Properties

Label 525.3.s.e.124.2
Level $525$
Weight $3$
Character 525.124
Analytic conductor $14.305$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,3,Mod(124,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.124");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.3052138789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.124
Dual form 525.3.s.e.199.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.59808 + 1.50000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(2.50000 + 4.33013i) q^{4} -5.19615i q^{6} +(-2.59808 - 6.50000i) q^{7} +3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(2.59808 + 1.50000i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(2.50000 + 4.33013i) q^{4} -5.19615i q^{6} +(-2.59808 - 6.50000i) q^{7} +3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-7.50000 - 12.9904i) q^{11} +(4.33013 - 7.50000i) q^{12} -13.8564 q^{13} +(3.00000 - 20.7846i) q^{14} +(5.50000 - 9.52628i) q^{16} +(-5.19615 - 9.00000i) q^{17} +(-7.79423 + 4.50000i) q^{18} +(9.00000 + 5.19615i) q^{19} +(-7.50000 + 9.52628i) q^{21} -45.0000i q^{22} +(4.50000 - 2.59808i) q^{24} +(-36.0000 - 20.7846i) q^{26} +5.19615 q^{27} +(21.6506 - 27.5000i) q^{28} +9.00000 q^{29} +(-10.5000 + 6.06218i) q^{31} +(38.9711 - 22.5000i) q^{32} +(-12.9904 + 22.5000i) q^{33} -31.1769i q^{34} -15.0000 q^{36} +(8.66025 + 5.00000i) q^{37} +(15.5885 + 27.0000i) q^{38} +(12.0000 + 20.7846i) q^{39} +10.3923i q^{41} +(-33.7750 + 13.5000i) q^{42} -74.0000i q^{43} +(37.5000 - 64.9519i) q^{44} -19.0526 q^{48} +(-35.5000 + 33.7750i) q^{49} +(-9.00000 + 15.5885i) q^{51} +(-34.6410 - 60.0000i) q^{52} +(28.5788 - 16.5000i) q^{53} +(13.5000 + 7.79423i) q^{54} +(19.5000 - 7.79423i) q^{56} -18.0000i q^{57} +(23.3827 + 13.5000i) q^{58} +(-13.5000 + 7.79423i) q^{59} +(78.0000 + 45.0333i) q^{61} -36.3731 q^{62} +(20.7846 + 3.00000i) q^{63} +91.0000 q^{64} +(-67.5000 + 38.9711i) q^{66} +(65.8179 - 38.0000i) q^{67} +(25.9808 - 45.0000i) q^{68} +84.0000 q^{71} +(-7.79423 - 4.50000i) q^{72} +(-31.1769 - 54.0000i) q^{73} +(15.0000 + 25.9808i) q^{74} +51.9615i q^{76} +(-64.9519 + 82.5000i) q^{77} +72.0000i q^{78} +(-21.5000 + 37.2391i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-15.5885 + 27.0000i) q^{82} -119.512 q^{83} +(-60.0000 - 8.66025i) q^{84} +(111.000 - 192.258i) q^{86} +(-7.79423 - 13.5000i) q^{87} +(38.9711 - 22.5000i) q^{88} +(63.0000 + 36.3731i) q^{89} +(36.0000 + 90.0666i) q^{91} +(18.1865 + 10.5000i) q^{93} +(-67.5000 - 38.9711i) q^{96} -185.329 q^{97} +(-142.894 + 34.5000i) q^{98} +45.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 10 q^{4} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 10 q^{4} - 6 q^{9} - 30 q^{11} + 12 q^{14} + 22 q^{16} + 36 q^{19} - 30 q^{21} + 18 q^{24} - 144 q^{26} + 36 q^{29} - 42 q^{31} - 60 q^{36} + 48 q^{39} + 150 q^{44} - 142 q^{49} - 36 q^{51} + 54 q^{54} + 78 q^{56} - 54 q^{59} + 312 q^{61} + 364 q^{64} - 270 q^{66} + 336 q^{71} + 60 q^{74} - 86 q^{79} - 18 q^{81} - 240 q^{84} + 444 q^{86} + 252 q^{89} + 144 q^{91} - 270 q^{96} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.59808 + 1.50000i 1.29904 + 0.750000i 0.980238 0.197822i \(-0.0633868\pi\)
0.318800 + 0.947822i \(0.396720\pi\)
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(5\) 0 0
\(6\) 5.19615i 0.866025i
\(7\) −2.59808 6.50000i −0.371154 0.928571i
\(8\) 3.00000i 0.375000i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −7.50000 12.9904i −0.681818 1.18094i −0.974425 0.224711i \(-0.927856\pi\)
0.292607 0.956233i \(-0.405477\pi\)
\(12\) 4.33013 7.50000i 0.360844 0.625000i
\(13\) −13.8564 −1.06588 −0.532939 0.846154i \(-0.678912\pi\)
−0.532939 + 0.846154i \(0.678912\pi\)
\(14\) 3.00000 20.7846i 0.214286 1.48461i
\(15\) 0 0
\(16\) 5.50000 9.52628i 0.343750 0.595392i
\(17\) −5.19615 9.00000i −0.305656 0.529412i 0.671751 0.740777i \(-0.265542\pi\)
−0.977407 + 0.211365i \(0.932209\pi\)
\(18\) −7.79423 + 4.50000i −0.433013 + 0.250000i
\(19\) 9.00000 + 5.19615i 0.473684 + 0.273482i 0.717781 0.696269i \(-0.245158\pi\)
−0.244096 + 0.969751i \(0.578491\pi\)
\(20\) 0 0
\(21\) −7.50000 + 9.52628i −0.357143 + 0.453632i
\(22\) 45.0000i 2.04545i
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 4.50000 2.59808i 0.187500 0.108253i
\(25\) 0 0
\(26\) −36.0000 20.7846i −1.38462 0.799408i
\(27\) 5.19615 0.192450
\(28\) 21.6506 27.5000i 0.773237 0.982143i
\(29\) 9.00000 0.310345 0.155172 0.987887i \(-0.450407\pi\)
0.155172 + 0.987887i \(0.450407\pi\)
\(30\) 0 0
\(31\) −10.5000 + 6.06218i −0.338710 + 0.195554i −0.659701 0.751528i \(-0.729317\pi\)
0.320992 + 0.947082i \(0.395984\pi\)
\(32\) 38.9711 22.5000i 1.21785 0.703125i
\(33\) −12.9904 + 22.5000i −0.393648 + 0.681818i
\(34\) 31.1769i 0.916968i
\(35\) 0 0
\(36\) −15.0000 −0.416667
\(37\) 8.66025 + 5.00000i 0.234061 + 0.135135i 0.612444 0.790514i \(-0.290186\pi\)
−0.378383 + 0.925649i \(0.623520\pi\)
\(38\) 15.5885 + 27.0000i 0.410223 + 0.710526i
\(39\) 12.0000 + 20.7846i 0.307692 + 0.532939i
\(40\) 0 0
\(41\) 10.3923i 0.253471i 0.991937 + 0.126735i \(0.0404499\pi\)
−0.991937 + 0.126735i \(0.959550\pi\)
\(42\) −33.7750 + 13.5000i −0.804166 + 0.321429i
\(43\) 74.0000i 1.72093i −0.509509 0.860465i \(-0.670173\pi\)
0.509509 0.860465i \(-0.329827\pi\)
\(44\) 37.5000 64.9519i 0.852273 1.47618i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −19.0526 −0.396928
\(49\) −35.5000 + 33.7750i −0.724490 + 0.689286i
\(50\) 0 0
\(51\) −9.00000 + 15.5885i −0.176471 + 0.305656i
\(52\) −34.6410 60.0000i −0.666173 1.15385i
\(53\) 28.5788 16.5000i 0.539223 0.311321i −0.205541 0.978649i \(-0.565895\pi\)
0.744764 + 0.667328i \(0.232562\pi\)
\(54\) 13.5000 + 7.79423i 0.250000 + 0.144338i
\(55\) 0 0
\(56\) 19.5000 7.79423i 0.348214 0.139183i
\(57\) 18.0000i 0.315789i
\(58\) 23.3827 + 13.5000i 0.403150 + 0.232759i
\(59\) −13.5000 + 7.79423i −0.228814 + 0.132106i −0.610025 0.792382i \(-0.708840\pi\)
0.381211 + 0.924488i \(0.375507\pi\)
\(60\) 0 0
\(61\) 78.0000 + 45.0333i 1.27869 + 0.738251i 0.976607 0.215031i \(-0.0689853\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(62\) −36.3731 −0.586662
\(63\) 20.7846 + 3.00000i 0.329914 + 0.0476190i
\(64\) 91.0000 1.42188
\(65\) 0 0
\(66\) −67.5000 + 38.9711i −1.02273 + 0.590472i
\(67\) 65.8179 38.0000i 0.982357 0.567164i 0.0793762 0.996845i \(-0.474707\pi\)
0.902981 + 0.429681i \(0.141374\pi\)
\(68\) 25.9808 45.0000i 0.382070 0.661765i
\(69\) 0 0
\(70\) 0 0
\(71\) 84.0000 1.18310 0.591549 0.806269i \(-0.298517\pi\)
0.591549 + 0.806269i \(0.298517\pi\)
\(72\) −7.79423 4.50000i −0.108253 0.0625000i
\(73\) −31.1769 54.0000i −0.427081 0.739726i 0.569531 0.821970i \(-0.307125\pi\)
−0.996612 + 0.0822437i \(0.973791\pi\)
\(74\) 15.0000 + 25.9808i 0.202703 + 0.351091i
\(75\) 0 0
\(76\) 51.9615i 0.683704i
\(77\) −64.9519 + 82.5000i −0.843531 + 1.07143i
\(78\) 72.0000i 0.923077i
\(79\) −21.5000 + 37.2391i −0.272152 + 0.471381i −0.969413 0.245437i \(-0.921069\pi\)
0.697261 + 0.716818i \(0.254402\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −15.5885 + 27.0000i −0.190103 + 0.329268i
\(83\) −119.512 −1.43990 −0.719949 0.694027i \(-0.755835\pi\)
−0.719949 + 0.694027i \(0.755835\pi\)
\(84\) −60.0000 8.66025i −0.714286 0.103098i
\(85\) 0 0
\(86\) 111.000 192.258i 1.29070 2.23555i
\(87\) −7.79423 13.5000i −0.0895888 0.155172i
\(88\) 38.9711 22.5000i 0.442854 0.255682i
\(89\) 63.0000 + 36.3731i 0.707865 + 0.408686i 0.810270 0.586057i \(-0.199320\pi\)
−0.102405 + 0.994743i \(0.532654\pi\)
\(90\) 0 0
\(91\) 36.0000 + 90.0666i 0.395604 + 0.989743i
\(92\) 0 0
\(93\) 18.1865 + 10.5000i 0.195554 + 0.112903i
\(94\) 0 0
\(95\) 0 0
\(96\) −67.5000 38.9711i −0.703125 0.405949i
\(97\) −185.329 −1.91061 −0.955306 0.295618i \(-0.904475\pi\)
−0.955306 + 0.295618i \(0.904475\pi\)
\(98\) −142.894 + 34.5000i −1.45810 + 0.352041i
\(99\) 45.0000 0.454545
\(100\) 0 0
\(101\) −126.000 + 72.7461i −1.24752 + 0.720259i −0.970615 0.240637i \(-0.922644\pi\)
−0.276910 + 0.960896i \(0.589310\pi\)
\(102\) −46.7654 + 27.0000i −0.458484 + 0.264706i
\(103\) 34.6410 60.0000i 0.336321 0.582524i −0.647417 0.762136i \(-0.724151\pi\)
0.983738 + 0.179612i \(0.0574841\pi\)
\(104\) 41.5692i 0.399704i
\(105\) 0 0
\(106\) 99.0000 0.933962
\(107\) 80.5404 + 46.5000i 0.752714 + 0.434579i 0.826674 0.562682i \(-0.190230\pi\)
−0.0739599 + 0.997261i \(0.523564\pi\)
\(108\) 12.9904 + 22.5000i 0.120281 + 0.208333i
\(109\) −4.00000 6.92820i −0.0366972 0.0635615i 0.847093 0.531444i \(-0.178350\pi\)
−0.883791 + 0.467882i \(0.845017\pi\)
\(110\) 0 0
\(111\) 17.3205i 0.156041i
\(112\) −76.2102 11.0000i −0.680449 0.0982143i
\(113\) 42.0000i 0.371681i 0.982580 + 0.185841i \(0.0595008\pi\)
−0.982580 + 0.185841i \(0.940499\pi\)
\(114\) 27.0000 46.7654i 0.236842 0.410223i
\(115\) 0 0
\(116\) 22.5000 + 38.9711i 0.193966 + 0.335958i
\(117\) 20.7846 36.0000i 0.177646 0.307692i
\(118\) −46.7654 −0.396317
\(119\) −45.0000 + 57.1577i −0.378151 + 0.480317i
\(120\) 0 0
\(121\) −52.0000 + 90.0666i −0.429752 + 0.744352i
\(122\) 135.100 + 234.000i 1.10738 + 1.91803i
\(123\) 15.5885 9.00000i 0.126735 0.0731707i
\(124\) −52.5000 30.3109i −0.423387 0.244443i
\(125\) 0 0
\(126\) 49.5000 + 38.9711i 0.392857 + 0.309295i
\(127\) 35.0000i 0.275591i −0.990461 0.137795i \(-0.955998\pi\)
0.990461 0.137795i \(-0.0440016\pi\)
\(128\) 80.5404 + 46.5000i 0.629222 + 0.363281i
\(129\) −111.000 + 64.0859i −0.860465 + 0.496790i
\(130\) 0 0
\(131\) 148.500 + 85.7365i 1.13359 + 0.654477i 0.944835 0.327547i \(-0.106222\pi\)
0.188753 + 0.982025i \(0.439555\pi\)
\(132\) −129.904 −0.984120
\(133\) 10.3923 72.0000i 0.0781376 0.541353i
\(134\) 228.000 1.70149
\(135\) 0 0
\(136\) 27.0000 15.5885i 0.198529 0.114621i
\(137\) 83.1384 48.0000i 0.606850 0.350365i −0.164882 0.986313i \(-0.552724\pi\)
0.771732 + 0.635948i \(0.219391\pi\)
\(138\) 0 0
\(139\) 183.597i 1.32084i −0.750894 0.660422i \(-0.770377\pi\)
0.750894 0.660422i \(-0.229623\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 218.238 + 126.000i 1.53689 + 0.887324i
\(143\) 103.923 + 180.000i 0.726735 + 1.25874i
\(144\) 16.5000 + 28.5788i 0.114583 + 0.198464i
\(145\) 0 0
\(146\) 187.061i 1.28124i
\(147\) 81.4064 + 24.0000i 0.553785 + 0.163265i
\(148\) 50.0000i 0.337838i
\(149\) −93.0000 + 161.081i −0.624161 + 1.08108i 0.364541 + 0.931187i \(0.381226\pi\)
−0.988702 + 0.149892i \(0.952108\pi\)
\(150\) 0 0
\(151\) −39.5000 68.4160i −0.261589 0.453086i 0.705075 0.709133i \(-0.250913\pi\)
−0.966664 + 0.256047i \(0.917580\pi\)
\(152\) −15.5885 + 27.0000i −0.102556 + 0.177632i
\(153\) 31.1769 0.203771
\(154\) −292.500 + 116.913i −1.89935 + 0.759178i
\(155\) 0 0
\(156\) −60.0000 + 103.923i −0.384615 + 0.666173i
\(157\) 10.3923 + 18.0000i 0.0661930 + 0.114650i 0.897223 0.441579i \(-0.145581\pi\)
−0.831030 + 0.556228i \(0.812248\pi\)
\(158\) −111.717 + 64.5000i −0.707071 + 0.408228i
\(159\) −49.5000 28.5788i −0.311321 0.179741i
\(160\) 0 0
\(161\) 0 0
\(162\) 27.0000i 0.166667i
\(163\) 180.133 + 104.000i 1.10511 + 0.638037i 0.937559 0.347826i \(-0.113080\pi\)
0.167553 + 0.985863i \(0.446413\pi\)
\(164\) −45.0000 + 25.9808i −0.274390 + 0.158419i
\(165\) 0 0
\(166\) −310.500 179.267i −1.87048 1.07992i
\(167\) 249.415 1.49350 0.746752 0.665102i \(-0.231612\pi\)
0.746752 + 0.665102i \(0.231612\pi\)
\(168\) −28.5788 22.5000i −0.170112 0.133929i
\(169\) 23.0000 0.136095
\(170\) 0 0
\(171\) −27.0000 + 15.5885i −0.157895 + 0.0911606i
\(172\) 320.429 185.000i 1.86296 1.07558i
\(173\) 114.315 198.000i 0.660782 1.14451i −0.319628 0.947543i \(-0.603558\pi\)
0.980410 0.196966i \(-0.0631087\pi\)
\(174\) 46.7654i 0.268767i
\(175\) 0 0
\(176\) −165.000 −0.937500
\(177\) 23.3827 + 13.5000i 0.132106 + 0.0762712i
\(178\) 109.119 + 189.000i 0.613029 + 1.06180i
\(179\) 45.0000 + 77.9423i 0.251397 + 0.435432i 0.963911 0.266226i \(-0.0857768\pi\)
−0.712514 + 0.701658i \(0.752443\pi\)
\(180\) 0 0
\(181\) 10.3923i 0.0574160i 0.999588 + 0.0287080i \(0.00913930\pi\)
−0.999588 + 0.0287080i \(0.990861\pi\)
\(182\) −41.5692 + 288.000i −0.228402 + 1.58242i
\(183\) 156.000i 0.852459i
\(184\) 0 0
\(185\) 0 0
\(186\) 31.5000 + 54.5596i 0.169355 + 0.293331i
\(187\) −77.9423 + 135.000i −0.416804 + 0.721925i
\(188\) 0 0
\(189\) −13.5000 33.7750i −0.0714286 0.178704i
\(190\) 0 0
\(191\) 156.000 270.200i 0.816754 1.41466i −0.0913077 0.995823i \(-0.529105\pi\)
0.908062 0.418837i \(-0.137562\pi\)
\(192\) −78.8083 136.500i −0.410460 0.710938i
\(193\) −160.215 + 92.5000i −0.830128 + 0.479275i −0.853896 0.520443i \(-0.825767\pi\)
0.0237685 + 0.999717i \(0.492434\pi\)
\(194\) −481.500 277.994i −2.48196 1.43296i
\(195\) 0 0
\(196\) −235.000 69.2820i −1.19898 0.353480i
\(197\) 330.000i 1.67513i −0.546340 0.837563i \(-0.683979\pi\)
0.546340 0.837563i \(-0.316021\pi\)
\(198\) 116.913 + 67.5000i 0.590472 + 0.340909i
\(199\) −6.00000 + 3.46410i −0.0301508 + 0.0174075i −0.515000 0.857190i \(-0.672208\pi\)
0.484849 + 0.874598i \(0.338875\pi\)
\(200\) 0 0
\(201\) −114.000 65.8179i −0.567164 0.327452i
\(202\) −436.477 −2.16078
\(203\) −23.3827 58.5000i −0.115186 0.288177i
\(204\) −90.0000 −0.441176
\(205\) 0 0
\(206\) 180.000 103.923i 0.873786 0.504481i
\(207\) 0 0
\(208\) −76.2102 + 132.000i −0.366395 + 0.634615i
\(209\) 155.885i 0.745859i
\(210\) 0 0
\(211\) −248.000 −1.17536 −0.587678 0.809095i \(-0.699958\pi\)
−0.587678 + 0.809095i \(0.699958\pi\)
\(212\) 142.894 + 82.5000i 0.674029 + 0.389151i
\(213\) −72.7461 126.000i −0.341531 0.591549i
\(214\) 139.500 + 241.621i 0.651869 + 1.12907i
\(215\) 0 0
\(216\) 15.5885i 0.0721688i
\(217\) 66.6840 + 52.5000i 0.307299 + 0.241935i
\(218\) 24.0000i 0.110092i
\(219\) −54.0000 + 93.5307i −0.246575 + 0.427081i
\(220\) 0 0
\(221\) 72.0000 + 124.708i 0.325792 + 0.564288i
\(222\) 25.9808 45.0000i 0.117030 0.202703i
\(223\) −192.258 −0.862142 −0.431071 0.902318i \(-0.641864\pi\)
−0.431071 + 0.902318i \(0.641864\pi\)
\(224\) −247.500 194.856i −1.10491 0.869892i
\(225\) 0 0
\(226\) −63.0000 + 109.119i −0.278761 + 0.482828i
\(227\) 44.1673 + 76.5000i 0.194570 + 0.337004i 0.946759 0.321942i \(-0.104336\pi\)
−0.752190 + 0.658947i \(0.771002\pi\)
\(228\) 77.9423 45.0000i 0.341852 0.197368i
\(229\) −285.000 164.545i −1.24454 0.718536i −0.274526 0.961580i \(-0.588521\pi\)
−0.970015 + 0.243043i \(0.921854\pi\)
\(230\) 0 0
\(231\) 180.000 + 25.9808i 0.779221 + 0.112471i
\(232\) 27.0000i 0.116379i
\(233\) −233.827 135.000i −1.00355 0.579399i −0.0942524 0.995548i \(-0.530046\pi\)
−0.909296 + 0.416149i \(0.863379\pi\)
\(234\) 108.000 62.3538i 0.461538 0.266469i
\(235\) 0 0
\(236\) −67.5000 38.9711i −0.286017 0.165132i
\(237\) 74.4782 0.314254
\(238\) −202.650 + 81.0000i −0.851470 + 0.340336i
\(239\) 228.000 0.953975 0.476987 0.878910i \(-0.341729\pi\)
0.476987 + 0.878910i \(0.341729\pi\)
\(240\) 0 0
\(241\) 385.500 222.569i 1.59959 0.923521i 0.608018 0.793923i \(-0.291965\pi\)
0.991567 0.129598i \(-0.0413687\pi\)
\(242\) −270.200 + 156.000i −1.11653 + 0.644628i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 450.333i 1.84563i
\(245\) 0 0
\(246\) 54.0000 0.219512
\(247\) −124.708 72.0000i −0.504889 0.291498i
\(248\) −18.1865 31.5000i −0.0733328 0.127016i
\(249\) 103.500 + 179.267i 0.415663 + 0.719949i
\(250\) 0 0
\(251\) 5.19615i 0.0207018i 0.999946 + 0.0103509i \(0.00329485\pi\)
−0.999946 + 0.0103509i \(0.996705\pi\)
\(252\) 38.9711 + 97.5000i 0.154647 + 0.386905i
\(253\) 0 0
\(254\) 52.5000 90.9327i 0.206693 0.358003i
\(255\) 0 0
\(256\) −42.5000 73.6122i −0.166016 0.287547i
\(257\) 57.1577 99.0000i 0.222403 0.385214i −0.733134 0.680084i \(-0.761943\pi\)
0.955537 + 0.294870i \(0.0952765\pi\)
\(258\) −384.515 −1.49037
\(259\) 10.0000 69.2820i 0.0386100 0.267498i
\(260\) 0 0
\(261\) −13.5000 + 23.3827i −0.0517241 + 0.0895888i
\(262\) 257.210 + 445.500i 0.981716 + 1.70038i
\(263\) 161.081 93.0000i 0.612474 0.353612i −0.161459 0.986879i \(-0.551620\pi\)
0.773933 + 0.633267i \(0.218287\pi\)
\(264\) −67.5000 38.9711i −0.255682 0.147618i
\(265\) 0 0
\(266\) 135.000 171.473i 0.507519 0.644635i
\(267\) 126.000i 0.471910i
\(268\) 329.090 + 190.000i 1.22795 + 0.708955i
\(269\) 292.500 168.875i 1.08736 0.627788i 0.154488 0.987995i \(-0.450627\pi\)
0.932873 + 0.360207i \(0.117294\pi\)
\(270\) 0 0
\(271\) 79.5000 + 45.8993i 0.293358 + 0.169370i 0.639455 0.768828i \(-0.279160\pi\)
−0.346097 + 0.938199i \(0.612493\pi\)
\(272\) −114.315 −0.420277
\(273\) 103.923 132.000i 0.380671 0.483516i
\(274\) 288.000 1.05109
\(275\) 0 0
\(276\) 0 0
\(277\) −329.090 + 190.000i −1.18805 + 0.685921i −0.957863 0.287226i \(-0.907267\pi\)
−0.230186 + 0.973147i \(0.573934\pi\)
\(278\) 275.396 477.000i 0.990633 1.71583i
\(279\) 36.3731i 0.130369i
\(280\) 0 0
\(281\) 300.000 1.06762 0.533808 0.845606i \(-0.320761\pi\)
0.533808 + 0.845606i \(0.320761\pi\)
\(282\) 0 0
\(283\) 102.191 + 177.000i 0.361099 + 0.625442i 0.988142 0.153543i \(-0.0490683\pi\)
−0.627043 + 0.778985i \(0.715735\pi\)
\(284\) 210.000 + 363.731i 0.739437 + 1.28074i
\(285\) 0 0
\(286\) 623.538i 2.18020i
\(287\) 67.5500 27.0000i 0.235366 0.0940767i
\(288\) 135.000i 0.468750i
\(289\) 90.5000 156.751i 0.313149 0.542390i
\(290\) 0 0
\(291\) 160.500 + 277.994i 0.551546 + 0.955306i
\(292\) 155.885 270.000i 0.533851 0.924658i
\(293\) 545.596 1.86210 0.931051 0.364889i \(-0.118893\pi\)
0.931051 + 0.364889i \(0.118893\pi\)
\(294\) 175.500 + 184.463i 0.596939 + 0.627427i
\(295\) 0 0
\(296\) −15.0000 + 25.9808i −0.0506757 + 0.0877728i
\(297\) −38.9711 67.5000i −0.131216 0.227273i
\(298\) −483.242 + 279.000i −1.62162 + 0.936242i
\(299\) 0 0
\(300\) 0 0
\(301\) −481.000 + 192.258i −1.59801 + 0.638730i
\(302\) 237.000i 0.784768i
\(303\) 218.238 + 126.000i 0.720259 + 0.415842i
\(304\) 99.0000 57.1577i 0.325658 0.188019i
\(305\) 0 0
\(306\) 81.0000 + 46.7654i 0.264706 + 0.152828i
\(307\) −173.205 −0.564186 −0.282093 0.959387i \(-0.591029\pi\)
−0.282093 + 0.959387i \(0.591029\pi\)
\(308\) −519.615 75.0000i −1.68706 0.243506i
\(309\) −120.000 −0.388350
\(310\) 0 0
\(311\) −153.000 + 88.3346i −0.491961 + 0.284034i −0.725388 0.688340i \(-0.758340\pi\)
0.233426 + 0.972374i \(0.425006\pi\)
\(312\) −62.3538 + 36.0000i −0.199852 + 0.115385i
\(313\) 106.521 184.500i 0.340323 0.589457i −0.644170 0.764883i \(-0.722797\pi\)
0.984493 + 0.175426i \(0.0561302\pi\)
\(314\) 62.3538i 0.198579i
\(315\) 0 0
\(316\) −215.000 −0.680380
\(317\) 101.325 + 58.5000i 0.319637 + 0.184543i 0.651231 0.758880i \(-0.274253\pi\)
−0.331594 + 0.943422i \(0.607586\pi\)
\(318\) −85.7365 148.500i −0.269612 0.466981i
\(319\) −67.5000 116.913i −0.211599 0.366500i
\(320\) 0 0
\(321\) 161.081i 0.501809i
\(322\) 0 0
\(323\) 108.000i 0.334365i
\(324\) 22.5000 38.9711i 0.0694444 0.120281i
\(325\) 0 0
\(326\) 312.000 + 540.400i 0.957055 + 1.65767i
\(327\) −6.92820 + 12.0000i −0.0211872 + 0.0366972i
\(328\) −31.1769 −0.0950516
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 + 34.6410i −0.0604230 + 0.104656i −0.894655 0.446759i \(-0.852578\pi\)
0.834232 + 0.551414i \(0.185912\pi\)
\(332\) −298.779 517.500i −0.899936 1.55873i
\(333\) −25.9808 + 15.0000i −0.0780203 + 0.0450450i
\(334\) 648.000 + 374.123i 1.94012 + 1.12013i
\(335\) 0 0
\(336\) 49.5000 + 123.842i 0.147321 + 0.368576i
\(337\) 91.0000i 0.270030i −0.990844 0.135015i \(-0.956892\pi\)
0.990844 0.135015i \(-0.0431082\pi\)
\(338\) 59.7558 + 34.5000i 0.176792 + 0.102071i
\(339\) 63.0000 36.3731i 0.185841 0.107295i
\(340\) 0 0
\(341\) 157.500 + 90.9327i 0.461877 + 0.266665i
\(342\) −93.5307 −0.273482
\(343\) 311.769 + 143.000i 0.908948 + 0.416910i
\(344\) 222.000 0.645349
\(345\) 0 0
\(346\) 594.000 342.946i 1.71676 0.991174i
\(347\) −181.865 + 105.000i −0.524108 + 0.302594i −0.738614 0.674129i \(-0.764519\pi\)
0.214506 + 0.976723i \(0.431186\pi\)
\(348\) 38.9711 67.5000i 0.111986 0.193966i
\(349\) 304.841i 0.873470i −0.899590 0.436735i \(-0.856135\pi\)
0.899590 0.436735i \(-0.143865\pi\)
\(350\) 0 0
\(351\) −72.0000 −0.205128
\(352\) −584.567 337.500i −1.66070 0.958807i
\(353\) 197.454 + 342.000i 0.559359 + 0.968839i 0.997550 + 0.0699566i \(0.0222861\pi\)
−0.438191 + 0.898882i \(0.644381\pi\)
\(354\) 40.5000 + 70.1481i 0.114407 + 0.198158i
\(355\) 0 0
\(356\) 363.731i 1.02172i
\(357\) 124.708 + 18.0000i 0.349321 + 0.0504202i
\(358\) 270.000i 0.754190i
\(359\) 246.000 426.084i 0.685237 1.18686i −0.288126 0.957593i \(-0.593032\pi\)
0.973362 0.229272i \(-0.0736346\pi\)
\(360\) 0 0
\(361\) −126.500 219.104i −0.350416 0.606937i
\(362\) −15.5885 + 27.0000i −0.0430620 + 0.0745856i
\(363\) 180.133 0.496235
\(364\) −300.000 + 381.051i −0.824176 + 1.04684i
\(365\) 0 0
\(366\) 234.000 405.300i 0.639344 1.10738i
\(367\) 163.679 + 283.500i 0.445991 + 0.772480i 0.998121 0.0612789i \(-0.0195179\pi\)
−0.552129 + 0.833758i \(0.686185\pi\)
\(368\) 0 0
\(369\) −27.0000 15.5885i −0.0731707 0.0422451i
\(370\) 0 0
\(371\) −181.500 142.894i −0.489218 0.385160i
\(372\) 105.000i 0.282258i
\(373\) −147.224 85.0000i −0.394703 0.227882i 0.289493 0.957180i \(-0.406513\pi\)
−0.684196 + 0.729298i \(0.739847\pi\)
\(374\) −405.000 + 233.827i −1.08289 + 0.625206i
\(375\) 0 0
\(376\) 0 0
\(377\) −124.708 −0.330790
\(378\) 15.5885 108.000i 0.0412393 0.285714i
\(379\) −82.0000 −0.216359 −0.108179 0.994131i \(-0.534502\pi\)
−0.108179 + 0.994131i \(0.534502\pi\)
\(380\) 0 0
\(381\) −52.5000 + 30.3109i −0.137795 + 0.0795561i
\(382\) 810.600 468.000i 2.12199 1.22513i
\(383\) −109.119 + 189.000i −0.284907 + 0.493473i −0.972587 0.232541i \(-0.925296\pi\)
0.687680 + 0.726014i \(0.258629\pi\)
\(384\) 161.081i 0.419481i
\(385\) 0 0
\(386\) −555.000 −1.43782
\(387\) 192.258 + 111.000i 0.496790 + 0.286822i
\(388\) −463.324 802.500i −1.19413 2.06830i
\(389\) 153.000 + 265.004i 0.393316 + 0.681244i 0.992885 0.119080i \(-0.0379944\pi\)
−0.599568 + 0.800323i \(0.704661\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −101.325 106.500i −0.258482 0.271684i
\(393\) 297.000i 0.755725i
\(394\) 495.000 857.365i 1.25635 2.17605i
\(395\) 0 0
\(396\) 112.500 + 194.856i 0.284091 + 0.492060i
\(397\) −128.172 + 222.000i −0.322851 + 0.559194i −0.981075 0.193628i \(-0.937975\pi\)
0.658224 + 0.752822i \(0.271308\pi\)
\(398\) −20.7846 −0.0522226
\(399\) −117.000 + 46.7654i −0.293233 + 0.117206i
\(400\) 0 0
\(401\) −66.0000 + 114.315i −0.164589 + 0.285076i −0.936509 0.350643i \(-0.885963\pi\)
0.771921 + 0.635719i \(0.219296\pi\)
\(402\) −197.454 342.000i −0.491179 0.850746i
\(403\) 145.492 84.0000i 0.361023 0.208437i
\(404\) −630.000 363.731i −1.55941 0.900323i
\(405\) 0 0
\(406\) 27.0000 187.061i 0.0665025 0.460743i
\(407\) 150.000i 0.368550i
\(408\) −46.7654 27.0000i −0.114621 0.0661765i
\(409\) 313.500 180.999i 0.766504 0.442541i −0.0651223 0.997877i \(-0.520744\pi\)
0.831626 + 0.555336i \(0.187410\pi\)
\(410\) 0 0
\(411\) −144.000 83.1384i −0.350365 0.202283i
\(412\) 346.410 0.840801
\(413\) 85.7365 + 67.5000i 0.207594 + 0.163438i
\(414\) 0 0
\(415\) 0 0
\(416\) −540.000 + 311.769i −1.29808 + 0.749445i
\(417\) −275.396 + 159.000i −0.660422 + 0.381295i
\(418\) 233.827 405.000i 0.559394 0.968900i
\(419\) 644.323i 1.53776i 0.639391 + 0.768882i \(0.279187\pi\)
−0.639391 + 0.768882i \(0.720813\pi\)
\(420\) 0 0
\(421\) 752.000 1.78622 0.893112 0.449835i \(-0.148517\pi\)
0.893112 + 0.449835i \(0.148517\pi\)
\(422\) −644.323 372.000i −1.52683 0.881517i
\(423\) 0 0
\(424\) 49.5000 + 85.7365i 0.116745 + 0.202209i
\(425\) 0 0
\(426\) 436.477i 1.02459i
\(427\) 90.0666 624.000i 0.210929 1.46136i
\(428\) 465.000i 1.08645i
\(429\) 180.000 311.769i 0.419580 0.726735i
\(430\) 0 0
\(431\) −81.0000 140.296i −0.187935 0.325513i 0.756627 0.653847i \(-0.226846\pi\)
−0.944562 + 0.328334i \(0.893513\pi\)
\(432\) 28.5788 49.5000i 0.0661547 0.114583i
\(433\) −339.482 −0.784023 −0.392011 0.919960i \(-0.628221\pi\)
−0.392011 + 0.919960i \(0.628221\pi\)
\(434\) 94.5000 + 236.425i 0.217742 + 0.544758i
\(435\) 0 0
\(436\) 20.0000 34.6410i 0.0458716 0.0794519i
\(437\) 0 0
\(438\) −280.592 + 162.000i −0.640622 + 0.369863i
\(439\) −337.500 194.856i −0.768793 0.443863i 0.0636511 0.997972i \(-0.479726\pi\)
−0.832444 + 0.554110i \(0.813059\pi\)
\(440\) 0 0
\(441\) −34.5000 142.894i −0.0782313 0.324023i
\(442\) 432.000i 0.977376i
\(443\) 257.210 + 148.500i 0.580608 + 0.335214i 0.761375 0.648312i \(-0.224525\pi\)
−0.180767 + 0.983526i \(0.557858\pi\)
\(444\) 75.0000 43.3013i 0.168919 0.0975254i
\(445\) 0 0
\(446\) −499.500 288.386i −1.11996 0.646606i
\(447\) 322.161 0.720719
\(448\) −236.425 591.500i −0.527734 1.32031i
\(449\) 492.000 1.09577 0.547884 0.836554i \(-0.315433\pi\)
0.547884 + 0.836554i \(0.315433\pi\)
\(450\) 0 0
\(451\) 135.000 77.9423i 0.299335 0.172821i
\(452\) −181.865 + 105.000i −0.402357 + 0.232301i
\(453\) −68.4160 + 118.500i −0.151029 + 0.261589i
\(454\) 265.004i 0.583709i
\(455\) 0 0
\(456\) 54.0000 0.118421
\(457\) −383.649 221.500i −0.839495 0.484683i 0.0175975 0.999845i \(-0.494398\pi\)
−0.857093 + 0.515162i \(0.827732\pi\)
\(458\) −493.634 855.000i −1.07780 1.86681i
\(459\) −27.0000 46.7654i −0.0588235 0.101885i
\(460\) 0 0
\(461\) 415.692i 0.901718i −0.892595 0.450859i \(-0.851118\pi\)
0.892595 0.450859i \(-0.148882\pi\)
\(462\) 428.683 + 337.500i 0.927884 + 0.730519i
\(463\) 82.0000i 0.177106i −0.996071 0.0885529i \(-0.971776\pi\)
0.996071 0.0885529i \(-0.0282242\pi\)
\(464\) 49.5000 85.7365i 0.106681 0.184777i
\(465\) 0 0
\(466\) −405.000 701.481i −0.869099 1.50532i
\(467\) 135.100 234.000i 0.289293 0.501071i −0.684348 0.729156i \(-0.739913\pi\)
0.973641 + 0.228085i \(0.0732464\pi\)
\(468\) 207.846 0.444116
\(469\) −418.000 329.090i −0.891258 0.701684i
\(470\) 0 0
\(471\) 18.0000 31.1769i 0.0382166 0.0661930i
\(472\) −23.3827 40.5000i −0.0495396 0.0858051i
\(473\) −961.288 + 555.000i −2.03232 + 1.17336i
\(474\) 193.500 + 111.717i 0.408228 + 0.235690i
\(475\) 0 0
\(476\) −360.000 51.9615i −0.756303 0.109163i
\(477\) 99.0000i 0.207547i
\(478\) 592.361 + 342.000i 1.23925 + 0.715481i
\(479\) −297.000 + 171.473i −0.620042 + 0.357981i −0.776885 0.629642i \(-0.783202\pi\)
0.156844 + 0.987623i \(0.449868\pi\)
\(480\) 0 0
\(481\) −120.000 69.2820i −0.249480 0.144037i
\(482\) 1335.41 2.77056
\(483\) 0 0
\(484\) −520.000 −1.07438
\(485\) 0 0
\(486\) −40.5000 + 23.3827i −0.0833333 + 0.0481125i
\(487\) 274.530 158.500i 0.563717 0.325462i −0.190919 0.981606i \(-0.561147\pi\)
0.754636 + 0.656144i \(0.227814\pi\)
\(488\) −135.100 + 234.000i −0.276844 + 0.479508i
\(489\) 360.267i 0.736741i
\(490\) 0 0
\(491\) 27.0000 0.0549898 0.0274949 0.999622i \(-0.491247\pi\)
0.0274949 + 0.999622i \(0.491247\pi\)
\(492\) 77.9423 + 45.0000i 0.158419 + 0.0914634i
\(493\) −46.7654 81.0000i −0.0948588 0.164300i
\(494\) −216.000 374.123i −0.437247 0.757334i
\(495\) 0 0
\(496\) 133.368i 0.268887i
\(497\) −218.238 546.000i −0.439111 1.09859i
\(498\) 621.000i 1.24699i
\(499\) −223.000 + 386.247i −0.446894 + 0.774043i −0.998182 0.0602721i \(-0.980803\pi\)
0.551288 + 0.834315i \(0.314136\pi\)
\(500\) 0 0
\(501\) −216.000 374.123i −0.431138 0.746752i
\(502\) −7.79423 + 13.5000i −0.0155264 + 0.0268924i
\(503\) −488.438 −0.971050 −0.485525 0.874223i \(-0.661372\pi\)
−0.485525 + 0.874223i \(0.661372\pi\)
\(504\) −9.00000 + 62.3538i −0.0178571 + 0.123718i
\(505\) 0 0
\(506\) 0 0
\(507\) −19.9186 34.5000i −0.0392871 0.0680473i
\(508\) 151.554 87.5000i 0.298336 0.172244i
\(509\) −85.5000 49.3634i −0.167976 0.0969812i 0.413655 0.910434i \(-0.364252\pi\)
−0.581631 + 0.813453i \(0.697585\pi\)
\(510\) 0 0
\(511\) −270.000 + 342.946i −0.528376 + 0.671127i
\(512\) 627.000i 1.22461i
\(513\) 46.7654 + 27.0000i 0.0911606 + 0.0526316i
\(514\) 297.000 171.473i 0.577821 0.333605i
\(515\) 0 0
\(516\) −555.000 320.429i −1.07558 0.620987i
\(517\) 0 0
\(518\) 129.904 165.000i 0.250780 0.318533i
\(519\) −396.000 −0.763006
\(520\) 0 0
\(521\) −783.000 + 452.065i −1.50288 + 0.867688i −0.502885 + 0.864354i \(0.667728\pi\)
−0.999994 + 0.00333410i \(0.998939\pi\)
\(522\) −70.1481 + 40.5000i −0.134383 + 0.0775862i
\(523\) 349.874 606.000i 0.668976 1.15870i −0.309215 0.950992i \(-0.600066\pi\)
0.978191 0.207708i \(-0.0666003\pi\)
\(524\) 857.365i 1.63619i
\(525\) 0 0
\(526\) 558.000 1.06084
\(527\) 109.119 + 63.0000i 0.207057 + 0.119545i
\(528\) 142.894 + 247.500i 0.270633 + 0.468750i
\(529\) −264.500 458.127i −0.500000 0.866025i
\(530\) 0 0
\(531\) 46.7654i 0.0880704i
\(532\) 337.750 135.000i 0.634868 0.253759i
\(533\) 144.000i 0.270169i
\(534\) 189.000 327.358i 0.353933 0.613029i
\(535\) 0 0
\(536\) 114.000 + 197.454i 0.212687 + 0.368384i
\(537\) 77.9423 135.000i 0.145144 0.251397i
\(538\) 1013.25 1.88336
\(539\) 705.000 + 207.846i 1.30798 + 0.385614i
\(540\) 0 0
\(541\) −37.0000 + 64.0859i −0.0683919 + 0.118458i −0.898194 0.439600i \(-0.855120\pi\)
0.829802 + 0.558058i \(0.188453\pi\)
\(542\) 137.698 + 238.500i 0.254055 + 0.440037i
\(543\) 15.5885 9.00000i 0.0287080 0.0165746i
\(544\) −405.000 233.827i −0.744485 0.429829i
\(545\) 0 0
\(546\) 468.000 187.061i 0.857143 0.342603i
\(547\) 934.000i 1.70750i 0.520687 + 0.853748i \(0.325676\pi\)
−0.520687 + 0.853748i \(0.674324\pi\)
\(548\) 415.692 + 240.000i 0.758562 + 0.437956i
\(549\) −234.000 + 135.100i −0.426230 + 0.246084i
\(550\) 0 0
\(551\) 81.0000 + 46.7654i 0.147005 + 0.0848736i
\(552\) 0 0
\(553\) 297.913 + 43.0000i 0.538721 + 0.0777577i
\(554\) −1140.00 −2.05776
\(555\) 0 0
\(556\) 795.000 458.993i 1.42986 0.825528i
\(557\) −730.059 + 421.500i −1.31070 + 0.756732i −0.982212 0.187776i \(-0.939872\pi\)
−0.328487 + 0.944508i \(0.606539\pi\)
\(558\) 54.5596 94.5000i 0.0977771 0.169355i
\(559\) 1025.37i 1.83430i
\(560\) 0 0
\(561\) 270.000 0.481283
\(562\) 779.423 + 450.000i 1.38687 + 0.800712i
\(563\) 475.448 + 823.500i 0.844490 + 1.46270i 0.886063 + 0.463564i \(0.153430\pi\)
−0.0415731 + 0.999135i \(0.513237\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 613.146i 1.08330i
\(567\) −38.9711 + 49.5000i −0.0687322 + 0.0873016i
\(568\) 252.000i 0.443662i
\(569\) 111.000 192.258i 0.195079 0.337887i −0.751847 0.659337i \(-0.770837\pi\)
0.946926 + 0.321450i \(0.104170\pi\)
\(570\) 0 0
\(571\) −220.000 381.051i −0.385289 0.667340i 0.606520 0.795068i \(-0.292565\pi\)
−0.991809 + 0.127728i \(0.959232\pi\)
\(572\) −519.615 + 900.000i −0.908418 + 1.57343i
\(573\) −540.400 −0.943106
\(574\) 216.000 + 31.1769i 0.376307 + 0.0543152i
\(575\) 0 0
\(576\) −136.500 + 236.425i −0.236979 + 0.410460i
\(577\) −328.224 568.500i −0.568845 0.985269i −0.996681 0.0814120i \(-0.974057\pi\)
0.427835 0.903857i \(-0.359276\pi\)
\(578\) 470.252 271.500i 0.813584 0.469723i
\(579\) 277.500 + 160.215i 0.479275 + 0.276709i
\(580\) 0 0
\(581\) 310.500 + 776.825i 0.534423 + 1.33705i
\(582\) 963.000i 1.65464i
\(583\) −428.683 247.500i −0.735305 0.424528i
\(584\) 162.000 93.5307i 0.277397 0.160155i
\(585\) 0 0
\(586\) 1417.50 + 818.394i 2.41894 + 1.39658i
\(587\) 1054.82 1.79697 0.898483 0.439008i \(-0.144670\pi\)
0.898483 + 0.439008i \(0.144670\pi\)
\(588\) 99.5929 + 412.500i 0.169376 + 0.701531i
\(589\) −126.000 −0.213922
\(590\) 0 0
\(591\) −495.000 + 285.788i −0.837563 + 0.483567i
\(592\) 95.2628 55.0000i 0.160917 0.0929054i
\(593\) −353.338 + 612.000i −0.595849 + 1.03204i 0.397578 + 0.917569i \(0.369851\pi\)
−0.993426 + 0.114472i \(0.963482\pi\)
\(594\) 233.827i 0.393648i
\(595\) 0 0
\(596\) −930.000 −1.56040
\(597\) 10.3923 + 6.00000i 0.0174075 + 0.0100503i
\(598\) 0 0
\(599\) 258.000 + 446.869i 0.430718 + 0.746025i 0.996935 0.0782307i \(-0.0249271\pi\)
−0.566217 + 0.824256i \(0.691594\pi\)
\(600\) 0 0
\(601\) 247.683i 0.412119i 0.978540 + 0.206059i \(0.0660640\pi\)
−0.978540 + 0.206059i \(0.933936\pi\)
\(602\) −1538.06 222.000i −2.55492 0.368771i
\(603\) 228.000i 0.378109i
\(604\) 197.500 342.080i 0.326987 0.566358i
\(605\) 0 0
\(606\) 378.000 + 654.715i 0.623762 + 1.08039i
\(607\) −324.760 + 562.500i −0.535024 + 0.926689i 0.464138 + 0.885763i \(0.346364\pi\)
−0.999162 + 0.0409259i \(0.986969\pi\)
\(608\) 467.654 0.769167
\(609\) −67.5000 + 85.7365i −0.110837 + 0.140782i
\(610\) 0 0
\(611\) 0 0
\(612\) 77.9423 + 135.000i 0.127357 + 0.220588i
\(613\) −772.495 + 446.000i −1.26019 + 0.727569i −0.973111 0.230338i \(-0.926017\pi\)
−0.287076 + 0.957908i \(0.592683\pi\)
\(614\) −450.000 259.808i −0.732899 0.423139i
\(615\) 0 0
\(616\) −247.500 194.856i −0.401786 0.316324i
\(617\) 1224.00i 1.98379i 0.127050 + 0.991896i \(0.459449\pi\)
−0.127050 + 0.991896i \(0.540551\pi\)
\(618\) −311.769 180.000i −0.504481 0.291262i
\(619\) 348.000 200.918i 0.562197 0.324585i −0.191830 0.981428i \(-0.561442\pi\)
0.754027 + 0.656844i \(0.228109\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −530.008 −0.852102
\(623\) 72.7461 504.000i 0.116767 0.808989i
\(624\) 264.000 0.423077
\(625\) 0 0
\(626\) 553.500 319.563i 0.884185 0.510485i
\(627\) −233.827 + 135.000i −0.372930 + 0.215311i
\(628\) −51.9615 + 90.0000i −0.0827413 + 0.143312i
\(629\) 103.923i 0.165219i
\(630\) 0 0
\(631\) 1115.00 1.76704 0.883518 0.468397i \(-0.155168\pi\)
0.883518 + 0.468397i \(0.155168\pi\)
\(632\) −111.717 64.5000i −0.176768 0.102057i
\(633\) 214.774 + 372.000i 0.339296 + 0.587678i
\(634\) 175.500 + 303.975i 0.276814 + 0.479456i
\(635\) 0 0
\(636\) 285.788i 0.449353i
\(637\) 491.902 468.000i 0.772217 0.734694i
\(638\) 405.000i 0.634796i
\(639\) −126.000 + 218.238i −0.197183 + 0.341531i
\(640\) 0 0
\(641\) 192.000 + 332.554i 0.299532 + 0.518805i 0.976029 0.217641i \(-0.0698361\pi\)
−0.676497 + 0.736445i \(0.736503\pi\)
\(642\) 241.621 418.500i 0.376357 0.651869i
\(643\) −6.92820 −0.0107748 −0.00538741 0.999985i \(-0.501715\pi\)
−0.00538741 + 0.999985i \(0.501715\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 162.000 280.592i 0.250774 0.434353i
\(647\) −446.869 774.000i −0.690679 1.19629i −0.971616 0.236564i \(-0.923979\pi\)
0.280937 0.959726i \(-0.409355\pi\)
\(648\) 23.3827 13.5000i 0.0360844 0.0208333i
\(649\) 202.500 + 116.913i 0.312018 + 0.180144i
\(650\) 0 0
\(651\) 21.0000 145.492i 0.0322581 0.223490i
\(652\) 1040.00i 1.59509i
\(653\) −64.9519 37.5000i −0.0994669 0.0574273i 0.449441 0.893310i \(-0.351623\pi\)
−0.548908 + 0.835883i \(0.684956\pi\)
\(654\) −36.0000 + 20.7846i −0.0550459 + 0.0317807i
\(655\) 0 0
\(656\) 99.0000 + 57.1577i 0.150915 + 0.0871306i
\(657\) 187.061 0.284721
\(658\) 0 0
\(659\) −642.000 −0.974203 −0.487102 0.873345i \(-0.661946\pi\)
−0.487102 + 0.873345i \(0.661946\pi\)
\(660\) 0 0
\(661\) −243.000 + 140.296i −0.367625 + 0.212248i −0.672420 0.740170i \(-0.734745\pi\)
0.304795 + 0.952418i \(0.401412\pi\)
\(662\) −103.923 + 60.0000i −0.156983 + 0.0906344i
\(663\) 124.708 216.000i 0.188096 0.325792i
\(664\) 358.535i 0.539962i
\(665\) 0 0
\(666\) −90.0000 −0.135135
\(667\) 0 0
\(668\) 623.538 + 1080.00i 0.933441 + 1.61677i
\(669\) 166.500 + 288.386i 0.248879 + 0.431071i
\(670\) 0 0
\(671\) 1351.00i 2.01341i
\(672\) −77.9423 + 540.000i −0.115986 + 0.803571i
\(673\) 13.0000i 0.0193165i 0.999953 + 0.00965825i \(0.00307436\pi\)
−0.999953 + 0.00965825i \(0.996926\pi\)
\(674\) 136.500 236.425i 0.202522 0.350779i
\(675\) 0 0
\(676\) 57.5000 + 99.5929i 0.0850592 + 0.147327i
\(677\) −631.333 + 1093.50i −0.932544 + 1.61521i −0.153589 + 0.988135i \(0.549083\pi\)
−0.778955 + 0.627079i \(0.784250\pi\)
\(678\) 218.238 0.321886
\(679\) 481.500 + 1204.64i 0.709131 + 1.77414i
\(680\) 0 0
\(681\) 76.5000 132.502i 0.112335 0.194570i
\(682\) 272.798 + 472.500i 0.399997 + 0.692815i
\(683\) −839.179 + 484.500i −1.22867 + 0.709370i −0.966751 0.255721i \(-0.917687\pi\)
−0.261915 + 0.965091i \(0.584354\pi\)
\(684\) −135.000 77.9423i −0.197368 0.113951i
\(685\) 0 0
\(686\) 595.500 + 839.179i 0.868076 + 1.22329i
\(687\) 570.000i 0.829694i
\(688\) −704.945 407.000i −1.02463 0.591570i
\(689\) −396.000 + 228.631i −0.574746 + 0.331830i
\(690\) 0 0
\(691\) −87.0000 50.2295i −0.125904 0.0726910i 0.435725 0.900080i \(-0.356492\pi\)
−0.561629 + 0.827389i \(0.689825\pi\)
\(692\) 1143.15 1.65196
\(693\) −116.913 292.500i −0.168706 0.422078i
\(694\) −630.000 −0.907781
\(695\) 0 0
\(696\) 40.5000 23.3827i 0.0581897 0.0335958i
\(697\) 93.5307 54.0000i 0.134190 0.0774749i
\(698\) 457.261 792.000i 0.655102 1.13467i
\(699\) 467.654i 0.669033i
\(700\) 0 0
\(701\) 597.000 0.851641 0.425820 0.904808i \(-0.359986\pi\)
0.425820 + 0.904808i \(0.359986\pi\)
\(702\) −187.061 108.000i −0.266469 0.153846i
\(703\) 51.9615 + 90.0000i 0.0739140 + 0.128023i
\(704\) −682.500 1182.12i −0.969460 1.67915i
\(705\) 0 0
\(706\) 1184.72i 1.67808i
\(707\) 800.207 + 630.000i 1.13184 + 0.891089i
\(708\) 135.000i 0.190678i
\(709\) −415.000 + 718.801i −0.585331 + 1.01382i 0.409503 + 0.912309i \(0.365702\pi\)
−0.994834 + 0.101515i \(0.967631\pi\)
\(710\) 0 0
\(711\) −64.5000 111.717i −0.0907173 0.157127i
\(712\) −109.119 + 189.000i −0.153257 + 0.265449i
\(713\) 0 0
\(714\) 297.000 + 233.827i 0.415966 + 0.327489i
\(715\) 0 0
\(716\) −225.000 + 389.711i −0.314246 + 0.544290i
\(717\) −197.454 342.000i −0.275389 0.476987i
\(718\) 1278.25 738.000i 1.78030 1.02786i
\(719\) −297.000 171.473i −0.413074 0.238488i 0.279036 0.960281i \(-0.409985\pi\)
−0.692110 + 0.721792i \(0.743319\pi\)
\(720\) 0 0
\(721\) −480.000 69.2820i −0.665742 0.0960916i
\(722\) 759.000i 1.05125i
\(723\) −667.706 385.500i −0.923521 0.533195i
\(724\) −45.0000 + 25.9808i −0.0621547 + 0.0358850i
\(725\) 0 0
\(726\) 468.000 + 270.200i 0.644628 + 0.372176i
\(727\) −50.2295 −0.0690914 −0.0345457 0.999403i \(-0.510998\pi\)
−0.0345457 + 0.999403i \(0.510998\pi\)
\(728\) −270.200 + 108.000i −0.371154 + 0.148352i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −666.000 + 384.515i −0.911081 + 0.526013i
\(732\) 675.500 390.000i 0.922814 0.532787i
\(733\) 91.7987 159.000i 0.125237 0.216917i −0.796589 0.604522i \(-0.793364\pi\)
0.921826 + 0.387605i \(0.126698\pi\)
\(734\) 982.073i 1.33797i
\(735\) 0 0
\(736\) 0 0
\(737\) −987.269 570.000i −1.33958 0.773406i
\(738\) −46.7654 81.0000i −0.0633677 0.109756i
\(739\) −167.000 289.252i −0.225981 0.391411i 0.730632 0.682771i \(-0.239225\pi\)
−0.956613 + 0.291361i \(0.905892\pi\)
\(740\) 0 0
\(741\) 249.415i 0.336593i
\(742\) −257.210 643.500i −0.346644 0.867251i
\(743\) 84.0000i 0.113055i 0.998401 + 0.0565276i \(0.0180029\pi\)
−0.998401 + 0.0565276i \(0.981997\pi\)
\(744\) −31.5000 + 54.5596i −0.0423387 + 0.0733328i
\(745\) 0 0
\(746\) −255.000 441.673i −0.341823 0.592055i
\(747\) 179.267 310.500i 0.239983 0.415663i
\(748\) −779.423 −1.04201
\(749\) 93.0000 644.323i 0.124166 0.860244i
\(750\) 0 0
\(751\) 179.500 310.903i 0.239015 0.413986i −0.721417 0.692501i \(-0.756509\pi\)
0.960432 + 0.278515i \(0.0898423\pi\)
\(752\) 0 0
\(753\) 7.79423 4.50000i 0.0103509 0.00597610i
\(754\) −324.000 187.061i −0.429708 0.248092i
\(755\) 0 0
\(756\) 112.500 142.894i 0.148810 0.189013i
\(757\) 80.0000i 0.105680i 0.998603 + 0.0528402i \(0.0168274\pi\)
−0.998603 + 0.0528402i \(0.983173\pi\)
\(758\) −213.042 123.000i −0.281058 0.162269i
\(759\) 0 0
\(760\) 0 0
\(761\) −702.000 405.300i −0.922470 0.532589i −0.0380481 0.999276i \(-0.512114\pi\)
−0.884422 + 0.466687i \(0.845447\pi\)
\(762\) −181.865 −0.238668
\(763\) −34.6410 + 44.0000i −0.0454011 + 0.0576671i
\(764\) 1560.00 2.04188
\(765\) 0 0
\(766\) −567.000 + 327.358i −0.740209 + 0.427360i
\(767\) 187.061 108.000i 0.243887 0.140808i
\(768\) −73.6122 + 127.500i −0.0958492 + 0.166016i
\(769\) 774.227i 1.00680i −0.864054 0.503398i \(-0.832083\pi\)
0.864054 0.503398i \(-0.167917\pi\)
\(770\) 0 0
\(771\) −198.000 −0.256809
\(772\) −801.073 462.500i −1.03766 0.599093i
\(773\) −363.731 630.000i −0.470544 0.815006i 0.528888 0.848691i \(-0.322609\pi\)
−0.999433 + 0.0336850i \(0.989276\pi\)
\(774\) 333.000 + 576.773i 0.430233 + 0.745185i
\(775\) 0 0
\(776\) 555.988i 0.716480i
\(777\) −112.583 + 45.0000i −0.144895 + 0.0579151i
\(778\) 918.000i 1.17995i
\(779\) −54.0000 + 93.5307i −0.0693196 + 0.120065i
\(780\) 0 0
\(781\) −630.000 1091.19i −0.806658 1.39717i
\(782\) 0 0
\(783\) 46.7654 0.0597259
\(784\) 126.500 + 523.945i 0.161352 + 0.668298i
\(785\) 0 0
\(786\) 445.500 771.629i 0.566794 0.981716i
\(787\) 713.605 + 1236.00i 0.906741 + 1.57052i 0.818563 + 0.574416i \(0.194771\pi\)
0.0881773 + 0.996105i \(0.471896\pi\)
\(788\) 1428.94 825.000i 1.81338 1.04695i
\(789\) −279.000 161.081i −0.353612 0.204158i
\(790\) 0 0
\(791\) 273.000 109.119i 0.345133 0.137951i
\(792\) 135.000i 0.170455i
\(793\) −1080.80 624.000i −1.36293 0.786885i
\(794\) −666.000 + 384.515i −0.838791 + 0.484276i
\(795\) 0 0
\(796\) −30.0000 17.3205i −0.0376884 0.0217594i
\(797\) −607.950 −0.762798 −0.381399 0.924411i \(-0.624558\pi\)
−0.381399 + 0.924411i \(0.624558\pi\)
\(798\) −374.123 54.0000i −0.468826 0.0676692i
\(799\) 0 0
\(800\) 0 0
\(801\) −189.000 + 109.119i −0.235955 + 0.136229i
\(802\) −342.946 + 198.000i −0.427614 + 0.246883i
\(803\) −467.654 + 810.000i −0.582383 + 1.00872i
\(804\) 658.179i 0.818631i
\(805\) 0 0
\(806\) 504.000 0.625310
\(807\) −506.625 292.500i −0.627788 0.362454i
\(808\) −218.238 378.000i −0.270097 0.467822i
\(809\) −84.0000 145.492i −0.103832 0.179842i 0.809428 0.587218i \(-0.199777\pi\)
−0.913260 + 0.407376i \(0.866444\pi\)
\(810\) 0 0
\(811\) 353.338i 0.435682i −0.975984 0.217841i \(-0.930099\pi\)
0.975984 0.217841i \(-0.0699015\pi\)
\(812\) 194.856 247.500i 0.239970 0.304803i
\(813\) 159.000i 0.195572i
\(814\) 225.000 389.711i 0.276413 0.478761i
\(815\) 0 0
\(816\) 99.0000 + 171.473i 0.121324 + 0.210139i
\(817\) 384.515 666.000i 0.470643 0.815177i
\(818\) 1086.00 1.32762
\(819\) −288.000 41.5692i −0.351648 0.0507561i
\(820\) 0 0
\(821\) −142.500 + 246.817i −0.173569 + 0.300630i −0.939665 0.342096i \(-0.888863\pi\)
0.766096 + 0.642726i \(0.222197\pi\)
\(822\) −249.415 432.000i −0.303425 0.525547i
\(823\) −237.291 + 137.000i −0.288324 + 0.166464i −0.637186 0.770710i \(-0.719902\pi\)
0.348862 + 0.937174i \(0.386568\pi\)
\(824\) 180.000 + 103.923i 0.218447 + 0.126120i
\(825\) 0 0
\(826\) 121.500 + 303.975i 0.147094 + 0.368008i
\(827\) 429.000i 0.518742i −0.965778 0.259371i \(-0.916485\pi\)
0.965778 0.259371i \(-0.0835153\pi\)
\(828\) 0 0
\(829\) 819.000 472.850i 0.987937 0.570386i 0.0832802 0.996526i \(-0.473460\pi\)
0.904657 + 0.426140i \(0.140127\pi\)
\(830\) 0 0
\(831\) 570.000 + 329.090i 0.685921 + 0.396016i
\(832\) −1260.93 −1.51554
\(833\) 488.438 + 144.000i 0.586361 + 0.172869i
\(834\) −954.000 −1.14388
\(835\) 0 0
\(836\) 675.000 389.711i 0.807416 0.466162i
\(837\) −54.5596 + 31.5000i −0.0651847 + 0.0376344i
\(838\) −966.484 + 1674.00i −1.15332 + 1.99761i
\(839\) 259.808i 0.309663i 0.987941 + 0.154832i \(0.0494835\pi\)
−0.987941 + 0.154832i \(0.950516\pi\)
\(840\) 0 0
\(841\) −760.000 −0.903686
\(842\) 1953.75 + 1128.00i 2.32037 + 1.33967i
\(843\) −259.808 450.000i −0.308194 0.533808i
\(844\) −620.000 1073.87i −0.734597 1.27236i
\(845\) 0 0
\(846\) 0 0
\(847\) 720.533 + 104.000i 0.850688 + 0.122786i
\(848\) 363.000i 0.428066i
\(849\) 177.000 306.573i 0.208481 0.361099i
\(850\) 0 0
\(851\) 0 0
\(852\) 363.731 630.000i 0.426914 0.739437i
\(853\) 997.661 1.16959 0.584796 0.811181i \(-0.301175\pi\)
0.584796 + 0.811181i \(0.301175\pi\)
\(854\) 1170.00 1486.10i 1.37002 1.74016i
\(855\) 0 0
\(856\) −139.500 + 241.621i −0.162967 + 0.282268i
\(857\) −218.238 378.000i −0.254654 0.441074i 0.710148 0.704053i \(-0.248628\pi\)
−0.964801 + 0.262979i \(0.915295\pi\)
\(858\) 935.307 540.000i 1.09010 0.629371i
\(859\) 393.000 + 226.899i 0.457509 + 0.264143i 0.710996 0.703196i \(-0.248244\pi\)
−0.253487 + 0.967339i \(0.581578\pi\)
\(860\) 0 0
\(861\) −99.0000 77.9423i −0.114983 0.0905253i
\(862\) 486.000i 0.563805i
\(863\) 337.750 + 195.000i 0.391367 + 0.225956i 0.682752 0.730650i \(-0.260783\pi\)
−0.291385 + 0.956606i \(0.594116\pi\)
\(864\) 202.500 116.913i 0.234375 0.135316i
\(865\) 0 0
\(866\) −882.000 509.223i −1.01848 0.588017i
\(867\) −313.501 −0.361593
\(868\) −60.6218 + 420.000i −0.0698408 + 0.483871i
\(869\) 645.000 0.742232
\(870\) 0 0
\(871\) −912.000 + 526.543i −1.04707 + 0.604527i
\(872\) 20.7846 12.0000i 0.0238356 0.0137615i
\(873\) 277.994 481.500i 0.318435 0.551546i
\(874\) 0 0
\(875\) 0 0
\(876\) −540.000 −0.616438
\(877\) −471.118 272.000i −0.537192 0.310148i 0.206748 0.978394i \(-0.433712\pi\)
−0.743940 + 0.668246i \(0.767045\pi\)
\(878\) −584.567 1012.50i −0.665794 1.15319i
\(879\) −472.500 818.394i −0.537543 0.931051i
\(880\) 0 0
\(881\) 187.061i 0.212329i 0.994349 + 0.106164i \(0.0338569\pi\)
−0.994349 + 0.106164i \(0.966143\pi\)
\(882\) 124.708 423.000i 0.141392 0.479592i
\(883\) 322.000i 0.364666i 0.983237 + 0.182333i \(0.0583649\pi\)
−0.983237 + 0.182333i \(0.941635\pi\)
\(884\) −360.000 + 623.538i −0.407240 + 0.705360i
\(885\) 0 0
\(886\) 445.500 + 771.629i 0.502822 + 0.870913i
\(887\) 353.338 612.000i 0.398352 0.689966i −0.595171 0.803599i \(-0.702916\pi\)
0.993523 + 0.113633i \(0.0362489\pi\)
\(888\) 51.9615 0.0585152
\(889\) −227.500 + 90.9327i −0.255906 + 0.102286i
\(890\) 0 0
\(891\) −67.5000 + 116.913i −0.0757576 + 0.131216i
\(892\) −480.644 832.500i −0.538839 0.933296i
\(893\) 0 0
\(894\) 837.000 + 483.242i 0.936242 + 0.540539i
\(895\) 0 0
\(896\) 93.0000 644.323i 0.103795 0.719110i
\(897\) 0 0
\(898\) 1278.25 + 738.000i 1.42344 + 0.821826i
\(899\) −94.5000 + 54.5596i −0.105117 + 0.0606892i
\(900\) 0 0
\(901\) −297.000 171.473i −0.329634 0.190314i
\(902\) 467.654 0.518463
\(903\) 704.945 + 555.000i 0.780670 + 0.614618i
\(904\) −126.000 −0.139381
\(905\) 0 0
\(906\) −355.500 + 205.248i −0.392384 + 0.226543i
\(907\) 952.628 550.000i 1.05031 0.606395i 0.127571 0.991829i \(-0.459282\pi\)
0.922735 + 0.385435i \(0.125948\pi\)
\(908\) −220.836 + 382.500i −0.243212 + 0.421256i
\(909\) 436.477i 0.480173i
\(910\) 0 0
\(911\) 900.000 0.987925 0.493963 0.869483i \(-0.335548\pi\)
0.493963 + 0.869483i \(0.335548\pi\)
\(912\) −171.473 99.0000i −0.188019 0.108553i
\(913\) 896.336 + 1552.50i 0.981748 + 1.70044i
\(914\) −664.500 1150.95i −0.727024 1.25924i
\(915\) 0 0
\(916\) 1645.45i 1.79634i
\(917\) 171.473 1188.00i 0.186993 1.29553i
\(918\) 162.000i 0.176471i
\(919\) −859.000 + 1487.83i −0.934712 + 1.61897i −0.159564 + 0.987188i \(0.551009\pi\)
−0.775147 + 0.631781i \(0.782324\pi\)
\(920\) 0 0
\(921\) 150.000 + 259.808i 0.162866 + 0.282093i
\(922\) 623.538 1080.00i 0.676289 1.17137i
\(923\) −1163.94 −1.26104
\(924\) 337.500 + 844.375i 0.365260 + 0.913826i
\(925\) 0 0
\(926\) 123.000 213.042i 0.132829 0.230067i
\(927\) 103.923 + 180.000i 0.112107 + 0.194175i
\(928\) 350.740 202.500i 0.377953 0.218211i
\(929\) 1287.00 + 743.050i 1.38536 + 0.799838i 0.992788 0.119883i \(-0.0382519\pi\)
0.392573 + 0.919721i \(0.371585\pi\)
\(930\) 0 0
\(931\) −495.000 + 119.512i −0.531686 + 0.128369i
\(932\) 1350.00i 1.44850i
\(933\) 265.004 + 153.000i 0.284034 + 0.163987i
\(934\) 702.000 405.300i 0.751606 0.433940i
\(935\) 0 0
\(936\) 108.000 + 62.3538i 0.115385 + 0.0666173i
\(937\) 957.824 1.02222 0.511112 0.859514i \(-0.329234\pi\)
0.511112 + 0.859514i \(0.329234\pi\)
\(938\) −592.361 1482.00i −0.631515 1.57996i
\(939\) −369.000 −0.392971
\(940\) 0 0
\(941\) 310.500 179.267i 0.329968 0.190507i −0.325859 0.945418i \(-0.605653\pi\)
0.655827 + 0.754911i \(0.272320\pi\)
\(942\) 93.5307 54.0000i 0.0992895 0.0573248i
\(943\) 0 0
\(944\) 171.473i 0.181645i
\(945\) 0 0
\(946\) −3330.00 −3.52008
\(947\) 140.296 + 81.0000i 0.148148 + 0.0855333i 0.572242 0.820085i \(-0.306074\pi\)
−0.424094 + 0.905618i \(0.639407\pi\)
\(948\) 186.195 + 322.500i 0.196409 + 0.340190i
\(949\) 432.000 + 748.246i 0.455216 + 0.788457i
\(950\) 0 0
\(951\) 202.650i 0.213091i
\(952\) −171.473 135.000i −0.180119 0.141807i
\(953\) 954.000i 1.00105i −0.865722 0.500525i \(-0.833140\pi\)
0.865722 0.500525i \(-0.166860\pi\)
\(954\) −148.500 + 257.210i −0.155660 + 0.269612i
\(955\) 0 0
\(956\) 570.000 + 987.269i 0.596234 + 1.03271i
\(957\) −116.913 + 202.500i −0.122167 + 0.211599i
\(958\) −1028.84 −1.07394
\(959\) −528.000 415.692i −0.550574 0.433464i
\(960\) 0 0
\(961\) −407.000 + 704.945i −0.423517 + 0.733553i
\(962\) −207.846 360.000i −0.216056 0.374220i
\(963\) −241.621 + 139.500i −0.250905 + 0.144860i
\(964\) 1927.50 + 1112.84i 1.99948 + 1.15440i
\(965\) 0 0
\(966\) 0 0
\(967\) 751.000i 0.776629i 0.921527 + 0.388314i \(0.126943\pi\)
−0.921527 + 0.388314i \(0.873057\pi\)
\(968\) −270.200 156.000i −0.279132 0.161157i
\(969\) −162.000 + 93.5307i −0.167183 + 0.0965230i
\(970\) 0 0
\(971\) −247.500 142.894i −0.254892 0.147162i 0.367110 0.930177i \(-0.380347\pi\)
−0.622002 + 0.783016i \(0.713680\pi\)
\(972\) −77.9423 −0.0801875
\(973\) −1193.38 + 477.000i −1.22650 + 0.490236i
\(974\) 951.000 0.976386
\(975\) 0 0
\(976\) 858.000 495.367i 0.879098 0.507548i
\(977\) 15.5885 9.00000i 0.0159554 0.00921187i −0.492001 0.870595i \(-0.663734\pi\)
0.507957 + 0.861383i \(0.330401\pi\)
\(978\) 540.400 936.000i 0.552556 0.957055i
\(979\) 1091.19i 1.11460i
\(980\) 0 0
\(981\) 24.0000 0.0244648
\(982\) 70.1481 + 40.5000i 0.0714339 + 0.0412424i
\(983\) −493.634 855.000i −0.502171 0.869786i −0.999997 0.00250913i \(-0.999201\pi\)
0.497825 0.867277i \(-0.334132\pi\)
\(984\) 27.0000 + 46.7654i 0.0274390 + 0.0475258i
\(985\) 0 0
\(986\) 280.592i 0.284576i
\(987\) 0 0
\(988\) 720.000i 0.728745i
\(989\) 0 0
\(990\) 0 0
\(991\) −351.500 608.816i −0.354692 0.614345i 0.632373 0.774664i \(-0.282081\pi\)
−0.987065 + 0.160319i \(0.948748\pi\)
\(992\) −272.798 + 472.500i −0.274998 + 0.476310i
\(993\) 69.2820 0.0697704
\(994\) 252.000 1745.91i 0.253521 1.75645i
\(995\) 0 0
\(996\) −517.500 + 896.336i −0.519578 + 0.899936i
\(997\) −107.387 186.000i −0.107710 0.186560i 0.807132 0.590371i \(-0.201019\pi\)
−0.914842 + 0.403811i \(0.867685\pi\)
\(998\) −1158.74 + 669.000i −1.16106 + 0.670341i
\(999\) 45.0000 + 25.9808i 0.0450450 + 0.0260068i
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 525.3.s.e.124.2 4
5.2 odd 4 21.3.f.a.19.1 yes 2
5.3 odd 4 525.3.o.h.376.1 2
5.4 even 2 inner 525.3.s.e.124.1 4
7.3 odd 6 inner 525.3.s.e.199.1 4
15.2 even 4 63.3.m.d.19.1 2
20.7 even 4 336.3.bh.d.145.1 2
35.2 odd 12 147.3.d.c.97.1 2
35.3 even 12 525.3.o.h.451.1 2
35.12 even 12 147.3.d.c.97.2 2
35.17 even 12 21.3.f.a.10.1 2
35.24 odd 6 inner 525.3.s.e.199.2 4
35.27 even 4 147.3.f.a.19.1 2
35.32 odd 12 147.3.f.a.31.1 2
60.47 odd 4 1008.3.cg.a.145.1 2
105.2 even 12 441.3.d.a.244.2 2
105.17 odd 12 63.3.m.d.10.1 2
105.32 even 12 441.3.m.g.325.1 2
105.47 odd 12 441.3.d.a.244.1 2
105.62 odd 4 441.3.m.g.19.1 2
140.47 odd 12 2352.3.f.a.97.1 2
140.87 odd 12 336.3.bh.d.241.1 2
140.107 even 12 2352.3.f.a.97.2 2
420.227 even 12 1008.3.cg.a.577.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.f.a.10.1 2 35.17 even 12
21.3.f.a.19.1 yes 2 5.2 odd 4
63.3.m.d.10.1 2 105.17 odd 12
63.3.m.d.19.1 2 15.2 even 4
147.3.d.c.97.1 2 35.2 odd 12
147.3.d.c.97.2 2 35.12 even 12
147.3.f.a.19.1 2 35.27 even 4
147.3.f.a.31.1 2 35.32 odd 12
336.3.bh.d.145.1 2 20.7 even 4
336.3.bh.d.241.1 2 140.87 odd 12
441.3.d.a.244.1 2 105.47 odd 12
441.3.d.a.244.2 2 105.2 even 12
441.3.m.g.19.1 2 105.62 odd 4
441.3.m.g.325.1 2 105.32 even 12
525.3.o.h.376.1 2 5.3 odd 4
525.3.o.h.451.1 2 35.3 even 12
525.3.s.e.124.1 4 5.4 even 2 inner
525.3.s.e.124.2 4 1.1 even 1 trivial
525.3.s.e.199.1 4 7.3 odd 6 inner
525.3.s.e.199.2 4 35.24 odd 6 inner
1008.3.cg.a.145.1 2 60.47 odd 4
1008.3.cg.a.577.1 2 420.227 even 12
2352.3.f.a.97.1 2 140.47 odd 12
2352.3.f.a.97.2 2 140.107 even 12