Properties

Label 225.2.h.c.181.2
Level $225$
Weight $2$
Character 225.181
Analytic conductor $1.797$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.2
Root \(1.40799 + 0.132563i\) of defining polynomial
Character \(\chi\) \(=\) 225.181
Dual form 225.2.h.c.46.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.346820 + 1.06740i) q^{2} +(0.598970 - 0.435177i) q^{4} +(-0.407987 + 2.19853i) q^{5} +1.11373 q^{7} +(2.48822 + 1.80780i) q^{8} +O(q^{10})\) \(q+(0.346820 + 1.06740i) q^{2} +(0.598970 - 0.435177i) q^{4} +(-0.407987 + 2.19853i) q^{5} +1.11373 q^{7} +(2.48822 + 1.80780i) q^{8} +(-2.48822 + 0.327009i) q^{10} +(-1.13412 - 3.49045i) q^{11} +(-1.25215 + 3.85372i) q^{13} +(0.386266 + 1.18880i) q^{14} +(-0.609110 + 1.87465i) q^{16} +(1.71700 + 1.24748i) q^{17} +(3.28513 + 2.38678i) q^{19} +(0.712379 + 1.49440i) q^{20} +(3.33238 - 2.42112i) q^{22} +(-1.90799 - 5.87218i) q^{23} +(-4.66709 - 1.79395i) q^{25} -4.54774 q^{26} +(0.667093 - 0.484672i) q^{28} +(-1.82808 + 1.32818i) q^{29} +(-8.13227 - 5.90844i) q^{31} +3.93896 q^{32} +(-0.736068 + 2.26538i) q^{34} +(-0.454389 + 2.44858i) q^{35} +(2.27817 - 7.01149i) q^{37} +(-1.40831 + 4.33434i) q^{38} +(-4.98966 + 4.73287i) q^{40} +(2.30902 - 7.10642i) q^{41} +9.24998 q^{43} +(-2.19826 - 1.59713i) q^{44} +(5.60625 - 4.07318i) q^{46} +(-2.53032 + 1.83839i) q^{47} -5.75960 q^{49} +(0.296220 - 5.60384i) q^{50} +(0.927051 + 2.85317i) q^{52} +(-2.83934 + 2.06290i) q^{53} +(8.13657 - 1.06933i) q^{55} +(2.77121 + 2.01340i) q^{56} +(-2.05172 - 1.49066i) q^{58} +(2.03760 - 6.27109i) q^{59} +(-2.81332 - 8.65850i) q^{61} +(3.48625 - 10.7296i) q^{62} +(2.58433 + 7.95375i) q^{64} +(-7.96167 - 4.32516i) q^{65} +(-2.12499 - 1.54390i) q^{67} +1.57131 q^{68} +(-2.77121 + 0.364201i) q^{70} +(0.534620 - 0.388424i) q^{71} +(2.31003 + 7.10955i) q^{73} +8.27420 q^{74} +3.00637 q^{76} +(-1.26310 - 3.88743i) q^{77} +(-6.90667 + 5.01799i) q^{79} +(-3.87297 - 2.10398i) q^{80} +8.38623 q^{82} +(9.92170 + 7.20854i) q^{83} +(-3.44313 + 3.26594i) q^{85} +(3.20808 + 9.87345i) q^{86} +(3.48809 - 10.7352i) q^{88} +(4.72429 + 14.5399i) q^{89} +(-1.39456 + 4.29202i) q^{91} +(-3.69826 - 2.68695i) q^{92} +(-2.83986 - 2.06328i) q^{94} +(-6.58771 + 6.24868i) q^{95} +(-10.9217 + 7.93508i) q^{97} +(-1.99754 - 6.14781i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{11} - 8 q^{13} + 8 q^{14} - 17 q^{16} + q^{17} - 5 q^{19} + 10 q^{20} + 13 q^{22} - 7 q^{23} - 15 q^{25} - 6 q^{26} - 17 q^{28} - 5 q^{29} - 19 q^{31} - 24 q^{32} + 12 q^{34} + 10 q^{35} - q^{37} + 10 q^{38} + 25 q^{40} + 14 q^{41} + 32 q^{43} + 3 q^{44} + 16 q^{46} + q^{47} + 16 q^{49} - 10 q^{50} - 6 q^{52} + 3 q^{53} + 15 q^{55} + 15 q^{56} + 5 q^{58} - 30 q^{59} - 14 q^{61} + 17 q^{62} - 44 q^{64} - 25 q^{65} + 4 q^{67} + 22 q^{68} - 15 q^{70} - 21 q^{71} + 2 q^{73} + 38 q^{74} + 80 q^{76} + 37 q^{77} - 30 q^{79} + 50 q^{80} - 12 q^{82} - 2 q^{83} - 30 q^{85} + 34 q^{86} + 70 q^{88} + 21 q^{91} - 9 q^{92} - 33 q^{94} - 65 q^{95} - 6 q^{97} - 73 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.346820 + 1.06740i 0.245239 + 0.754768i 0.995597 + 0.0937362i \(0.0298810\pi\)
−0.750358 + 0.661031i \(0.770119\pi\)
\(3\) 0 0
\(4\) 0.598970 0.435177i 0.299485 0.217589i
\(5\) −0.407987 + 2.19853i −0.182457 + 0.983214i
\(6\) 0 0
\(7\) 1.11373 0.420952 0.210476 0.977599i \(-0.432499\pi\)
0.210476 + 0.977599i \(0.432499\pi\)
\(8\) 2.48822 + 1.80780i 0.879718 + 0.639152i
\(9\) 0 0
\(10\) −2.48822 + 0.327009i −0.786844 + 0.103409i
\(11\) −1.13412 3.49045i −0.341949 1.05241i −0.963197 0.268796i \(-0.913374\pi\)
0.621248 0.783614i \(-0.286626\pi\)
\(12\) 0 0
\(13\) −1.25215 + 3.85372i −0.347284 + 1.06883i 0.613066 + 0.790032i \(0.289936\pi\)
−0.960350 + 0.278798i \(0.910064\pi\)
\(14\) 0.386266 + 1.18880i 0.103234 + 0.317721i
\(15\) 0 0
\(16\) −0.609110 + 1.87465i −0.152277 + 0.468662i
\(17\) 1.71700 + 1.24748i 0.416435 + 0.302557i 0.776202 0.630485i \(-0.217144\pi\)
−0.359767 + 0.933042i \(0.617144\pi\)
\(18\) 0 0
\(19\) 3.28513 + 2.38678i 0.753660 + 0.547566i 0.896959 0.442113i \(-0.145771\pi\)
−0.143299 + 0.989679i \(0.545771\pi\)
\(20\) 0.712379 + 1.49440i 0.159293 + 0.334158i
\(21\) 0 0
\(22\) 3.33238 2.42112i 0.710466 0.516184i
\(23\) −1.90799 5.87218i −0.397843 1.22443i −0.926725 0.375739i \(-0.877389\pi\)
0.528883 0.848695i \(-0.322611\pi\)
\(24\) 0 0
\(25\) −4.66709 1.79395i −0.933419 0.358789i
\(26\) −4.54774 −0.891886
\(27\) 0 0
\(28\) 0.667093 0.484672i 0.126069 0.0915943i
\(29\) −1.82808 + 1.32818i −0.339466 + 0.246637i −0.744437 0.667693i \(-0.767282\pi\)
0.404970 + 0.914330i \(0.367282\pi\)
\(30\) 0 0
\(31\) −8.13227 5.90844i −1.46060 1.06119i −0.983206 0.182498i \(-0.941582\pi\)
−0.477393 0.878690i \(-0.658418\pi\)
\(32\) 3.93896 0.696316
\(33\) 0 0
\(34\) −0.736068 + 2.26538i −0.126235 + 0.388510i
\(35\) −0.454389 + 2.44858i −0.0768058 + 0.413886i
\(36\) 0 0
\(37\) 2.27817 7.01149i 0.374529 1.15268i −0.569267 0.822153i \(-0.692773\pi\)
0.943796 0.330529i \(-0.107227\pi\)
\(38\) −1.40831 + 4.33434i −0.228458 + 0.703123i
\(39\) 0 0
\(40\) −4.98966 + 4.73287i −0.788934 + 0.748333i
\(41\) 2.30902 7.10642i 0.360608 1.10984i −0.592078 0.805881i \(-0.701692\pi\)
0.952686 0.303956i \(-0.0983077\pi\)
\(42\) 0 0
\(43\) 9.24998 1.41061 0.705304 0.708905i \(-0.250810\pi\)
0.705304 + 0.708905i \(0.250810\pi\)
\(44\) −2.19826 1.59713i −0.331401 0.240777i
\(45\) 0 0
\(46\) 5.60625 4.07318i 0.826597 0.600558i
\(47\) −2.53032 + 1.83839i −0.369085 + 0.268156i −0.756831 0.653610i \(-0.773254\pi\)
0.387746 + 0.921766i \(0.373254\pi\)
\(48\) 0 0
\(49\) −5.75960 −0.822799
\(50\) 0.296220 5.60384i 0.0418918 0.792503i
\(51\) 0 0
\(52\) 0.927051 + 2.85317i 0.128559 + 0.395663i
\(53\) −2.83934 + 2.06290i −0.390013 + 0.283361i −0.765461 0.643483i \(-0.777489\pi\)
0.375448 + 0.926844i \(0.377489\pi\)
\(54\) 0 0
\(55\) 8.13657 1.06933i 1.09714 0.144189i
\(56\) 2.77121 + 2.01340i 0.370319 + 0.269053i
\(57\) 0 0
\(58\) −2.05172 1.49066i −0.269404 0.195733i
\(59\) 2.03760 6.27109i 0.265273 0.816427i −0.726357 0.687317i \(-0.758788\pi\)
0.991630 0.129110i \(-0.0412119\pi\)
\(60\) 0 0
\(61\) −2.81332 8.65850i −0.360208 1.10861i −0.952928 0.303198i \(-0.901946\pi\)
0.592719 0.805409i \(-0.298054\pi\)
\(62\) 3.48625 10.7296i 0.442754 1.36266i
\(63\) 0 0
\(64\) 2.58433 + 7.95375i 0.323041 + 0.994219i
\(65\) −7.96167 4.32516i −0.987524 0.536470i
\(66\) 0 0
\(67\) −2.12499 1.54390i −0.259609 0.188617i 0.450366 0.892844i \(-0.351294\pi\)
−0.709975 + 0.704227i \(0.751294\pi\)
\(68\) 1.57131 0.190549
\(69\) 0 0
\(70\) −2.77121 + 0.364201i −0.331223 + 0.0435304i
\(71\) 0.534620 0.388424i 0.0634477 0.0460975i −0.555609 0.831443i \(-0.687515\pi\)
0.619057 + 0.785346i \(0.287515\pi\)
\(72\) 0 0
\(73\) 2.31003 + 7.10955i 0.270369 + 0.832110i 0.990408 + 0.138176i \(0.0441239\pi\)
−0.720039 + 0.693934i \(0.755876\pi\)
\(74\) 8.27420 0.961856
\(75\) 0 0
\(76\) 3.00637 0.344854
\(77\) −1.26310 3.88743i −0.143944 0.443014i
\(78\) 0 0
\(79\) −6.90667 + 5.01799i −0.777061 + 0.564568i −0.904096 0.427330i \(-0.859454\pi\)
0.127034 + 0.991898i \(0.459454\pi\)
\(80\) −3.87297 2.10398i −0.433011 0.235232i
\(81\) 0 0
\(82\) 8.38623 0.926104
\(83\) 9.92170 + 7.20854i 1.08905 + 0.791240i 0.979238 0.202713i \(-0.0649758\pi\)
0.109810 + 0.993953i \(0.464976\pi\)
\(84\) 0 0
\(85\) −3.44313 + 3.26594i −0.373460 + 0.354240i
\(86\) 3.20808 + 9.87345i 0.345936 + 1.06468i
\(87\) 0 0
\(88\) 3.48809 10.7352i 0.371832 1.14438i
\(89\) 4.72429 + 14.5399i 0.500773 + 1.54122i 0.807762 + 0.589509i \(0.200679\pi\)
−0.306989 + 0.951713i \(0.599321\pi\)
\(90\) 0 0
\(91\) −1.39456 + 4.29202i −0.146190 + 0.449926i
\(92\) −3.69826 2.68695i −0.385571 0.280134i
\(93\) 0 0
\(94\) −2.83986 2.06328i −0.292910 0.212811i
\(95\) −6.58771 + 6.24868i −0.675885 + 0.641101i
\(96\) 0 0
\(97\) −10.9217 + 7.93508i −1.10893 + 0.805685i −0.982495 0.186290i \(-0.940354\pi\)
−0.126436 + 0.991975i \(0.540354\pi\)
\(98\) −1.99754 6.14781i −0.201782 0.621022i
\(99\) 0 0
\(100\) −3.57613 + 0.956493i −0.357613 + 0.0956493i
\(101\) −7.22642 −0.719055 −0.359528 0.933134i \(-0.617062\pi\)
−0.359528 + 0.933134i \(0.617062\pi\)
\(102\) 0 0
\(103\) −4.26957 + 3.10203i −0.420693 + 0.305652i −0.777917 0.628367i \(-0.783723\pi\)
0.357223 + 0.934019i \(0.383723\pi\)
\(104\) −10.0824 + 7.32526i −0.988657 + 0.718301i
\(105\) 0 0
\(106\) −3.18668 2.31526i −0.309518 0.224878i
\(107\) −5.46682 −0.528498 −0.264249 0.964455i \(-0.585124\pi\)
−0.264249 + 0.964455i \(0.585124\pi\)
\(108\) 0 0
\(109\) 3.50410 10.7845i 0.335632 1.03297i −0.630778 0.775963i \(-0.717264\pi\)
0.966410 0.257005i \(-0.0827358\pi\)
\(110\) 3.96334 + 8.31413i 0.377889 + 0.792721i
\(111\) 0 0
\(112\) −0.678387 + 2.08786i −0.0641015 + 0.197284i
\(113\) −1.49416 + 4.59855i −0.140559 + 0.432595i −0.996413 0.0846215i \(-0.973032\pi\)
0.855854 + 0.517217i \(0.173032\pi\)
\(114\) 0 0
\(115\) 13.6886 1.79900i 1.27647 0.167758i
\(116\) −0.516973 + 1.59108i −0.0479997 + 0.147728i
\(117\) 0 0
\(118\) 7.40046 0.681268
\(119\) 1.91229 + 1.38936i 0.175299 + 0.127362i
\(120\) 0 0
\(121\) −1.99783 + 1.45151i −0.181621 + 0.131955i
\(122\) 8.26639 6.00588i 0.748404 0.543747i
\(123\) 0 0
\(124\) −7.44220 −0.668330
\(125\) 5.84816 9.52885i 0.523075 0.852286i
\(126\) 0 0
\(127\) 0.234728 + 0.722418i 0.0208287 + 0.0641043i 0.960931 0.276789i \(-0.0892704\pi\)
−0.940102 + 0.340894i \(0.889270\pi\)
\(128\) −1.22019 + 0.886518i −0.107850 + 0.0783578i
\(129\) 0 0
\(130\) 1.85542 9.99836i 0.162731 0.876914i
\(131\) 11.8562 + 8.61406i 1.03588 + 0.752614i 0.969478 0.245179i \(-0.0788467\pi\)
0.0664061 + 0.997793i \(0.478847\pi\)
\(132\) 0 0
\(133\) 3.65876 + 2.65824i 0.317255 + 0.230499i
\(134\) 0.910969 2.80367i 0.0786958 0.242201i
\(135\) 0 0
\(136\) 2.01710 + 6.20799i 0.172965 + 0.532330i
\(137\) −3.79825 + 11.6898i −0.324506 + 0.998728i 0.647157 + 0.762357i \(0.275958\pi\)
−0.971663 + 0.236371i \(0.924042\pi\)
\(138\) 0 0
\(139\) 4.55306 + 14.0129i 0.386185 + 1.18856i 0.935617 + 0.353017i \(0.114844\pi\)
−0.549432 + 0.835539i \(0.685156\pi\)
\(140\) 0.793401 + 1.66437i 0.0670547 + 0.140665i
\(141\) 0 0
\(142\) 0.600022 + 0.435941i 0.0503527 + 0.0365834i
\(143\) 14.8713 1.24360
\(144\) 0 0
\(145\) −2.17421 4.56098i −0.180558 0.378768i
\(146\) −6.78758 + 4.93147i −0.561744 + 0.408131i
\(147\) 0 0
\(148\) −1.68668 5.19108i −0.138645 0.426704i
\(149\) −15.6498 −1.28208 −0.641041 0.767507i \(-0.721497\pi\)
−0.641041 + 0.767507i \(0.721497\pi\)
\(150\) 0 0
\(151\) 3.95819 0.322113 0.161056 0.986945i \(-0.448510\pi\)
0.161056 + 0.986945i \(0.448510\pi\)
\(152\) 3.85929 + 11.8777i 0.313030 + 0.963407i
\(153\) 0 0
\(154\) 3.71139 2.69648i 0.299072 0.217289i
\(155\) 16.3078 15.4685i 1.30987 1.24246i
\(156\) 0 0
\(157\) −4.50061 −0.359188 −0.179594 0.983741i \(-0.557478\pi\)
−0.179594 + 0.983741i \(0.557478\pi\)
\(158\) −7.75159 5.63186i −0.616683 0.448047i
\(159\) 0 0
\(160\) −1.60704 + 8.65993i −0.127048 + 0.684627i
\(161\) −2.12499 6.54005i −0.167473 0.515428i
\(162\) 0 0
\(163\) −0.758292 + 2.33378i −0.0593940 + 0.182796i −0.976352 0.216189i \(-0.930637\pi\)
0.916958 + 0.398985i \(0.130637\pi\)
\(164\) −1.70952 5.26137i −0.133491 0.410844i
\(165\) 0 0
\(166\) −4.25337 + 13.0905i −0.330125 + 1.01602i
\(167\) −2.47824 1.80055i −0.191772 0.139331i 0.487756 0.872980i \(-0.337816\pi\)
−0.679528 + 0.733649i \(0.737816\pi\)
\(168\) 0 0
\(169\) −2.76606 2.00966i −0.212774 0.154589i
\(170\) −4.68022 2.54252i −0.358956 0.195002i
\(171\) 0 0
\(172\) 5.54046 4.02538i 0.422456 0.306932i
\(173\) −3.47942 10.7085i −0.264535 0.814156i −0.991800 0.127799i \(-0.959209\pi\)
0.727265 0.686357i \(-0.240791\pi\)
\(174\) 0 0
\(175\) −5.19790 1.99798i −0.392925 0.151033i
\(176\) 7.23416 0.545296
\(177\) 0 0
\(178\) −13.8814 + 10.0854i −1.04046 + 0.755935i
\(179\) 8.13657 5.91157i 0.608156 0.441851i −0.240609 0.970622i \(-0.577347\pi\)
0.848764 + 0.528771i \(0.177347\pi\)
\(180\) 0 0
\(181\) 15.7503 + 11.4433i 1.17071 + 0.850571i 0.991094 0.133165i \(-0.0425141\pi\)
0.179617 + 0.983737i \(0.442514\pi\)
\(182\) −5.06498 −0.375441
\(183\) 0 0
\(184\) 5.86822 18.0605i 0.432611 1.33144i
\(185\) 14.4855 + 7.86923i 1.06500 + 0.578557i
\(186\) 0 0
\(187\) 2.40697 7.40790i 0.176015 0.541719i
\(188\) −0.715563 + 2.20227i −0.0521878 + 0.160617i
\(189\) 0 0
\(190\) −8.95461 4.86457i −0.649636 0.352913i
\(191\) 3.58739 11.0408i 0.259574 0.798888i −0.733320 0.679884i \(-0.762030\pi\)
0.992894 0.119003i \(-0.0379700\pi\)
\(192\) 0 0
\(193\) −3.38156 −0.243410 −0.121705 0.992566i \(-0.538836\pi\)
−0.121705 + 0.992566i \(0.538836\pi\)
\(194\) −12.2578 8.90581i −0.880058 0.639400i
\(195\) 0 0
\(196\) −3.44982 + 2.50644i −0.246416 + 0.179032i
\(197\) −14.2291 + 10.3380i −1.01378 + 0.736554i −0.964998 0.262256i \(-0.915534\pi\)
−0.0487811 + 0.998809i \(0.515534\pi\)
\(198\) 0 0
\(199\) 20.0102 1.41849 0.709244 0.704963i \(-0.249037\pi\)
0.709244 + 0.704963i \(0.249037\pi\)
\(200\) −8.36966 12.9009i −0.591824 0.912230i
\(201\) 0 0
\(202\) −2.50627 7.71350i −0.176340 0.542720i
\(203\) −2.03600 + 1.47924i −0.142899 + 0.103822i
\(204\) 0 0
\(205\) 14.6817 + 7.97578i 1.02541 + 0.557052i
\(206\) −4.79188 3.48151i −0.333866 0.242568i
\(207\) 0 0
\(208\) −6.46167 4.69468i −0.448036 0.325517i
\(209\) 4.60524 14.1735i 0.318551 0.980399i
\(210\) 0 0
\(211\) 0.754807 + 2.32306i 0.0519631 + 0.159926i 0.973671 0.227960i \(-0.0732055\pi\)
−0.921707 + 0.387886i \(0.873206\pi\)
\(212\) −0.802951 + 2.47123i −0.0551469 + 0.169725i
\(213\) 0 0
\(214\) −1.89600 5.83530i −0.129608 0.398893i
\(215\) −3.77387 + 20.3364i −0.257376 + 1.38693i
\(216\) 0 0
\(217\) −9.05719 6.58044i −0.614842 0.446709i
\(218\) 12.7267 0.861961
\(219\) 0 0
\(220\) 4.40821 4.18135i 0.297202 0.281906i
\(221\) −6.95737 + 5.05483i −0.468003 + 0.340024i
\(222\) 0 0
\(223\) −7.92223 24.3821i −0.530511 1.63275i −0.753153 0.657846i \(-0.771468\pi\)
0.222641 0.974900i \(-0.428532\pi\)
\(224\) 4.38695 0.293116
\(225\) 0 0
\(226\) −5.42671 −0.360979
\(227\) −2.02819 6.24212i −0.134616 0.414304i 0.860914 0.508750i \(-0.169892\pi\)
−0.995530 + 0.0944455i \(0.969892\pi\)
\(228\) 0 0
\(229\) 6.44293 4.68106i 0.425761 0.309333i −0.354191 0.935173i \(-0.615244\pi\)
0.779952 + 0.625840i \(0.215244\pi\)
\(230\) 6.66774 + 13.9873i 0.439658 + 0.922297i
\(231\) 0 0
\(232\) −6.94974 −0.456273
\(233\) −7.62181 5.53757i −0.499321 0.362778i 0.309436 0.950920i \(-0.399860\pi\)
−0.808758 + 0.588142i \(0.799860\pi\)
\(234\) 0 0
\(235\) −3.00941 6.31303i −0.196312 0.411817i
\(236\) −1.50857 4.64291i −0.0981998 0.302228i
\(237\) 0 0
\(238\) −0.819784 + 2.52304i −0.0531387 + 0.163544i
\(239\) 3.46814 + 10.6738i 0.224335 + 0.690433i 0.998358 + 0.0572756i \(0.0182414\pi\)
−0.774023 + 0.633157i \(0.781759\pi\)
\(240\) 0 0
\(241\) 7.00879 21.5708i 0.451476 1.38950i −0.423748 0.905780i \(-0.639286\pi\)
0.875223 0.483719i \(-0.160714\pi\)
\(242\) −2.24223 1.62908i −0.144136 0.104721i
\(243\) 0 0
\(244\) −5.45307 3.96189i −0.349097 0.253634i
\(245\) 2.34984 12.6627i 0.150126 0.808988i
\(246\) 0 0
\(247\) −13.3115 + 9.67135i −0.846989 + 0.615373i
\(248\) −9.55361 29.4030i −0.606655 1.86709i
\(249\) 0 0
\(250\) 12.1994 + 2.93754i 0.771557 + 0.185787i
\(251\) 6.76819 0.427205 0.213602 0.976921i \(-0.431480\pi\)
0.213602 + 0.976921i \(0.431480\pi\)
\(252\) 0 0
\(253\) −18.3327 + 13.3195i −1.15257 + 0.837387i
\(254\) −0.689703 + 0.501098i −0.0432758 + 0.0314417i
\(255\) 0 0
\(256\) 12.1623 + 8.83640i 0.760142 + 0.552275i
\(257\) 14.7934 0.922786 0.461393 0.887196i \(-0.347350\pi\)
0.461393 + 0.887196i \(0.347350\pi\)
\(258\) 0 0
\(259\) 2.53728 7.80894i 0.157659 0.485224i
\(260\) −6.65101 + 0.874096i −0.412478 + 0.0542092i
\(261\) 0 0
\(262\) −5.08269 + 15.6429i −0.314009 + 0.966422i
\(263\) −6.17070 + 18.9915i −0.380502 + 1.17106i 0.559189 + 0.829040i \(0.311113\pi\)
−0.939691 + 0.342024i \(0.888887\pi\)
\(264\) 0 0
\(265\) −3.37694 7.08401i −0.207444 0.435167i
\(266\) −1.56849 + 4.82730i −0.0961700 + 0.295981i
\(267\) 0 0
\(268\) −1.94467 −0.118790
\(269\) −8.28280 6.01780i −0.505011 0.366912i 0.305917 0.952058i \(-0.401037\pi\)
−0.810928 + 0.585146i \(0.801037\pi\)
\(270\) 0 0
\(271\) −9.95701 + 7.23419i −0.604845 + 0.439446i −0.847595 0.530643i \(-0.821950\pi\)
0.242750 + 0.970089i \(0.421950\pi\)
\(272\) −3.38442 + 2.45893i −0.205211 + 0.149094i
\(273\) 0 0
\(274\) −13.7950 −0.833389
\(275\) −0.968651 + 18.3248i −0.0584118 + 1.10503i
\(276\) 0 0
\(277\) 9.75011 + 30.0077i 0.585827 + 1.80299i 0.595923 + 0.803041i \(0.296786\pi\)
−0.0100963 + 0.999949i \(0.503214\pi\)
\(278\) −13.3783 + 9.71989i −0.802376 + 0.582960i
\(279\) 0 0
\(280\) −5.55716 + 5.27116i −0.332104 + 0.315012i
\(281\) −17.2417 12.5268i −1.02855 0.747288i −0.0605353 0.998166i \(-0.519281\pi\)
−0.968019 + 0.250878i \(0.919281\pi\)
\(282\) 0 0
\(283\) 0.699317 + 0.508083i 0.0415701 + 0.0302024i 0.608376 0.793649i \(-0.291821\pi\)
−0.566806 + 0.823851i \(0.691821\pi\)
\(284\) 0.151188 0.465309i 0.00897135 0.0276110i
\(285\) 0 0
\(286\) 5.15767 + 15.8737i 0.304979 + 0.938629i
\(287\) 2.57163 7.91467i 0.151799 0.467188i
\(288\) 0 0
\(289\) −3.86138 11.8841i −0.227140 0.699066i
\(290\) 4.11434 3.90260i 0.241602 0.229168i
\(291\) 0 0
\(292\) 4.47755 + 3.25313i 0.262029 + 0.190375i
\(293\) −3.17701 −0.185603 −0.0928014 0.995685i \(-0.529582\pi\)
−0.0928014 + 0.995685i \(0.529582\pi\)
\(294\) 0 0
\(295\) 12.9559 + 7.03826i 0.754321 + 0.409783i
\(296\) 18.3439 13.3276i 1.06622 0.774653i
\(297\) 0 0
\(298\) −5.42766 16.7046i −0.314416 0.967673i
\(299\) 25.0188 1.44688
\(300\) 0 0
\(301\) 10.3020 0.593799
\(302\) 1.37278 + 4.22498i 0.0789945 + 0.243120i
\(303\) 0 0
\(304\) −6.47538 + 4.70464i −0.371389 + 0.269830i
\(305\) 20.1838 2.65262i 1.15572 0.151888i
\(306\) 0 0
\(307\) −0.507986 −0.0289923 −0.0144961 0.999895i \(-0.504614\pi\)
−0.0144961 + 0.999895i \(0.504614\pi\)
\(308\) −2.44828 1.77878i −0.139504 0.101356i
\(309\) 0 0
\(310\) 22.1670 + 12.0422i 1.25900 + 0.683949i
\(311\) 4.52519 + 13.9271i 0.256600 + 0.789734i 0.993510 + 0.113743i \(0.0362841\pi\)
−0.736910 + 0.675991i \(0.763716\pi\)
\(312\) 0 0
\(313\) −4.62171 + 14.2241i −0.261234 + 0.803996i 0.731303 + 0.682053i \(0.238913\pi\)
−0.992537 + 0.121943i \(0.961087\pi\)
\(314\) −1.56090 4.80397i −0.0880869 0.271103i
\(315\) 0 0
\(316\) −1.95317 + 6.01125i −0.109875 + 0.338159i
\(317\) 14.6586 + 10.6501i 0.823310 + 0.598170i 0.917659 0.397369i \(-0.130077\pi\)
−0.0943487 + 0.995539i \(0.530077\pi\)
\(318\) 0 0
\(319\) 6.70920 + 4.87452i 0.375643 + 0.272921i
\(320\) −18.5409 + 2.43671i −1.03647 + 0.136216i
\(321\) 0 0
\(322\) 6.24388 4.53644i 0.347958 0.252806i
\(323\) 2.66312 + 8.19624i 0.148180 + 0.456051i
\(324\) 0 0
\(325\) 12.7573 15.7394i 0.707646 0.873064i
\(326\) −2.75408 −0.152534
\(327\) 0 0
\(328\) 18.5923 13.5081i 1.02659 0.745860i
\(329\) −2.81811 + 2.04747i −0.155367 + 0.112881i
\(330\) 0 0
\(331\) −21.3188 15.4890i −1.17178 0.851351i −0.180563 0.983563i \(-0.557792\pi\)
−0.991221 + 0.132212i \(0.957792\pi\)
\(332\) 9.07979 0.498318
\(333\) 0 0
\(334\) 1.06241 3.26975i 0.0581322 0.178913i
\(335\) 4.26127 4.04197i 0.232818 0.220837i
\(336\) 0 0
\(337\) −3.30488 + 10.1714i −0.180028 + 0.554070i −0.999827 0.0185811i \(-0.994085\pi\)
0.819799 + 0.572651i \(0.194085\pi\)
\(338\) 1.18579 3.64949i 0.0644986 0.198506i
\(339\) 0 0
\(340\) −0.641073 + 3.45457i −0.0347670 + 0.187350i
\(341\) −11.4002 + 35.0861i −0.617354 + 1.90002i
\(342\) 0 0
\(343\) −14.2108 −0.767311
\(344\) 23.0160 + 16.7221i 1.24094 + 0.901594i
\(345\) 0 0
\(346\) 10.2236 7.42788i 0.549624 0.399325i
\(347\) 13.0850 9.50682i 0.702441 0.510353i −0.178286 0.983979i \(-0.557055\pi\)
0.880726 + 0.473626i \(0.157055\pi\)
\(348\) 0 0
\(349\) 15.2383 0.815688 0.407844 0.913052i \(-0.366281\pi\)
0.407844 + 0.913052i \(0.366281\pi\)
\(350\) 0.329910 6.24119i 0.0176344 0.333606i
\(351\) 0 0
\(352\) −4.46723 13.7487i −0.238104 0.732810i
\(353\) −23.8970 + 17.3622i −1.27191 + 0.924097i −0.999277 0.0380214i \(-0.987894\pi\)
−0.272633 + 0.962118i \(0.587894\pi\)
\(354\) 0 0
\(355\) 0.635845 + 1.33385i 0.0337472 + 0.0707935i
\(356\) 9.15712 + 6.65304i 0.485326 + 0.352610i
\(357\) 0 0
\(358\) 9.13195 + 6.63475i 0.482638 + 0.350657i
\(359\) 4.06875 12.5223i 0.214740 0.660903i −0.784431 0.620216i \(-0.787045\pi\)
0.999172 0.0406876i \(-0.0129549\pi\)
\(360\) 0 0
\(361\) −0.776002 2.38829i −0.0408422 0.125699i
\(362\) −6.75205 + 20.7807i −0.354880 + 1.09221i
\(363\) 0 0
\(364\) 1.03249 + 3.17767i 0.0541171 + 0.166555i
\(365\) −16.5730 + 2.17808i −0.867472 + 0.114006i
\(366\) 0 0
\(367\) 3.14622 + 2.28586i 0.164232 + 0.119321i 0.666865 0.745178i \(-0.267636\pi\)
−0.502634 + 0.864499i \(0.667636\pi\)
\(368\) 12.1704 0.634428
\(369\) 0 0
\(370\) −3.37576 + 18.1911i −0.175498 + 0.945710i
\(371\) −3.16227 + 2.29752i −0.164177 + 0.119281i
\(372\) 0 0
\(373\) −2.51641 7.74470i −0.130295 0.401006i 0.864534 0.502575i \(-0.167614\pi\)
−0.994829 + 0.101569i \(0.967614\pi\)
\(374\) 8.74200 0.452038
\(375\) 0 0
\(376\) −9.61941 −0.496083
\(377\) −2.82940 8.70799i −0.145721 0.448484i
\(378\) 0 0
\(379\) −8.01509 + 5.82330i −0.411708 + 0.299123i −0.774293 0.632828i \(-0.781894\pi\)
0.362585 + 0.931951i \(0.381894\pi\)
\(380\) −1.22656 + 6.60960i −0.0629211 + 0.339065i
\(381\) 0 0
\(382\) 13.0292 0.666632
\(383\) −4.22481 3.06951i −0.215878 0.156844i 0.474591 0.880206i \(-0.342596\pi\)
−0.690469 + 0.723362i \(0.742596\pi\)
\(384\) 0 0
\(385\) 9.06198 1.19095i 0.461841 0.0606966i
\(386\) −1.17279 3.60949i −0.0596937 0.183718i
\(387\) 0 0
\(388\) −3.08860 + 9.50575i −0.156800 + 0.482581i
\(389\) 1.15255 + 3.54719i 0.0584367 + 0.179850i 0.976014 0.217708i \(-0.0698579\pi\)
−0.917577 + 0.397557i \(0.869858\pi\)
\(390\) 0 0
\(391\) 4.04938 12.4627i 0.204786 0.630267i
\(392\) −14.3311 10.4122i −0.723831 0.525894i
\(393\) 0 0
\(394\) −15.9698 11.6027i −0.804545 0.584536i
\(395\) −8.21438 17.2318i −0.413310 0.867027i
\(396\) 0 0
\(397\) −3.24870 + 2.36032i −0.163048 + 0.118461i −0.666317 0.745668i \(-0.732130\pi\)
0.503270 + 0.864130i \(0.332130\pi\)
\(398\) 6.93995 + 21.3590i 0.347868 + 1.07063i
\(399\) 0 0
\(400\) 6.20579 7.65645i 0.310289 0.382822i
\(401\) 24.9890 1.24789 0.623945 0.781468i \(-0.285529\pi\)
0.623945 + 0.781468i \(0.285529\pi\)
\(402\) 0 0
\(403\) 32.9523 23.9413i 1.64147 1.19260i
\(404\) −4.32841 + 3.14477i −0.215346 + 0.156458i
\(405\) 0 0
\(406\) −2.28507 1.66020i −0.113406 0.0823943i
\(407\) −27.0570 −1.34116
\(408\) 0 0
\(409\) −7.84186 + 24.1348i −0.387755 + 1.19339i 0.546707 + 0.837324i \(0.315881\pi\)
−0.934462 + 0.356063i \(0.884119\pi\)
\(410\) −3.42147 + 18.4374i −0.168974 + 0.910558i
\(411\) 0 0
\(412\) −1.20741 + 3.71604i −0.0594850 + 0.183076i
\(413\) 2.26935 6.98433i 0.111667 0.343677i
\(414\) 0 0
\(415\) −19.8961 + 18.8722i −0.976663 + 0.926400i
\(416\) −4.93216 + 15.1796i −0.241819 + 0.744243i
\(417\) 0 0
\(418\) 16.7260 0.818094
\(419\) −24.9354 18.1166i −1.21817 0.885056i −0.222227 0.974995i \(-0.571333\pi\)
−0.995947 + 0.0899392i \(0.971333\pi\)
\(420\) 0 0
\(421\) −6.91425 + 5.02350i −0.336980 + 0.244830i −0.743387 0.668862i \(-0.766782\pi\)
0.406406 + 0.913692i \(0.366782\pi\)
\(422\) −2.21785 + 1.61137i −0.107963 + 0.0784401i
\(423\) 0 0
\(424\) −10.7942 −0.524212
\(425\) −5.77551 8.90230i −0.280154 0.431825i
\(426\) 0 0
\(427\) −3.13329 9.64327i −0.151630 0.466670i
\(428\) −3.27446 + 2.37904i −0.158277 + 0.114995i
\(429\) 0 0
\(430\) −23.0160 + 3.02483i −1.10993 + 0.145870i
\(431\) −21.3431 15.5067i −1.02806 0.746929i −0.0601403 0.998190i \(-0.519155\pi\)
−0.967919 + 0.251261i \(0.919155\pi\)
\(432\) 0 0
\(433\) 7.58269 + 5.50914i 0.364401 + 0.264753i 0.754885 0.655857i \(-0.227693\pi\)
−0.390485 + 0.920609i \(0.627693\pi\)
\(434\) 3.88276 11.9499i 0.186378 0.573613i
\(435\) 0 0
\(436\) −2.59432 7.98450i −0.124245 0.382388i
\(437\) 7.74765 23.8448i 0.370620 1.14065i
\(438\) 0 0
\(439\) −0.159447 0.490727i −0.00760998 0.0234211i 0.947179 0.320704i \(-0.103920\pi\)
−0.954789 + 0.297283i \(0.903920\pi\)
\(440\) 22.1787 + 12.0485i 1.05733 + 0.574391i
\(441\) 0 0
\(442\) −7.80849 5.67320i −0.371412 0.269847i
\(443\) 17.8348 0.847357 0.423678 0.905813i \(-0.360739\pi\)
0.423678 + 0.905813i \(0.360739\pi\)
\(444\) 0 0
\(445\) −33.8938 + 4.45443i −1.60672 + 0.211160i
\(446\) 23.2779 16.9124i 1.10224 0.800826i
\(447\) 0 0
\(448\) 2.87826 + 8.85836i 0.135985 + 0.418518i
\(449\) 4.16533 0.196574 0.0982870 0.995158i \(-0.468664\pi\)
0.0982870 + 0.995158i \(0.468664\pi\)
\(450\) 0 0
\(451\) −27.4233 −1.29131
\(452\) 1.10623 + 3.40462i 0.0520325 + 0.160140i
\(453\) 0 0
\(454\) 5.95944 4.32979i 0.279691 0.203207i
\(455\) −8.86719 4.81708i −0.415700 0.225828i
\(456\) 0 0
\(457\) −17.6734 −0.826725 −0.413362 0.910567i \(-0.635646\pi\)
−0.413362 + 0.910567i \(0.635646\pi\)
\(458\) 7.23112 + 5.25371i 0.337888 + 0.245490i
\(459\) 0 0
\(460\) 7.41618 7.03452i 0.345781 0.327986i
\(461\) 0.0633350 + 0.194925i 0.00294981 + 0.00907857i 0.952521 0.304474i \(-0.0984807\pi\)
−0.949571 + 0.313553i \(0.898481\pi\)
\(462\) 0 0
\(463\) −3.96084 + 12.1902i −0.184076 + 0.566528i −0.999931 0.0117286i \(-0.996267\pi\)
0.815855 + 0.578256i \(0.196267\pi\)
\(464\) −1.37636 4.23601i −0.0638961 0.196652i
\(465\) 0 0
\(466\) 3.26742 10.0561i 0.151360 0.465839i
\(467\) 0.901030 + 0.654637i 0.0416947 + 0.0302930i 0.608437 0.793602i \(-0.291797\pi\)
−0.566743 + 0.823895i \(0.691797\pi\)
\(468\) 0 0
\(469\) −2.36668 1.71949i −0.109283 0.0793987i
\(470\) 5.69482 5.40174i 0.262682 0.249164i
\(471\) 0 0
\(472\) 16.4069 11.9203i 0.755187 0.548675i
\(473\) −10.4905 32.2866i −0.482356 1.48454i
\(474\) 0 0
\(475\) −11.0502 17.0327i −0.507020 0.781513i
\(476\) 1.75002 0.0802120
\(477\) 0 0
\(478\) −10.1905 + 7.40380i −0.466101 + 0.338642i
\(479\) −20.3670 + 14.7975i −0.930590 + 0.676113i −0.946137 0.323766i \(-0.895051\pi\)
0.0155470 + 0.999879i \(0.495051\pi\)
\(480\) 0 0
\(481\) 24.1677 + 17.5589i 1.10195 + 0.800615i
\(482\) 25.4555 1.15947
\(483\) 0 0
\(484\) −0.564977 + 1.73882i −0.0256808 + 0.0790373i
\(485\) −12.9896 27.2491i −0.589828 1.23732i
\(486\) 0 0
\(487\) 3.20135 9.85274i 0.145067 0.446470i −0.851953 0.523619i \(-0.824582\pi\)
0.997020 + 0.0771487i \(0.0245816\pi\)
\(488\) 8.65265 26.6301i 0.391687 1.20549i
\(489\) 0 0
\(490\) 14.3311 1.88344i 0.647414 0.0850852i
\(491\) 4.83831 14.8908i 0.218350 0.672012i −0.780549 0.625095i \(-0.785060\pi\)
0.998899 0.0469170i \(-0.0149396\pi\)
\(492\) 0 0
\(493\) −4.79569 −0.215987
\(494\) −14.9399 10.8545i −0.672178 0.488366i
\(495\) 0 0
\(496\) 16.0297 11.6463i 0.719754 0.522932i
\(497\) 0.595425 0.432601i 0.0267084 0.0194048i
\(498\) 0 0
\(499\) 35.7864 1.60202 0.801010 0.598651i \(-0.204296\pi\)
0.801010 + 0.598651i \(0.204296\pi\)
\(500\) −0.643866 8.25248i −0.0287946 0.369062i
\(501\) 0 0
\(502\) 2.34735 + 7.22439i 0.104767 + 0.322440i
\(503\) −9.52947 + 6.92356i −0.424898 + 0.308706i −0.779606 0.626271i \(-0.784580\pi\)
0.354708 + 0.934977i \(0.384580\pi\)
\(504\) 0 0
\(505\) 2.94828 15.8875i 0.131197 0.706985i
\(506\) −20.5754 14.9489i −0.914687 0.664559i
\(507\) 0 0
\(508\) 0.454975 + 0.330559i 0.0201862 + 0.0146662i
\(509\) −10.3986 + 32.0037i −0.460912 + 1.41854i 0.403141 + 0.915138i \(0.367918\pi\)
−0.864052 + 0.503402i \(0.832082\pi\)
\(510\) 0 0
\(511\) 2.57276 + 7.91815i 0.113812 + 0.350278i
\(512\) −6.14602 + 18.9155i −0.271618 + 0.835955i
\(513\) 0 0
\(514\) 5.13064 + 15.7905i 0.226303 + 0.696489i
\(515\) −5.07798 10.6524i −0.223762 0.469400i
\(516\) 0 0
\(517\) 9.28647 + 6.74701i 0.408418 + 0.296733i
\(518\) 9.21526 0.404895
\(519\) 0 0
\(520\) −11.9914 25.1550i −0.525856 1.10312i
\(521\) −9.58263 + 6.96219i −0.419823 + 0.305019i −0.777566 0.628801i \(-0.783546\pi\)
0.357744 + 0.933820i \(0.383546\pi\)
\(522\) 0 0
\(523\) 1.26602 + 3.89642i 0.0553593 + 0.170379i 0.974913 0.222586i \(-0.0714497\pi\)
−0.919554 + 0.392964i \(0.871450\pi\)
\(524\) 10.8502 0.473992
\(525\) 0 0
\(526\) −22.4117 −0.977195
\(527\) −6.59250 20.2896i −0.287174 0.883830i
\(528\) 0 0
\(529\) −12.2347 + 8.88902i −0.531943 + 0.386479i
\(530\) 6.39030 6.06143i 0.277577 0.263292i
\(531\) 0 0
\(532\) 3.34829 0.145167
\(533\) 24.4949 + 17.7966i 1.06099 + 0.770857i
\(534\) 0 0
\(535\) 2.23039 12.0190i 0.0964282 0.519626i
\(536\) −2.49639 7.68310i −0.107828 0.331859i
\(537\) 0 0
\(538\) 3.55078 10.9282i 0.153085 0.471147i
\(539\) 6.53205 + 20.1036i 0.281355 + 0.865922i
\(540\) 0 0
\(541\) 4.31332 13.2750i 0.185444 0.570738i −0.814512 0.580147i \(-0.802995\pi\)
0.999956 + 0.00940920i \(0.00299509\pi\)
\(542\) −11.1751 8.11917i −0.480011 0.348748i
\(543\) 0 0
\(544\) 6.76321 + 4.91376i 0.289970 + 0.210676i
\(545\) 22.2805 + 12.1038i 0.954390 + 0.518470i
\(546\) 0 0
\(547\) 21.4426 15.5789i 0.916818 0.666107i −0.0259119 0.999664i \(-0.508249\pi\)
0.942730 + 0.333557i \(0.108249\pi\)
\(548\) 2.81210 + 8.65476i 0.120127 + 0.369713i
\(549\) 0 0
\(550\) −19.8959 + 5.32147i −0.848363 + 0.226908i
\(551\) −9.17556 −0.390892
\(552\) 0 0
\(553\) −7.69220 + 5.58871i −0.327105 + 0.237656i
\(554\) −28.6488 + 20.8146i −1.21717 + 0.884327i
\(555\) 0 0
\(556\) 8.82522 + 6.41190i 0.374273 + 0.271925i
\(557\) −10.6860 −0.452781 −0.226391 0.974037i \(-0.572693\pi\)
−0.226391 + 0.974037i \(0.572693\pi\)
\(558\) 0 0
\(559\) −11.5824 + 35.6468i −0.489882 + 1.50770i
\(560\) −4.31345 2.34327i −0.182277 0.0990214i
\(561\) 0 0
\(562\) 7.39140 22.7484i 0.311788 0.959583i
\(563\) 7.90310 24.3232i 0.333076 1.02510i −0.634586 0.772852i \(-0.718829\pi\)
0.967662 0.252250i \(-0.0811706\pi\)
\(564\) 0 0
\(565\) −9.50047 5.16111i −0.399688 0.217129i
\(566\) −0.299792 + 0.922666i −0.0126012 + 0.0387825i
\(567\) 0 0
\(568\) 2.03244 0.0852794
\(569\) 4.93670 + 3.58672i 0.206957 + 0.150363i 0.686436 0.727190i \(-0.259174\pi\)
−0.479479 + 0.877554i \(0.659174\pi\)
\(570\) 0 0
\(571\) −19.2058 + 13.9538i −0.803737 + 0.583949i −0.912008 0.410173i \(-0.865468\pi\)
0.108271 + 0.994121i \(0.465468\pi\)
\(572\) 8.90746 6.47165i 0.372440 0.270593i
\(573\) 0 0
\(574\) 9.34003 0.389845
\(575\) −1.62962 + 30.8288i −0.0679597 + 1.28565i
\(576\) 0 0
\(577\) −13.6474 42.0024i −0.568149 1.74858i −0.658405 0.752664i \(-0.728769\pi\)
0.0902565 0.995919i \(-0.471231\pi\)
\(578\) 11.3459 8.24330i 0.471929 0.342876i
\(579\) 0 0
\(580\) −3.28712 1.78572i −0.136490 0.0741480i
\(581\) 11.0501 + 8.02840i 0.458437 + 0.333074i
\(582\) 0 0
\(583\) 10.4206 + 7.57100i 0.431576 + 0.313559i
\(584\) −7.10475 + 21.8662i −0.293997 + 0.904828i
\(585\) 0 0
\(586\) −1.10185 3.39115i −0.0455170 0.140087i
\(587\) −0.158206 + 0.486909i −0.00652987 + 0.0200969i −0.954268 0.298951i \(-0.903363\pi\)
0.947738 + 0.319048i \(0.103363\pi\)
\(588\) 0 0
\(589\) −12.6134 38.8200i −0.519725 1.59955i
\(590\) −3.01929 + 16.2702i −0.124302 + 0.669832i
\(591\) 0 0
\(592\) 11.7564 + 8.54153i 0.483186 + 0.351055i
\(593\) 18.8405 0.773687 0.386844 0.922145i \(-0.373565\pi\)
0.386844 + 0.922145i \(0.373565\pi\)
\(594\) 0 0
\(595\) −3.83474 + 3.63738i −0.157209 + 0.149118i
\(596\) −9.37376 + 6.81043i −0.383964 + 0.278966i
\(597\) 0 0
\(598\) 8.67703 + 26.7052i 0.354830 + 1.09206i
\(599\) −6.20712 −0.253616 −0.126808 0.991927i \(-0.540473\pi\)
−0.126808 + 0.991927i \(0.540473\pi\)
\(600\) 0 0
\(601\) 34.0303 1.38813 0.694063 0.719915i \(-0.255819\pi\)
0.694063 + 0.719915i \(0.255819\pi\)
\(602\) 3.57295 + 10.9964i 0.145623 + 0.448180i
\(603\) 0 0
\(604\) 2.37083 1.72251i 0.0964679 0.0700880i
\(605\) −2.37610 4.98450i −0.0966023 0.202649i
\(606\) 0 0
\(607\) 16.2488 0.659518 0.329759 0.944065i \(-0.393032\pi\)
0.329759 + 0.944065i \(0.393032\pi\)
\(608\) 12.9400 + 9.40144i 0.524785 + 0.381279i
\(609\) 0 0
\(610\) 9.83155 + 20.6242i 0.398068 + 0.835051i
\(611\) −3.91628 12.0531i −0.158436 0.487615i
\(612\) 0 0
\(613\) −0.0210086 + 0.0646578i −0.000848529 + 0.00261150i −0.951480 0.307711i \(-0.900437\pi\)
0.950631 + 0.310322i \(0.100437\pi\)
\(614\) −0.176180 0.542225i −0.00711004 0.0218824i
\(615\) 0 0
\(616\) 3.88481 11.9562i 0.156523 0.481730i
\(617\) 26.5445 + 19.2857i 1.06864 + 0.776413i 0.975667 0.219256i \(-0.0703629\pi\)
0.0929733 + 0.995669i \(0.470363\pi\)
\(618\) 0 0
\(619\) 5.48280 + 3.98349i 0.220372 + 0.160110i 0.692494 0.721423i \(-0.256512\pi\)
−0.472122 + 0.881533i \(0.656512\pi\)
\(620\) 3.03632 16.3619i 0.121942 0.657111i
\(621\) 0 0
\(622\) −13.2964 + 9.66040i −0.533137 + 0.387347i
\(623\) 5.26160 + 16.1935i 0.210802 + 0.648780i
\(624\) 0 0
\(625\) 18.5635 + 16.7450i 0.742541 + 0.669801i
\(626\) −16.7858 −0.670895
\(627\) 0 0
\(628\) −2.69573 + 1.95856i −0.107571 + 0.0781552i
\(629\) 12.6583 9.19679i 0.504719 0.366700i
\(630\) 0 0
\(631\) 6.20352 + 4.50712i 0.246958 + 0.179426i 0.704378 0.709825i \(-0.251226\pi\)
−0.457419 + 0.889251i \(0.651226\pi\)
\(632\) −26.2568 −1.04444
\(633\) 0 0
\(634\) −6.28405 + 19.3403i −0.249572 + 0.768102i
\(635\) −1.68403 + 0.221320i −0.0668285 + 0.00878281i
\(636\) 0 0
\(637\) 7.21188 22.1959i 0.285745 0.879432i
\(638\) −2.87619 + 8.85199i −0.113869 + 0.350454i
\(639\) 0 0
\(640\) −1.45122 3.04431i −0.0573644 0.120337i
\(641\) 7.32096 22.5316i 0.289161 0.889945i −0.695960 0.718081i \(-0.745021\pi\)
0.985121 0.171864i \(-0.0549791\pi\)
\(642\) 0 0
\(643\) 2.16861 0.0855218 0.0427609 0.999085i \(-0.486385\pi\)
0.0427609 + 0.999085i \(0.486385\pi\)
\(644\) −4.11889 2.99255i −0.162307 0.117923i
\(645\) 0 0
\(646\) −7.82506 + 5.68524i −0.307873 + 0.223683i
\(647\) 2.06737 1.50203i 0.0812767 0.0590510i −0.546405 0.837521i \(-0.684004\pi\)
0.627682 + 0.778470i \(0.284004\pi\)
\(648\) 0 0
\(649\) −24.1998 −0.949926
\(650\) 21.2247 + 8.15840i 0.832503 + 0.319999i
\(651\) 0 0
\(652\) 0.561415 + 1.72786i 0.0219867 + 0.0676681i
\(653\) 26.2233 19.0523i 1.02620 0.745575i 0.0586517 0.998279i \(-0.481320\pi\)
0.967544 + 0.252704i \(0.0813199\pi\)
\(654\) 0 0
\(655\) −23.7755 + 22.5519i −0.928985 + 0.881175i
\(656\) 11.9156 + 8.65719i 0.465226 + 0.338006i
\(657\) 0 0
\(658\) −3.16285 2.29795i −0.123301 0.0895833i
\(659\) −0.139043 + 0.427929i −0.00541633 + 0.0166697i −0.953728 0.300670i \(-0.902790\pi\)
0.948312 + 0.317340i \(0.102790\pi\)
\(660\) 0 0
\(661\) −8.33812 25.6621i −0.324315 0.998140i −0.971749 0.236018i \(-0.924158\pi\)
0.647433 0.762122i \(-0.275842\pi\)
\(662\) 9.13921 28.1276i 0.355205 1.09321i
\(663\) 0 0
\(664\) 11.6558 + 35.8728i 0.452332 + 1.39214i
\(665\) −7.33696 + 6.95937i −0.284515 + 0.269873i
\(666\) 0 0
\(667\) 11.2873 + 8.20067i 0.437044 + 0.317531i
\(668\) −2.26795 −0.0877496
\(669\) 0 0
\(670\) 5.79231 + 3.14666i 0.223776 + 0.121566i
\(671\) −27.0314 + 19.6395i −1.04354 + 0.758174i
\(672\) 0 0
\(673\) 5.44561 + 16.7599i 0.209913 + 0.646046i 0.999476 + 0.0323758i \(0.0103073\pi\)
−0.789563 + 0.613670i \(0.789693\pi\)
\(674\) −12.0032 −0.462344
\(675\) 0 0
\(676\) −2.53135 −0.0973595
\(677\) 5.97899 + 18.4014i 0.229791 + 0.707225i 0.997770 + 0.0667494i \(0.0212628\pi\)
−0.767978 + 0.640476i \(0.778737\pi\)
\(678\) 0 0
\(679\) −12.1639 + 8.83757i −0.466807 + 0.339155i
\(680\) −14.4714 + 1.90188i −0.554953 + 0.0729336i
\(681\) 0 0
\(682\) −41.4049 −1.58547
\(683\) −24.2268 17.6018i −0.927015 0.673515i 0.0182455 0.999834i \(-0.494192\pi\)
−0.945260 + 0.326318i \(0.894192\pi\)
\(684\) 0 0
\(685\) −24.1508 13.1199i −0.922755 0.501284i
\(686\) −4.92859 15.1686i −0.188175 0.579142i
\(687\) 0 0
\(688\) −5.63426 + 17.3405i −0.214804 + 0.661099i
\(689\) −4.39456 13.5251i −0.167419 0.515264i
\(690\) 0 0
\(691\) −6.16024 + 18.9593i −0.234346 + 0.721244i 0.762861 + 0.646563i \(0.223794\pi\)
−0.997207 + 0.0746817i \(0.976206\pi\)
\(692\) −6.74418 4.89993i −0.256375 0.186268i
\(693\) 0 0
\(694\) 14.6858 + 10.6698i 0.557464 + 0.405021i
\(695\) −32.6653 + 4.29298i −1.23907 + 0.162842i
\(696\) 0 0
\(697\) 12.8297 9.32131i 0.485959 0.353070i
\(698\) 5.28495 + 16.2654i 0.200038 + 0.615655i
\(699\) 0 0
\(700\) −3.98286 + 1.06528i −0.150538 + 0.0402638i
\(701\) 49.0150 1.85127 0.925636 0.378415i \(-0.123531\pi\)
0.925636 + 0.378415i \(0.123531\pi\)
\(702\) 0 0
\(703\) 24.2190 17.5961i 0.913437 0.663651i
\(704\) 24.8312 18.0409i 0.935862 0.679944i
\(705\) 0 0
\(706\) −26.8204 19.4862i −1.00940 0.733372i
\(707\) −8.04831 −0.302688
\(708\) 0 0
\(709\) −1.48744 + 4.57788i −0.0558621 + 0.171926i −0.975095 0.221789i \(-0.928810\pi\)
0.919233 + 0.393715i \(0.128810\pi\)
\(710\) −1.20323 + 1.14131i −0.0451565 + 0.0428326i
\(711\) 0 0
\(712\) −14.5300 + 44.7189i −0.544536 + 1.67591i
\(713\) −19.1792 + 59.0274i −0.718265 + 2.21059i
\(714\) 0 0
\(715\) −6.06730 + 32.6950i −0.226904 + 1.22273i
\(716\) 2.30098 7.08170i 0.0859918 0.264656i
\(717\) 0 0
\(718\) 14.7775 0.551491
\(719\) 26.0917 + 18.9568i 0.973058 + 0.706968i 0.956146 0.292889i \(-0.0946167\pi\)
0.0169113 + 0.999857i \(0.494617\pi\)
\(720\) 0 0
\(721\) −4.75517 + 3.45483i −0.177092 + 0.128665i
\(722\) 2.28013 1.65661i 0.0848578 0.0616528i
\(723\) 0 0
\(724\) 14.4138 0.535685
\(725\) 10.9145 2.91926i 0.405355 0.108418i
\(726\) 0 0
\(727\) −9.01548 27.7468i −0.334366 1.02907i −0.967034 0.254648i \(-0.918040\pi\)
0.632668 0.774423i \(-0.281960\pi\)
\(728\) −11.2291 + 8.15840i −0.416177 + 0.302370i
\(729\) 0 0
\(730\) −8.07275 16.9347i −0.298786 0.626781i
\(731\) 15.8823 + 11.5391i 0.587426 + 0.426790i
\(732\) 0 0
\(733\) −4.20771 3.05708i −0.155415 0.112916i 0.507360 0.861734i \(-0.330622\pi\)
−0.662775 + 0.748818i \(0.730622\pi\)
\(734\) −1.34876 + 4.15107i −0.0497838 + 0.153219i
\(735\) 0 0
\(736\) −7.51548 23.1303i −0.277024 0.852593i
\(737\) −2.97891 + 9.16813i −0.109729 + 0.337712i
\(738\) 0 0
\(739\) −5.04334 15.5218i −0.185522 0.570979i 0.814435 0.580255i \(-0.197047\pi\)
−0.999957 + 0.00927620i \(0.997047\pi\)
\(740\) 12.1009 1.59034i 0.444838 0.0584620i
\(741\) 0 0
\(742\) −3.54912 2.57859i −0.130292 0.0946629i
\(743\) −53.4487 −1.96084 −0.980421 0.196914i \(-0.936908\pi\)
−0.980421 + 0.196914i \(0.936908\pi\)
\(744\) 0 0
\(745\) 6.38491 34.4066i 0.233925 1.26056i
\(746\) 7.39398 5.37204i 0.270713 0.196684i
\(747\) 0 0
\(748\) −1.78204 5.48457i −0.0651580 0.200536i
\(749\) −6.08859 −0.222472
\(750\) 0 0
\(751\) −0.566970 −0.0206890 −0.0103445 0.999946i \(-0.503293\pi\)
−0.0103445 + 0.999946i \(0.503293\pi\)
\(752\) −1.90508 5.86324i −0.0694712 0.213810i
\(753\) 0 0
\(754\) 8.31364 6.04021i 0.302765 0.219972i
\(755\) −1.61489 + 8.70220i −0.0587718 + 0.316706i
\(756\) 0 0
\(757\) 53.0708 1.92889 0.964445 0.264282i \(-0.0851350\pi\)
0.964445 + 0.264282i \(0.0851350\pi\)
\(758\) −8.99560 6.53569i −0.326735 0.237387i
\(759\) 0 0
\(760\) −27.6880 + 3.63884i −1.00435 + 0.131995i
\(761\) 8.49970 + 26.1594i 0.308114 + 0.948277i 0.978497 + 0.206262i \(0.0661298\pi\)
−0.670383 + 0.742015i \(0.733870\pi\)
\(762\) 0 0
\(763\) 3.90264 12.0111i 0.141285 0.434830i
\(764\) −2.65599 8.17428i −0.0960902 0.295735i
\(765\) 0 0
\(766\) 1.81115 5.57414i 0.0654394 0.201402i
\(767\) 21.6157 + 15.7047i 0.780496 + 0.567064i
\(768\) 0 0
\(769\) −12.1123 8.80007i −0.436779 0.317339i 0.347575 0.937652i \(-0.387005\pi\)
−0.784354 + 0.620314i \(0.787005\pi\)
\(770\) 4.41410 + 9.25974i 0.159073 + 0.333698i
\(771\) 0 0
\(772\) −2.02546 + 1.47158i −0.0728977 + 0.0529633i
\(773\) 0.634806 + 1.95373i 0.0228324 + 0.0702708i 0.961823 0.273671i \(-0.0882378\pi\)
−0.938991 + 0.343941i \(0.888238\pi\)
\(774\) 0 0
\(775\) 27.3547 + 42.1641i 0.982608 + 1.51458i
\(776\) −41.5206 −1.49050
\(777\) 0 0
\(778\) −3.38655 + 2.46048i −0.121414 + 0.0882123i
\(779\) 24.5469 17.8344i 0.879485 0.638983i
\(780\) 0 0
\(781\) −1.96210 1.42555i −0.0702093 0.0510100i
\(782\) 14.7072 0.525927
\(783\) 0 0
\(784\) 3.50823 10.7972i 0.125294 0.385615i
\(785\) 1.83619 9.89475i 0.0655365 0.353159i
\(786\) 0 0
\(787\) −5.19981 + 16.0034i −0.185353 + 0.570458i −0.999954 0.00956327i \(-0.996956\pi\)
0.814601 + 0.580022i \(0.196956\pi\)
\(788\) −4.02391 + 12.3843i −0.143346 + 0.441174i
\(789\) 0 0
\(790\) 15.5444 14.7444i 0.553044 0.524582i
\(791\) −1.66410 + 5.12156i −0.0591685 + 0.182102i
\(792\) 0 0
\(793\) 36.8901 1.31001
\(794\) −3.64613 2.64907i −0.129396 0.0940118i
\(795\) 0 0
\(796\) 11.9855 8.70799i 0.424816 0.308647i
\(797\) −0.168996 + 0.122783i −0.00598616 + 0.00434920i −0.590774 0.806837i \(-0.701178\pi\)
0.584788 + 0.811186i \(0.301178\pi\)
\(798\) 0 0
\(799\) −6.63791 −0.234832
\(800\) −18.3835 7.06627i −0.649954 0.249830i
\(801\) 0 0
\(802\) 8.66668 + 26.6733i 0.306031 + 0.941867i
\(803\) 22.1957 16.1261i 0.783268 0.569078i
\(804\) 0 0
\(805\) 15.2455 2.00361i 0.537333 0.0706179i
\(806\) 36.9835 + 26.8701i 1.30269 + 0.946458i
\(807\) 0 0
\(808\) −17.9809 13.0639i −0.632566 0.459586i
\(809\) 5.24264 16.1352i 0.184321 0.567283i −0.815615 0.578595i \(-0.803601\pi\)
0.999936 + 0.0113128i \(0.00360104\pi\)
\(810\) 0 0
\(811\) −6.32508 19.4666i −0.222103 0.683564i −0.998573 0.0534090i \(-0.982991\pi\)
0.776469 0.630155i \(-0.217009\pi\)
\(812\) −0.575770 + 1.77204i −0.0202056 + 0.0621864i
\(813\) 0 0
\(814\) −9.38390 28.8807i −0.328905 1.01227i
\(815\) −4.82153 2.61928i −0.168891 0.0917495i
\(816\) 0 0
\(817\) 30.3874 + 22.0777i 1.06312 + 0.772401i
\(818\) −28.4812 −0.995822
\(819\) 0 0
\(820\) 12.2647 1.61187i 0.428304 0.0562890i
\(821\) 31.0368 22.5496i 1.08319 0.786985i 0.104955 0.994477i \(-0.466530\pi\)
0.978237 + 0.207492i \(0.0665301\pi\)
\(822\) 0 0
\(823\) −8.96451 27.5899i −0.312483 0.961725i −0.976778 0.214254i \(-0.931268\pi\)
0.664295 0.747471i \(-0.268732\pi\)
\(824\) −16.2315 −0.565449
\(825\) 0 0
\(826\) 8.24215 0.286781
\(827\) −4.43648 13.6541i −0.154271 0.474799i 0.843815 0.536634i \(-0.180305\pi\)
−0.998086 + 0.0618356i \(0.980305\pi\)
\(828\) 0 0
\(829\) −3.75031 + 2.72476i −0.130254 + 0.0946347i −0.651004 0.759074i \(-0.725652\pi\)
0.520751 + 0.853709i \(0.325652\pi\)
\(830\) −27.0446 14.6919i −0.938732 0.509964i
\(831\) 0 0
\(832\) −33.8875 −1.17484
\(833\) −9.88925 7.18496i −0.342642 0.248944i
\(834\) 0 0
\(835\) 4.96965 4.71390i 0.171982 0.163131i
\(836\) −3.40957 10.4936i −0.117922 0.362928i
\(837\) 0 0
\(838\) 10.6896 32.8993i 0.369268 1.13649i
\(839\) −1.52235 4.68531i −0.0525573 0.161755i 0.921333 0.388775i \(-0.127102\pi\)
−0.973890 + 0.227020i \(0.927102\pi\)
\(840\) 0 0
\(841\) −7.38367 + 22.7246i −0.254609 + 0.783607i
\(842\) −7.76010 5.63804i −0.267431 0.194300i
\(843\) 0 0
\(844\) 1.46305 + 1.06297i 0.0503602 + 0.0365888i
\(845\) 5.54683 5.26137i 0.190817 0.180996i
\(846\) 0 0
\(847\) −2.22505 + 1.61660i −0.0764538 + 0.0555469i
\(848\) −2.13774 6.57929i −0.0734103 0.225934i
\(849\) 0 0
\(850\) 7.49927 9.25229i 0.257223 0.317351i
\(851\) −45.5194 −1.56039
\(852\) 0 0
\(853\) −43.4018 + 31.5333i −1.48605 + 1.07968i −0.510507 + 0.859874i \(0.670542\pi\)
−0.975544 + 0.219805i \(0.929458\pi\)
\(854\) 9.20656 6.68896i 0.315042 0.228891i
\(855\) 0 0
\(856\) −13.6026 9.88290i −0.464929 0.337790i
\(857\) 27.1144 0.926210 0.463105 0.886303i \(-0.346735\pi\)
0.463105 + 0.886303i \(0.346735\pi\)
\(858\) 0 0
\(859\) 3.21966 9.90910i 0.109853 0.338094i −0.880985 0.473143i \(-0.843119\pi\)
0.990839 + 0.135049i \(0.0431193\pi\)
\(860\) 6.58950 + 13.8232i 0.224700 + 0.471367i
\(861\) 0 0
\(862\) 9.14963 28.1597i 0.311638 0.959122i
\(863\) 13.4865 41.5072i 0.459086 1.41292i −0.407185 0.913346i \(-0.633490\pi\)
0.866271 0.499575i \(-0.166510\pi\)
\(864\) 0 0
\(865\) 24.9626 3.28067i 0.848756 0.111546i
\(866\) −3.25065 + 10.0045i −0.110461 + 0.339965i
\(867\) 0 0
\(868\) −8.28864 −0.281335
\(869\) 25.3480 + 18.4164i 0.859872 + 0.624734i
\(870\) 0 0
\(871\) 8.61055 6.25593i 0.291757 0.211974i
\(872\) 28.2151 20.4995i 0.955485 0.694201i
\(873\) 0 0
\(874\) 28.1391 0.951818
\(875\) 6.51330 10.6126i 0.220190 0.358772i
\(876\) 0 0
\(877\) 16.5767 + 51.0180i 0.559757 + 1.72275i 0.683038 + 0.730383i \(0.260658\pi\)
−0.123281 + 0.992372i \(0.539342\pi\)
\(878\) 0.468503 0.340388i 0.0158112 0.0114875i
\(879\) 0 0
\(880\) −2.95144 + 15.9045i −0.0994931 + 0.536142i
\(881\) −44.4110 32.2665i −1.49625 1.08709i −0.971847 0.235613i \(-0.924290\pi\)
−0.524398 0.851473i \(-0.675710\pi\)
\(882\) 0 0
\(883\) 15.4483 + 11.2239i 0.519877 + 0.377713i 0.816558 0.577264i \(-0.195880\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(884\) −1.96751 + 6.05538i −0.0661746 + 0.203664i
\(885\) 0 0
\(886\) 6.18547 + 19.0369i 0.207805 + 0.639558i
\(887\) 3.46598 10.6672i 0.116376 0.358170i −0.875855 0.482574i \(-0.839702\pi\)
0.992232 + 0.124404i \(0.0397020\pi\)
\(888\) 0 0
\(889\) 0.261425 + 0.804582i 0.00876790 + 0.0269848i
\(890\) −16.5097 34.6334i −0.553407 1.16092i
\(891\) 0 0
\(892\) −15.3557 11.1566i −0.514147 0.373550i
\(893\) −12.7003 −0.424998
\(894\) 0 0
\(895\) 9.67716 + 20.3004i 0.323472 + 0.678566i
\(896\) −1.35896 + 0.987345i −0.0453998 + 0.0329849i
\(897\) 0 0
\(898\) 1.44462 + 4.44608i 0.0482076 + 0.148368i
\(899\) 22.7139 0.757552
\(900\) 0 0
\(901\) −7.44857 −0.248148
\(902\) −9.51095 29.2717i −0.316680 0.974641i
\(903\) 0 0
\(904\) −12.0310 + 8.74106i −0.400146 + 0.290723i
\(905\) −31.5843 + 29.9589i −1.04990 + 0.995866i
\(906\) 0 0
\(907\) −36.4513 −1.21034 −0.605172 0.796095i \(-0.706896\pi\)
−0.605172 + 0.796095i \(0.706896\pi\)
\(908\) −3.93125 2.85622i −0.130463 0.0947871i
\(909\) 0 0
\(910\) 2.06644 11.1355i 0.0685020 0.369139i
\(911\) −0.360106 1.10829i −0.0119309 0.0367194i 0.944914 0.327319i \(-0.106145\pi\)
−0.956845 + 0.290600i \(0.906145\pi\)
\(912\) 0 0
\(913\) 13.9087 42.8065i 0.460310 1.41669i
\(914\) −6.12948 18.8646i −0.202745 0.623985i
\(915\) 0 0
\(916\) 1.82203 5.60763i 0.0602016 0.185281i
\(917\) 13.2047 + 9.59377i 0.436057 + 0.316814i
\(918\) 0 0
\(919\) −35.5543 25.8317i −1.17283 0.852109i −0.181482 0.983394i \(-0.558089\pi\)
−0.991345 + 0.131286i \(0.958089\pi\)
\(920\) 37.3125 + 20.2699i 1.23016 + 0.668279i
\(921\) 0 0
\(922\) −0.186098 + 0.135208i −0.00612880 + 0.00445283i
\(923\) 0.827454 + 2.54664i 0.0272360 + 0.0838237i
\(924\) 0 0
\(925\) −23.2107 + 28.6364i −0.763162 + 0.941558i
\(926\) −14.3856 −0.472739
\(927\) 0 0
\(928\) −7.20073 + 5.23164i −0.236376 + 0.171737i
\(929\) 25.2512 18.3460i 0.828464 0.601914i −0.0906606 0.995882i \(-0.528898\pi\)
0.919124 + 0.393968i \(0.128898\pi\)
\(930\) 0 0
\(931\) −18.9210 13.7469i −0.620111 0.450537i
\(932\) −6.97506 −0.228476
\(933\) 0 0
\(934\) −0.386266 + 1.18880i −0.0126390 + 0.0388988i
\(935\) 15.3045 + 8.31413i 0.500510 + 0.271901i
\(936\) 0 0
\(937\) −13.9385 + 42.8983i −0.455351 + 1.40143i 0.415371 + 0.909652i \(0.363652\pi\)
−0.870722 + 0.491775i \(0.836348\pi\)
\(938\) 1.01458 3.12255i 0.0331271 0.101955i
\(939\) 0 0
\(940\) −4.54983 2.47169i −0.148399 0.0806175i
\(941\) 12.0931 37.2187i 0.394224 1.21330i −0.535341 0.844636i \(-0.679817\pi\)
0.929565 0.368659i \(-0.120183\pi\)
\(942\) 0 0
\(943\) −46.1358 −1.50239
\(944\) 10.5150 + 7.63957i 0.342233 + 0.248647i
\(945\) 0 0
\(946\) 30.8245 22.3953i 1.00219 0.728133i
\(947\) −39.5235 + 28.7155i −1.28434 + 0.933128i −0.999675 0.0254991i \(-0.991883\pi\)
−0.284665 + 0.958627i \(0.591883\pi\)
\(948\) 0 0
\(949\) −30.2907 −0.983278
\(950\) 14.3483 17.7023i 0.465520 0.574339i
\(951\) 0 0
\(952\) 2.24651 + 6.91405i 0.0728098 + 0.224086i
\(953\) 18.4314 13.3912i 0.597051 0.433783i −0.247780 0.968816i \(-0.579701\pi\)
0.844831 + 0.535034i \(0.179701\pi\)
\(954\) 0 0
\(955\) 22.8101 + 12.3915i 0.738116 + 0.400980i
\(956\) 6.72232 + 4.88405i 0.217415 + 0.157961i
\(957\) 0 0
\(958\) −22.8585 16.6077i −0.738525 0.536570i
\(959\) −4.23024 + 13.0193i −0.136602 + 0.420417i
\(960\) 0 0
\(961\) 21.6446 + 66.6154i 0.698214 + 2.14888i
\(962\) −10.3605 + 31.8864i −0.334037 + 1.02806i
\(963\) 0 0
\(964\) −5.18908 15.9703i −0.167129 0.514370i
\(965\) 1.37963 7.43448i 0.0444120 0.239324i
\(966\) 0 0
\(967\) −34.9436 25.3880i −1.12371 0.816425i −0.138944 0.990300i \(-0.544371\pi\)
−0.984768 + 0.173876i \(0.944371\pi\)
\(968\) −7.59507 −0.244115
\(969\) 0 0
\(970\) 24.5807 23.3157i 0.789239 0.748622i
\(971\) −25.9089 + 18.8239i −0.831457 + 0.604089i −0.919971 0.391986i \(-0.871788\pi\)
0.0885142 + 0.996075i \(0.471788\pi\)
\(972\) 0 0
\(973\) 5.07090 + 15.6066i 0.162565 + 0.500325i
\(974\) 11.6271 0.372557
\(975\) 0 0
\(976\) 17.9452 0.574413
\(977\) 2.24659 + 6.91428i 0.0718747 + 0.221208i 0.980541 0.196316i \(-0.0628980\pi\)
−0.908666 + 0.417524i \(0.862898\pi\)
\(978\) 0 0
\(979\) 45.3927 32.9798i 1.45076 1.05404i
\(980\) −4.10302 8.60715i −0.131066 0.274945i
\(981\) 0 0
\(982\) 17.5725 0.560760
\(983\) −4.11915 2.99274i −0.131380 0.0954535i 0.520154 0.854072i \(-0.325874\pi\)
−0.651535 + 0.758619i \(0.725874\pi\)
\(984\) 0 0
\(985\) −16.9232 35.5009i −0.539219 1.13115i
\(986\) −1.66324 5.11894i −0.0529685 0.163020i
\(987\) 0 0
\(988\) −3.76442 + 11.5857i −0.119762 + 0.368590i
\(989\) −17.6488 54.3176i −0.561201 1.72720i
\(990\) 0 0
\(991\) −19.1826 + 59.0380i −0.609356 + 1.87540i −0.145859 + 0.989305i \(0.546594\pi\)
−0.463497 + 0.886098i \(0.653406\pi\)
\(992\) −32.0327 23.2731i −1.01704 0.738922i
\(993\) 0 0
\(994\) 0.668265 + 0.485523i 0.0211961 + 0.0153999i
\(995\) −8.16391 + 43.9931i −0.258813 + 1.39468i
\(996\) 0 0
\(997\) −2.07832 + 1.50999i −0.0658212 + 0.0478219i −0.620209 0.784436i \(-0.712952\pi\)
0.554388 + 0.832258i \(0.312952\pi\)
\(998\) 12.4114 + 38.1985i 0.392878 + 1.20915i
\(999\) 0 0
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 225.2.h.c.181.2 8
3.2 odd 2 75.2.g.b.31.1 8
15.2 even 4 375.2.i.b.349.3 16
15.8 even 4 375.2.i.b.349.2 16
15.14 odd 2 375.2.g.b.151.2 8
25.11 even 5 5625.2.a.i.1.3 4
25.14 even 10 5625.2.a.n.1.2 4
25.21 even 5 inner 225.2.h.c.46.2 8
75.2 even 20 1875.2.b.c.1249.4 8
75.11 odd 10 1875.2.a.h.1.2 4
75.14 odd 10 1875.2.a.e.1.3 4
75.23 even 20 1875.2.b.c.1249.5 8
75.29 odd 10 375.2.g.b.226.2 8
75.47 even 20 375.2.i.b.274.2 16
75.53 even 20 375.2.i.b.274.3 16
75.71 odd 10 75.2.g.b.46.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.b.31.1 8 3.2 odd 2
75.2.g.b.46.1 yes 8 75.71 odd 10
225.2.h.c.46.2 8 25.21 even 5 inner
225.2.h.c.181.2 8 1.1 even 1 trivial
375.2.g.b.151.2 8 15.14 odd 2
375.2.g.b.226.2 8 75.29 odd 10
375.2.i.b.274.2 16 75.47 even 20
375.2.i.b.274.3 16 75.53 even 20
375.2.i.b.349.2 16 15.8 even 4
375.2.i.b.349.3 16 15.2 even 4
1875.2.a.e.1.3 4 75.14 odd 10
1875.2.a.h.1.2 4 75.11 odd 10
1875.2.b.c.1249.4 8 75.2 even 20
1875.2.b.c.1249.5 8 75.23 even 20
5625.2.a.i.1.3 4 25.11 even 5
5625.2.a.n.1.2 4 25.14 even 10