.5776 23.1404i −1.07427 0.901420i −0.0788382 0.996887i \(-0.525121\pi\)
−0.995433 + 0.0954672i \(0.969565\pi\)
\(660\) 0 0
\(661\) −37.5877 + 13.6808i −1.46199 + 0.532122i −0.945913 0.324419i \(-0.894831\pi\)
−0.516079 + 0.856541i \(0.672609\pi\)
\(662\) −3.83022 + 3.21394i −0.148866 + 0.124913i
\(663\) −2.08378 11.8177i −0.0809272 0.458961i
\(664\) 3.00000 0.116423
\(665\) 0 0
\(666\) −20.0000 −0.774984
\(667\) 0 0
\(668\) 18.3851 15.4269i 0.711340 0.596885i
\(669\) −13.1557 + 4.78828i −0.508629 + 0.185126i
\(670\) 0 0
\(671\) −9.19253 7.71345i −0.354874 0.297774i
\(672\) −2.00000 + 3.46410i −0.0771517 + 0.133631i
\(673\) 7.00000 + 12.1244i 0.269830 + 0.467360i 0.968818 0.247774i \(-0.0796991\pi\)
−0.698988 + 0.715134i \(0.746366\pi\)
\(674\) −1.91013 + 10.8329i −0.0735755 + 0.417267i
\(675\) −4.34120 + 24.6202i −0.167093 + 0.947632i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −21.0000 + 36.3731i −0.807096 + 1.39793i 0.107772 + 0.994176i \(0.465628\pi\)
−0.914867 + 0.403755i \(0.867705\pi\)
\(678\) 11.4907 + 9.64181i 0.441296 + 0.370292i
\(679\) −63.8991 23.2574i −2.45222 0.892536i
\(680\) 0 0
\(681\) 2.29813 1.92836i 0.0880647 0.0738950i
\(682\) −1.04189 5.90885i −0.0398960 0.226261i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.38919 7.87846i −0.0530393 0.300801i
\(687\) 12.2567 10.2846i 0.467623 0.392382i
\(688\) 3.75877 1.36808i 0.143302 0.0521576i
\(689\) −11.2763 4.10424i −0.429593 0.156359i
\(690\) 0 0
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 4.16756 23.6354i 0.158312 0.897834i
\(694\) −1.56283 + 8.86327i −0.0593244 + 0.336445i
\(695\) 0 0
\(696\) 0 0
\(697\) 41.3664 + 34.7105i 1.56686 + 1.31476i
\(698\) 3.75877 + 1.36808i 0.142272 + 0.0517826i
\(699\) 2.81908 1.02606i 0.106627 0.0388092i
\(700\) 15.3209 12.8558i 0.579075 0.485902i
\(701\) −4.16756 23.6354i −0.157406 0.892696i −0.956553 0.291560i \(-0.905826\pi\)
0.799146 0.601137i \(-0.205285\pi\)
\(702\) −10.0000 −0.377426
\(703\) 0 0
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 2.29813 1.92836i 0.0864914 0.0725749i
\(707\) 0 0
\(708\) 8.45723 + 3.07818i 0.317842 + 0.115685i
\(709\) 10.7246 + 8.99903i 0.402772 + 0.337966i 0.821564 0.570117i \(-0.193102\pi\)
−0.418792 + 0.908082i \(0.637546\pi\)
\(710\) 0 0
\(711\) 4.00000 + 6.92820i 0.150012 + 0.259828i
\(712\) −1.04189 + 5.90885i −0.0390464 + 0.221443i
\(713\) 2.08378 11.8177i 0.0780381 0.442576i
\(714\) 12.0000 + 20.7846i 0.449089 + 0.777844i
\(715\) 0 0
\(716\) −6.89440 5.78509i −0.257656 0.216199i
\(717\) −11.2763 4.10424i −0.421122 0.153276i
\(718\) 5.63816 2.05212i 0.210414 0.0765845i
\(719\) 22.9813 19.2836i 0.857059 0.719158i −0.104273 0.994549i \(-0.533252\pi\)
0.961332 + 0.275391i \(0.0888072\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) 5.00000 0.185952
\(724\) −0.347296 1.96962i −0.0129072 0.0732002i
\(725\) 0 0
\(726\) −1.87939 + 0.684040i −0.0697505 + 0.0253871i
\(727\) −30.0702 10.9446i −1.11524 0.405914i −0.282327 0.959318i \(-0.591106\pi\)
−0.832913 + 0.553404i \(0.813329\pi\)
\(728\) 6.12836 + 5.14230i 0.227132 + 0.190586i
\(729\) −6.50000 + 11.2583i −0.240741 + 0.416975i
\(730\) 0 0
\(731\) 4.16756 23.6354i 0.154143 0.874186i
\(732\) 0.694593 3.93923i 0.0256729 0.145598i
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 11.0000 19.0526i 0.406017 0.703243i
\(735\) 0 0
\(736\) 5.63816 + 2.05212i 0.207825 + 0.0756422i
\(737\) −19.7335 + 7.18242i −0.726894 + 0.264568i
\(738\) 13.7888 11.5702i 0.507573 0.425904i
\(739\) 6.07769 + 34.4683i 0.223571 + 1.26794i 0.865398 + 0.501086i \(0.167066\pi\)
−0.641826 + 0.766850i \(0.721823\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 24.0000 0.881068
\(743\) 3.12567 + 17.7265i 0.114670 + 0.650324i 0.986913 + 0.161252i \(0.0515532\pi\)
−0.872244 + 0.489072i \(0.837336\pi\)
\(744\) 1.53209 1.28558i 0.0561691 0.0471315i
\(745\) 0 0
\(746\) −3.75877 1.36808i −0.137618 0.0500890i
\(747\) −4.59627 3.85673i −0.168169 0.141110i
\(748\) 9.00000 15.5885i 0.329073 0.569970i
\(749\) 0 0
\(750\) 0 0
\(751\) −6.59863 + 37.4227i −0.240787 + 1.36557i 0.589288 + 0.807923i \(0.299408\pi\)
−0.830076 + 0.557651i \(0.811703\pi\)
\(752\) 0 0
\(753\) −1.50000 + 2.59808i −0.0546630 + 0.0946792i
\(754\) 0 0
\(755\) 0 0
\(756\) 18.7939 6.84040i 0.683526 0.248783i
\(757\) −7.66044 + 6.42788i −0.278424 + 0.233625i −0.771296 0.636476i \(-0.780391\pi\)
0.492873 + 0.870101i \(0.335947\pi\)
\(758\) 4.86215 + 27.5746i 0.176601 + 1.00156i
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) −39.0000 −1.41375 −0.706874 0.707339i \(-0.749895\pi\)
−0.706874 + 0.707339i \(0.749895\pi\)
\(762\) 0.347296 + 1.96962i 0.0125812 + 0.0713516i
\(763\) −49.0268 + 41.1384i −1.77489 + 1.48931i
\(764\) −11.2763 + 4.10424i −0.407963 + 0.148486i
\(765\) 0 0
\(766\) 27.5776 + 23.1404i 0.996419 + 0.836095i
\(767\) 9.00000 15.5885i 0.324971 0.562867i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 0.347296 1.96962i 0.0125238 0.0710262i −0.977905 0.209048i \(-0.932963\pi\)
0.990429 + 0.138022i \(0.0440745\pi\)
\(770\) 0 0
\(771\) −1.50000 2.59808i −0.0540212 0.0935674i
\(772\) 1.00000 1.73205i 0.0359908 0.0623379i
\(773\) 36.7701 + 30.8538i 1.32253 + 1.10973i 0.985762 + 0.168146i \(0.0537782\pi\)
0.336768 + 0.941588i \(0.390666\pi\)
\(774\) −7.51754 2.73616i −0.270212 0.0983493i
\(775\) −9.39693 + 3.42020i −0.337548 + 0.122857i
\(776\) −13.0228 + 10.9274i −0.467490 + 0.392270i
\(777\) 6.94593 + 39.3923i 0.249184 + 1.41319i
\(778\) −36.0000 −1.29066
\(779\) 0 0
\(780\) 0 0
\(781\) 3.12567 + 17.7265i 0.111845 + 0.634305i
\(782\) 27.5776 23.1404i 0.986173 0.827497i
\(783\) 0 0
\(784\) −8.45723 3.07818i −0.302044 0.109935i
\(785\) 0 0
\(786\) 4.50000 7.79423i 0.160510 0.278011i
\(787\) −3.50000 6.06218i −0.124762 0.216093i 0.796878 0.604140i \(-0.206483\pi\)
−0.921640 + 0.388047i \(0.873150\pi\)
\(788\) 3.12567 17.7265i 0.111347 0.631482i
\(789\) 2.08378 11.8177i 0.0741845 0.420721i
\(790\) 0 0
\(791\) −30.0000 + 51.9615i −1.06668 + 1.84754i
\(792\) −4.59627 3.85673i −0.163321 0.137043i
\(793\) −7.51754 2.73616i −0.266956 0.0971639i
\(794\) 9.39693 3.42020i 0.333484 0.121378i
\(795\) 0 0
\(796\) −1.73648 9.84808i −0.0615480 0.349056i
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.868241 4.92404i −0.0306970 0.174091i
\(801\) 9.19253 7.71345i 0.324802 0.272541i
\(802\) −25.3717 + 9.23454i −0.895906 + 0.326083i
\(803\) 2.81908 + 1.02606i 0.0994831 + 0.0362089i
\(804\) −5.36231 4.49951i −0.189114 0.158686i
\(805\) 0 0
\(806\) −2.00000 3.46410i −0.0704470 0.122018i
\(807\) 2.08378 11.8177i 0.0733525 0.416002i
\(808\) 0 0
\(809\) −22.5000 38.9711i −0.791058 1.37015i −0.925312 0.379206i \(-0.876197\pi\)
0.134255 0.990947i \(-0.457136\pi\)
\(810\) 0 0
\(811\) 12.2567 + 10.2846i 0.430391 + 0.361141i 0.832099 0.554627i \(-0.187139\pi\)
−0.401708 + 0.915768i \(0.631583\pi\)
\(812\) 0 0
\(813\) −15.0351 + 5.47232i −0.527303 + 0.191923i
\(814\) 22.9813 19.2836i 0.805495 0.675891i
\(815\) 0 0
\(816\) 6.00000 0.210042
\(817\) 0 0
\(818\) −5.00000 −0.174821
\(819\) −2.77837 15.7569i −0.0970841 0.550591i
\(820\) 0 0
\(821\) −16.9145 + 6.15636i −0.590319 + 0.214859i −0.619870 0.784705i \(-0.712815\pi\)
0.0295507 + 0.999563i \(0.490592\pi\)
\(822\) 8.45723 + 3.07818i 0.294980 + 0.107364i
\(823\) 10.7246 + 8.99903i 0.373837 + 0.313686i 0.810277 0.586047i \(-0.199317\pi\)
−0.436440 + 0.899733i \(0.643761\pi\)
\(824\) 1.00000 1.73205i 0.0348367 0.0603388i
\(825\) −7.50000 12.9904i −0.261116 0.452267i
\(826\) −6.25133 + 35.4531i −0.217512 + 1.23357i
\(827\) 6.77228 38.4075i 0.235495 1.33556i −0.606073 0.795409i \(-0.707256\pi\)
0.841568 0.540151i \(-0.181633\pi\)
\(828\) −6.00000 10.3923i −0.208514 0.361158i
\(829\) 22.0000 38.1051i 0.764092 1.32345i −0.176634 0.984277i \(-0.556521\pi\)
0.940726 0.339169i \(-0.110146\pi\)
\(830\) 0 0
\(831\) 7.51754 + 2.73616i 0.260781 + 0.0949164i
\(832\) 1.87939 0.684040i 0.0651560 0.0237148i
\(833\) −41.3664 + 34.7105i −1.43326 + 1.20265i
\(834\) −1.91013 10.8329i −0.0661424 0.375112i
\(835\) 0 0
\(836\) 0 0
\(837\) −10.0000 −0.345651
\(838\) −2.08378 11.8177i −0.0719829 0.408235i
\(839\) 9.19253 7.71345i 0.317361 0.266298i −0.470165 0.882578i \(-0.655806\pi\)
0.787527 + 0.616280i \(0.211361\pi\)
\(840\) 0 0
\(841\) 27.2511 + 9.91858i 0.939693 + 0.342020i
\(842\) 7.66044 + 6.42788i 0.263996 + 0.221519i
\(843\) −13.5000 + 23.3827i −0.464965 + 0.805342i
\(844\) 10.0000 + 17.3205i 0.344214 + 0.596196i
\(845\) 0 0
\(846\) 0 0
\(847\) −4.00000 6.92820i −0.137442 0.238056i
\(848\) 3.00000 5.19615i 0.103020 0.178437i
\(849\) −3.83022 3.21394i −0.131453 0.110302i
\(850\) −28.1908 10.2606i −0.966936 0.351936i
\(851\) 56.3816 20.5212i 1.93273 0.703458i
\(852\) −4.59627 + 3.85673i −0.157466 + 0.132129i
\(853\) −3.82026 21.6658i −0.130803 0.741822i −0.977691 0.210050i \(-0.932637\pi\)
0.846887 0.531772i \(-0.178474\pi\)
\(854\) 16.0000 0.547509
\(855\) 0 0
\(856\) 0 0
\(857\) 0.520945 + 2.95442i 0.0177951 + 0.100921i 0.992412 0.122959i \(-0.0392385\pi\)
−0.974617 + 0.223881i \(0.928127\pi\)
\(858\) 4.59627 3.85673i 0.156914 0.131666i
\(859\) 40.4068 14.7069i 1.37866 0.501792i 0.456889 0.889524i \(-0.348964\pi\)
0.921772 + 0.387732i \(0.126741\pi\)
\(860\) 0 0
\(861\) −27.5776 23.1404i −0.939842 0.788621i
\(862\) −15.0000 + 25.9808i −0.510902 + 0.884908i
\(863\) 9.00000 + 15.5885i 0.306364 + 0.530637i 0.977564 0.210639i \(-0.0675543\pi\)
−0.671200 + 0.741276i \(0.734221\pi\)
\(864\) 0.868241 4.92404i 0.0295382 0.167519i
\(865\) 0 0
\(866\) 13.0000 + 22.5167i 0.441758 + 0.765147i
\(867\) 9.50000 16.4545i 0.322637 0.558824i
\(868\) 6.12836 + 5.14230i 0.208010 + 0.174541i
\(869\) −11.2763 4.10424i −0.382523 0.139227i
\(870\) 0 0
\(871\) −10.7246 + 8.99903i −0.363390 + 0.304920i
\(872\) 2.77837 + 15.7569i 0.0940875 + 0.533597i
\(873\) 34.0000 1.15073
\(874\) 0 0
\(875\) 0 0
\(876\) 0.173648 + 0.984808i 0.00586703 + 0.0332736i
\(877\) −15.3209 + 12.8558i −0.517350 + 0.434108i −0.863707 0.503995i \(-0.831863\pi\)
0.346357 + 0.938103i \(0.387419\pi\)
\(878\) 13.1557 4.78828i 0.443983 0.161597i
\(879\) −22.5526 8.20848i −0.760681 0.276865i
\(880\) 0 0
\(881\) 4.50000 7.79423i 0.151609 0.262594i −0.780210 0.625517i \(-0.784888\pi\)
0.931819 + 0.362923i \(0.118221\pi\)
\(882\) 9.00000 + 15.5885i 0.303046 + 0.524891i
\(883\) −3.29932 + 18.7113i −0.111031 + 0.629687i 0.877608 + 0.479378i \(0.159138\pi\)
−0.988639 + 0.150309i \(0.951973\pi\)
\(884\) 2.08378 11.8177i 0.0700850 0.397472i
\(885\) 0 0
\(886\) −4.50000 + 7.79423i −0.151180 + 0.261852i
\(887\) −36.7701 30.8538i −1.23462 1.03597i −0.997925 0.0643854i \(-0.979491\pi\)
−0.236695 0.971584i \(-0.576064\pi\)
\(888\) 9.39693 + 3.42020i 0.315340 + 0.114774i
\(889\) −7.51754 + 2.73616i −0.252130 + 0.0917679i
\(890\) 0 0
\(891\) 0.520945 + 2.95442i 0.0174523 + 0.0989769i
\(892\) −14.0000 −0.468755
\(893\) 0 0
\(894\) −18.0000 −0.602010
\(895\) 0 0
\(896\) −3.06418 + 2.57115i −0.102367 + 0.0858961i
\(897\) 11.2763 4.10424i 0.376505 0.137037i
\(898\) 8.45723 + 3.07818i 0.282222 + 0.102720i
\(899\) 0 0
\(900\) −5.00000 + 8.66025i −0.166667 + 0.288675i
\(901\) −18.0000 31.1769i −0.599667 1.03865i
\(902\) −4.68850 + 26.5898i −0.156110 + 0.885344i
\(903\) −2.77837 + 15.7569i −0.0924584 + 0.524358i
\(904\) 7.50000 + 12.9904i 0.249446 + 0.432054i
\(905\) 0 0
\(906\) −7.66044 6.42788i −0.254501 0.213552i
\(907\) 15.9748 + 5.81434i 0.530434 + 0.193062i 0.593332 0.804958i \(-0.297812\pi\)
−0.0628983 + 0.998020i \(0.520034\pi\)
\(908\) 2.81908 1.02606i 0.0935544 0.0340510i
\(909\) 0 0
\(910\) 0 0
\(911\) −30.0000 −0.993944 −0.496972 0.867766i \(-0.665555\pi\)
−0.496972 + 0.867766i \(0.665555\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 0.868241 + 4.92404i 0.0287189 + 0.162873i
\(915\) 0 0
\(916\) 15.0351 5.47232i 0.496773 0.180811i
\(917\) 33.8289 + 12.3127i 1.11713 + 0.406602i
\(918\) −22.9813 19.2836i −0.758497 0.636455i
\(919\) 5.00000 8.66025i 0.164935 0.285675i −0.771697 0.635990i \(-0.780592\pi\)
0.936632 + 0.350315i \(0.113925\pi\)
\(920\) 0 0
\(921\) −1.21554 + 6.89365i −0.0400533 + 0.227154i
\(922\) 1.04189 5.90885i 0.0343128 0.194597i
\(923\) 6.00000 + 10.3923i 0.197492 + 0.342067i
\(924\) −6.00000 + 10.3923i −0.197386 + 0.341882i
\(925\) −38.3022 32.1394i −1.25937 1.05674i
\(926\) 31.9495 + 11.6287i 1.04993 + 0.382142i
\(927\) −3.75877 + 1.36808i −0.123454 + 0.0449337i
\(928\) 0 0
\(929\) −0.520945 2.95442i −0.0170916 0.0969315i 0.975069 0.221904i \(-0.0712270\pi\)
−0.992160 + 0.124972i \(0.960116\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 3.00000 0.0982683
\(933\) 5.20945 + 29.5442i 0.170550 + 0.967235i
\(934\) −20.6832 + 17.3553i −0.676775 + 0.567882i
\(935\) 0 0
\(936\) −3.75877 1.36808i −0.122859 0.0447171i
\(937\) 26.8116 + 22.4976i 0.875895 + 0.734963i 0.965331 0.261029i \(-0.0840619\pi\)
−0.0894356 + 0.995993i \(0.528506\pi\)
\(938\) 14.0000 24.2487i 0.457116 0.791748i
\(939\) −9.50000 16.4545i −0.310021 0.536972i
\(940\) 0 0
\(941\) 7.29322 41.3619i 0.237752 1.34836i −0.598987 0.800759i \(-0.704430\pi\)
0.836739 0.547601i \(-0.184459\pi\)
\(942\) −8.00000 13.8564i −0.260654 0.451466i
\(943\) −27.0000 + 46.7654i −0.879241 + 1.52289i
\(944\) 6.89440 + 5.78509i 0.224394 + 0.188289i
\(945\) 0 0
\(946\) 11.2763 4.10424i 0.366625 0.133440i
\(947\) 45.9627 38.5673i 1.49359 1.25327i 0.603594 0.797292i \(-0.293735\pi\)
0.889992 0.455975i \(-0.150709\pi\)
\(948\) −0.694593 3.93923i −0.0225593 0.127940i
\(949\) 2.00000 0.0649227
\(950\) 0 0
\(951\) −18.0000 −0.583690
\(952\) 4.16756 + 23.6354i 0.135071 + 0.766027i
\(953\) 11.4907 9.64181i 0.372219 0.312329i −0.437420 0.899258i \(-0.644108\pi\)
0.809639 + 0.586929i \(0.199663\pi\)
\(954\) −11.2763 + 4.10424i −0.365084 + 0.132880i
\(955\) 0 0
\(956\) −9.19253 7.71345i −0.297308 0.249471i
\(957\) 0 0
\(958\) −18.0000 31.1769i −0.581554 1.00728i
\(959\) −6.25133 + 35.4531i −0.201866 + 1.14484i
\(960\) 0 0
\(961\) 13.5000 + 23.3827i 0.435484 + 0.754280i
\(962\) 10.0000 17.3205i 0.322413 0.558436i
\(963\) 0 0
\(964\) 4.69846 + 1.71010i 0.151327 + 0.0550786i
\(965\) 0 0
\(966\) −18.3851 + 15.4269i −0.591530 + 0.496352i
\(967\) −5.90404 33.4835i −0.189861 1.07676i −0.919549 0.392975i \(-0.871446\pi\)
0.729688 0.683780i \(-0.239665\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) −3.64661 20.6810i −0.117025 0.663684i −0.985727 0.168349i \(-0.946156\pi\)
0.868702 0.495335i \(-0.164955\pi\)
\(972\) −12.2567 + 10.2846i −0.393134 + 0.329879i
\(973\) 41.3465 15.0489i 1.32551 0.482445i
\(974\) 1.87939 + 0.684040i 0.0602194 + 0.0219181i
\(975\) −7.66044 6.42788i −0.245331 0.205857i
\(976\) 2.00000 3.46410i 0.0640184 0.110883i
\(977\) 16.5000 + 28.5788i 0.527882 + 0.914318i 0.999472 + 0.0325001i \(0.0103469\pi\)
−0.471590 + 0.881818i \(0.656320\pi\)
\(978\) 3.29932 18.7113i 0.105500 0.598323i
\(979\) −3.12567 + 17.7265i −0.0998968 + 0.566543i
\(980\) 0 0
\(981\) 16.0000 27.7128i 0.510841 0.884802i
\(982\) 0 0
\(983\) 22.5526 + 8.20848i 0.719317 + 0.261810i 0.675636 0.737236i \(-0.263869\pi\)
0.0436812 + 0.999046i \(0.486091\pi\)
\(984\) −8.45723 + 3.07818i −0.269607 + 0.0981288i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) −6.12836 + 5.14230i −0.194674 + 0.163351i −0.734914 0.678160i \(-0.762778\pi\)
0.540241 + 0.841511i \(0.318333\pi\)
\(992\) 1.87939 0.684040i 0.0596705 0.0217183i
\(993\) −4.69846 1.71010i −0.149101 0.0542684i
\(994\) −18.3851 15.4269i −0.583139 0.489312i
\(995\) 0 0
\(996\) 1.50000 + 2.59808i 0.0475293 + 0.0823232i
\(997\) −0.694593 + 3.93923i −0.0219980 + 0.124757i −0.993829 0.110921i \(-0.964620\pi\)
0.971831 + 0.235678i \(0.0757310\pi\)
\(998\) −4.34120 + 24.6202i −0.137418 + 0.779339i
\(999\) −25.0000 43.3013i −0.790965 1.36999i
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 722.2.e.i.389.1 6
19.2 odd 18 722.2.e.j.245.1 6
19.3 odd 18 722.2.e.j.423.1 6
19.4 even 9 722.2.c.b.429.1 2
19.5 even 9 inner 722.2.e.i.415.1 6
19.6 even 9 722.2.a.d.1.1 1
19.7 even 3 inner 722.2.e.i.99.1 6
19.8 odd 6 722.2.e.j.595.1 6
19.9 even 9 722.2.c.b.653.1 2
19.10 odd 18 38.2.c.a.7.1 2
19.11 even 3 inner 722.2.e.i.595.1 6
19.12 odd 6 722.2.e.j.99.1 6
19.13 odd 18 722.2.a.c.1.1 1
19.14 odd 18 722.2.e.j.415.1 6
19.15 odd 18 38.2.c.a.11.1 yes 2
19.16 even 9 inner 722.2.e.i.423.1 6
19.17 even 9 inner 722.2.e.i.245.1 6
19.18 odd 2 722.2.e.j.389.1 6
57.29 even 18 342.2.g.b.235.1 2
57.32 even 18 6498.2.a.s.1.1 1
57.44 odd 18 6498.2.a.e.1.1 1
57.53 even 18 342.2.g.b.163.1 2
76.15 even 18 304.2.i.c.49.1 2
76.51 even 18 5776.2.a.g.1.1 1
76.63 odd 18 5776.2.a.n.1.1 1
76.67 even 18 304.2.i.c.273.1 2
95.29 odd 18 950.2.e.d.501.1 2
95.34 odd 18 950.2.e.d.201.1 2
95.48 even 36 950.2.j.e.349.2 4
95.53 even 36 950.2.j.e.49.1 4
95.67 even 36 950.2.j.e.349.1 4
95.72 even 36 950.2.j.e.49.2 4
152.29 odd 18 1216.2.i.h.577.1 2
152.53 odd 18 1216.2.i.h.961.1 2
152.67 even 18 1216.2.i.d.577.1 2
152.91 even 18 1216.2.i.d.961.1 2
228.143 odd 18 2736.2.s.m.577.1 2
228.167 odd 18 2736.2.s.m.1873.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.c.a.7.1 2 19.10 odd 18
38.2.c.a.11.1 yes 2 19.15 odd 18
304.2.i.c.49.1 2 76.15 even 18
304.2.i.c.273.1 2 76.67 even 18
342.2.g.b.163.1 2 57.53 even 18
342.2.g.b.235.1 2 57.29 even 18
722.2.a.c.1.1 1 19.13 odd 18
722.2.a.d.1.1 1 19.6 even 9
722.2.c.b.429.1 2 19.4 even 9
722.2.c.b.653.1 2 19.9 even 9
722.2.e.i.99.1 6 19.7 even 3 inner
722.2.e.i.245.1 6 19.17 even 9 inner
722.2.e.i.389.1 6 1.1 even 1 trivial
722.2.e.i.415.1 6 19.5 even 9 inner
722.2.e.i.423.1 6 19.16 even 9 inner
722.2.e.i.595.1 6 19.11 even 3 inner
722.2.e.j.99.1 6 19.12 odd 6
722.2.e.j.245.1 6 19.2 odd 18
722.2.e.j.389.1 6 19.18 odd 2
722.2.e.j.415.1 6 19.14 odd 18
722.2.e.j.423.1 6 19.3 odd 18
722.2.e.j.595.1 6 19.8 odd 6
950.2.e.d.201.1 2 95.34 odd 18
950.2.e.d.501.1 2 95.29 odd 18
950.2.j.e.49.1 4 95.53 even 36
950.2.j.e.49.2 4 95.72 even 36
950.2.j.e.349.1 4 95.67 even 36
950.2.j.e.349.2 4 95.48 even 36
1216.2.i.d.577.1 2 152.67 even 18
1216.2.i.d.961.1 2 152.91 even 18
1216.2.i.h.577.1 2 152.29 odd 18
1216.2.i.h.961.1 2 152.53 odd 18
2736.2.s.m.577.1 2 228.143 odd 18
2736.2.s.m.1873.1 2 228.167 odd 18
5776.2.a.g.1.1 1 76.51 even 18
5776.2.a.n.1.1 1 76.63 odd 18
6498.2.a.e.1.1 1 57.44 odd 18
6498.2.a.s.1.1 1 57.32 even 18