Properties

Label 21.3.f.a.10.1
Level $21$
Weight $3$
Character 21.10
Analytic conductor $0.572$
Analytic rank $0$
Dimension $2$
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] = [21,3,Mod(10,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.10");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 21.f (of order \(6\), degree \(2\), 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: \(0.572208555157\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 21.10
Dual form 21.3.f.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.50000 + 4.33013i) q^{4} +(4.50000 - 2.59808i) q^{5} +5.19615i q^{6} +(6.50000 + 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-2.50000 + 4.33013i) q^{4} +(4.50000 - 2.59808i) q^{5} +5.19615i q^{6} +(6.50000 + 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-13.5000 - 7.79423i) q^{10} +(-7.50000 + 12.9904i) q^{11} +(7.50000 - 4.33013i) q^{12} -13.8564i q^{13} +(-3.00000 - 20.7846i) q^{14} -9.00000 q^{15} +(5.50000 + 9.52628i) q^{16} +(9.00000 + 5.19615i) q^{17} +(4.50000 - 7.79423i) q^{18} +(-9.00000 + 5.19615i) q^{19} +25.9808i q^{20} +(-7.50000 - 9.52628i) q^{21} +45.0000 q^{22} +(-4.50000 - 2.59808i) q^{24} +(1.00000 - 1.73205i) q^{25} +(-36.0000 + 20.7846i) q^{26} -5.19615i q^{27} +(-27.5000 + 21.6506i) q^{28} -9.00000 q^{29} +(13.5000 + 23.3827i) q^{30} +(-10.5000 - 6.06218i) q^{31} +(22.5000 - 38.9711i) q^{32} +(22.5000 - 12.9904i) q^{33} -31.1769i q^{34} +(36.0000 - 5.19615i) q^{35} -15.0000 q^{36} +(-5.00000 - 8.66025i) q^{37} +(27.0000 + 15.5885i) q^{38} +(-12.0000 + 20.7846i) q^{39} +(13.5000 - 7.79423i) q^{40} -10.3923i q^{41} +(-13.5000 + 33.7750i) q^{42} -74.0000 q^{43} +(-37.5000 - 64.9519i) q^{44} +(13.5000 + 7.79423i) q^{45} -19.0526i q^{48} +(35.5000 + 33.7750i) q^{49} -6.00000 q^{50} +(-9.00000 - 15.5885i) q^{51} +(60.0000 + 34.6410i) q^{52} +(-16.5000 + 28.5788i) q^{53} +(-13.5000 + 7.79423i) q^{54} +77.9423i q^{55} +(19.5000 + 7.79423i) q^{56} +18.0000 q^{57} +(13.5000 + 23.3827i) q^{58} +(13.5000 + 7.79423i) q^{59} +(22.5000 - 38.9711i) q^{60} +(78.0000 - 45.0333i) q^{61} +36.3731i q^{62} +(3.00000 + 20.7846i) q^{63} -91.0000 q^{64} +(-36.0000 - 62.3538i) q^{65} +(-67.5000 - 38.9711i) q^{66} +(38.0000 - 65.8179i) q^{67} +(-45.0000 + 25.9808i) q^{68} +(-67.5000 - 85.7365i) q^{70} +84.0000 q^{71} +(4.50000 + 7.79423i) q^{72} +(-54.0000 - 31.1769i) q^{73} +(-15.0000 + 25.9808i) q^{74} +(-3.00000 + 1.73205i) q^{75} -51.9615i q^{76} +(-82.5000 + 64.9519i) q^{77} +72.0000 q^{78} +(21.5000 + 37.2391i) q^{79} +(49.5000 + 28.5788i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-27.0000 + 15.5885i) q^{82} -119.512i q^{83} +(60.0000 - 8.66025i) q^{84} +54.0000 q^{85} +(111.000 + 192.258i) q^{86} +(13.5000 + 7.79423i) q^{87} +(-22.5000 + 38.9711i) q^{88} +(-63.0000 + 36.3731i) q^{89} -46.7654i q^{90} +(36.0000 - 90.0666i) q^{91} +(10.5000 + 18.1865i) q^{93} +(-27.0000 + 46.7654i) q^{95} +(-67.5000 + 38.9711i) q^{96} +185.329i q^{97} +(34.5000 - 142.894i) q^{98} -45.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 9 q^{5} + 13 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 9 q^{5} + 13 q^{7} + 6 q^{8} + 3 q^{9} - 27 q^{10} - 15 q^{11} + 15 q^{12} - 6 q^{14} - 18 q^{15} + 11 q^{16} + 18 q^{17} + 9 q^{18} - 18 q^{19} - 15 q^{21} + 90 q^{22} - 9 q^{24} + 2 q^{25} - 72 q^{26} - 55 q^{28} - 18 q^{29} + 27 q^{30} - 21 q^{31} + 45 q^{32} + 45 q^{33} + 72 q^{35} - 30 q^{36} - 10 q^{37} + 54 q^{38} - 24 q^{39} + 27 q^{40} - 27 q^{42} - 148 q^{43} - 75 q^{44} + 27 q^{45} + 71 q^{49} - 12 q^{50} - 18 q^{51} + 120 q^{52} - 33 q^{53} - 27 q^{54} + 39 q^{56} + 36 q^{57} + 27 q^{58} + 27 q^{59} + 45 q^{60} + 156 q^{61} + 6 q^{63} - 182 q^{64} - 72 q^{65} - 135 q^{66} + 76 q^{67} - 90 q^{68} - 135 q^{70} + 168 q^{71} + 9 q^{72} - 108 q^{73} - 30 q^{74} - 6 q^{75} - 165 q^{77} + 144 q^{78} + 43 q^{79} + 99 q^{80} - 9 q^{81} - 54 q^{82} + 120 q^{84} + 108 q^{85} + 222 q^{86} + 27 q^{87} - 45 q^{88} - 126 q^{89} + 72 q^{91} + 21 q^{93} - 54 q^{95} - 135 q^{96} + 69 q^{98} - 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 2.59808i −0.750000 1.29904i −0.947822 0.318800i \(-0.896720\pi\)
0.197822 0.980238i \(-0.436613\pi\)
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −2.50000 + 4.33013i −0.625000 + 1.08253i
\(5\) 4.50000 2.59808i 0.900000 0.519615i 0.0227998 0.999740i \(-0.492742\pi\)
0.877200 + 0.480125i \(0.159409\pi\)
\(6\) 5.19615i 0.866025i
\(7\) 6.50000 + 2.59808i 0.928571 + 0.371154i
\(8\) 3.00000 0.375000
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −13.5000 7.79423i −1.35000 0.779423i
\(11\) −7.50000 + 12.9904i −0.681818 + 1.18094i 0.292607 + 0.956233i \(0.405477\pi\)
−0.974425 + 0.224711i \(0.927856\pi\)
\(12\) 7.50000 4.33013i 0.625000 0.360844i
\(13\) 13.8564i 1.06588i −0.846154 0.532939i \(-0.821088\pi\)
0.846154 0.532939i \(-0.178912\pi\)
\(14\) −3.00000 20.7846i −0.214286 1.48461i
\(15\) −9.00000 −0.600000
\(16\) 5.50000 + 9.52628i 0.343750 + 0.595392i
\(17\) 9.00000 + 5.19615i 0.529412 + 0.305656i 0.740777 0.671751i \(-0.234458\pi\)
−0.211365 + 0.977407i \(0.567791\pi\)
\(18\) 4.50000 7.79423i 0.250000 0.433013i
\(19\) −9.00000 + 5.19615i −0.473684 + 0.273482i −0.717781 0.696269i \(-0.754842\pi\)
0.244096 + 0.969751i \(0.421509\pi\)
\(20\) 25.9808i 1.29904i
\(21\) −7.50000 9.52628i −0.357143 0.453632i
\(22\) 45.0000 2.04545
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −4.50000 2.59808i −0.187500 0.108253i
\(25\) 1.00000 1.73205i 0.0400000 0.0692820i
\(26\) −36.0000 + 20.7846i −1.38462 + 0.799408i
\(27\) 5.19615i 0.192450i
\(28\) −27.5000 + 21.6506i −0.982143 + 0.773237i
\(29\) −9.00000 −0.310345 −0.155172 0.987887i \(-0.549593\pi\)
−0.155172 + 0.987887i \(0.549593\pi\)
\(30\) 13.5000 + 23.3827i 0.450000 + 0.779423i
\(31\) −10.5000 6.06218i −0.338710 0.195554i 0.320992 0.947082i \(-0.395984\pi\)
−0.659701 + 0.751528i \(0.729317\pi\)
\(32\) 22.5000 38.9711i 0.703125 1.21785i
\(33\) 22.5000 12.9904i 0.681818 0.393648i
\(34\) 31.1769i 0.916968i
\(35\) 36.0000 5.19615i 1.02857 0.148461i
\(36\) −15.0000 −0.416667
\(37\) −5.00000 8.66025i −0.135135 0.234061i 0.790514 0.612444i \(-0.209814\pi\)
−0.925649 + 0.378383i \(0.876480\pi\)
\(38\) 27.0000 + 15.5885i 0.710526 + 0.410223i
\(39\) −12.0000 + 20.7846i −0.307692 + 0.532939i
\(40\) 13.5000 7.79423i 0.337500 0.194856i
\(41\) 10.3923i 0.253471i −0.991937 0.126735i \(-0.959550\pi\)
0.991937 0.126735i \(-0.0404499\pi\)
\(42\) −13.5000 + 33.7750i −0.321429 + 0.804166i
\(43\) −74.0000 −1.72093 −0.860465 0.509509i \(-0.829827\pi\)
−0.860465 + 0.509509i \(0.829827\pi\)
\(44\) −37.5000 64.9519i −0.852273 1.47618i
\(45\) 13.5000 + 7.79423i 0.300000 + 0.173205i
\(46\) 0 0
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 19.0526i 0.396928i
\(49\) 35.5000 + 33.7750i 0.724490 + 0.689286i
\(50\) −6.00000 −0.120000
\(51\) −9.00000 15.5885i −0.176471 0.305656i
\(52\) 60.0000 + 34.6410i 1.15385 + 0.666173i
\(53\) −16.5000 + 28.5788i −0.311321 + 0.539223i −0.978649 0.205541i \(-0.934105\pi\)
0.667328 + 0.744764i \(0.267438\pi\)
\(54\) −13.5000 + 7.79423i −0.250000 + 0.144338i
\(55\) 77.9423i 1.41713i
\(56\) 19.5000 + 7.79423i 0.348214 + 0.139183i
\(57\) 18.0000 0.315789
\(58\) 13.5000 + 23.3827i 0.232759 + 0.403150i
\(59\) 13.5000 + 7.79423i 0.228814 + 0.132106i 0.610025 0.792382i \(-0.291160\pi\)
−0.381211 + 0.924488i \(0.624493\pi\)
\(60\) 22.5000 38.9711i 0.375000 0.649519i
\(61\) 78.0000 45.0333i 1.27869 0.738251i 0.302081 0.953282i \(-0.402319\pi\)
0.976607 + 0.215031i \(0.0689853\pi\)
\(62\) 36.3731i 0.586662i
\(63\) 3.00000 + 20.7846i 0.0476190 + 0.329914i
\(64\) −91.0000 −1.42188
\(65\) −36.0000 62.3538i −0.553846 0.959290i
\(66\) −67.5000 38.9711i −1.02273 0.590472i
\(67\) 38.0000 65.8179i 0.567164 0.982357i −0.429681 0.902981i \(-0.641374\pi\)
0.996845 0.0793762i \(-0.0252928\pi\)
\(68\) −45.0000 + 25.9808i −0.661765 + 0.382070i
\(69\) 0 0
\(70\) −67.5000 85.7365i −0.964286 1.22481i
\(71\) 84.0000 1.18310 0.591549 0.806269i \(-0.298517\pi\)
0.591549 + 0.806269i \(0.298517\pi\)
\(72\) 4.50000 + 7.79423i 0.0625000 + 0.108253i
\(73\) −54.0000 31.1769i −0.739726 0.427081i 0.0822437 0.996612i \(-0.473791\pi\)
−0.821970 + 0.569531i \(0.807125\pi\)
\(74\) −15.0000 + 25.9808i −0.202703 + 0.351091i
\(75\) −3.00000 + 1.73205i −0.0400000 + 0.0230940i
\(76\) 51.9615i 0.683704i
\(77\) −82.5000 + 64.9519i −1.07143 + 0.843531i
\(78\) 72.0000 0.923077
\(79\) 21.5000 + 37.2391i 0.272152 + 0.471381i 0.969413 0.245437i \(-0.0789313\pi\)
−0.697261 + 0.716818i \(0.745598\pi\)
\(80\) 49.5000 + 28.5788i 0.618750 + 0.357235i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −27.0000 + 15.5885i −0.329268 + 0.190103i
\(83\) 119.512i 1.43990i −0.694027 0.719949i \(-0.744165\pi\)
0.694027 0.719949i \(-0.255835\pi\)
\(84\) 60.0000 8.66025i 0.714286 0.103098i
\(85\) 54.0000 0.635294
\(86\) 111.000 + 192.258i 1.29070 + 2.23555i
\(87\) 13.5000 + 7.79423i 0.155172 + 0.0895888i
\(88\) −22.5000 + 38.9711i −0.255682 + 0.442854i
\(89\) −63.0000 + 36.3731i −0.707865 + 0.408686i −0.810270 0.586057i \(-0.800680\pi\)
0.102405 + 0.994743i \(0.467346\pi\)
\(90\) 46.7654i 0.519615i
\(91\) 36.0000 90.0666i 0.395604 0.989743i
\(92\) 0 0
\(93\) 10.5000 + 18.1865i 0.112903 + 0.195554i
\(94\) 0 0
\(95\) −27.0000 + 46.7654i −0.284211 + 0.492267i
\(96\) −67.5000 + 38.9711i −0.703125 + 0.405949i
\(97\) 185.329i 1.91061i 0.295618 + 0.955306i \(0.404475\pi\)
−0.295618 + 0.955306i \(0.595525\pi\)
\(98\) 34.5000 142.894i 0.352041 1.45810i
\(99\) −45.0000 −0.454545
\(100\) 5.00000 + 8.66025i 0.0500000 + 0.0866025i
\(101\) −126.000 72.7461i −1.24752 0.720259i −0.276910 0.960896i \(-0.589310\pi\)
−0.970615 + 0.240637i \(0.922644\pi\)
\(102\) −27.0000 + 46.7654i −0.264706 + 0.458484i
\(103\) −60.0000 + 34.6410i −0.582524 + 0.336321i −0.762136 0.647417i \(-0.775849\pi\)
0.179612 + 0.983738i \(0.442516\pi\)
\(104\) 41.5692i 0.399704i
\(105\) −58.5000 23.3827i −0.557143 0.222692i
\(106\) 99.0000 0.933962
\(107\) −46.5000 80.5404i −0.434579 0.752714i 0.562682 0.826674i \(-0.309770\pi\)
−0.997261 + 0.0739599i \(0.976436\pi\)
\(108\) 22.5000 + 12.9904i 0.208333 + 0.120281i
\(109\) 4.00000 6.92820i 0.0366972 0.0635615i −0.847093 0.531444i \(-0.821650\pi\)
0.883791 + 0.467882i \(0.154983\pi\)
\(110\) 202.500 116.913i 1.84091 1.06285i
\(111\) 17.3205i 0.156041i
\(112\) 11.0000 + 76.2102i 0.0982143 + 0.680449i
\(113\) 42.0000 0.371681 0.185841 0.982580i \(-0.440499\pi\)
0.185841 + 0.982580i \(0.440499\pi\)
\(114\) −27.0000 46.7654i −0.236842 0.410223i
\(115\) 0 0
\(116\) 22.5000 38.9711i 0.193966 0.335958i
\(117\) 36.0000 20.7846i 0.307692 0.177646i
\(118\) 46.7654i 0.396317i
\(119\) 45.0000 + 57.1577i 0.378151 + 0.480317i
\(120\) −27.0000 −0.225000
\(121\) −52.0000 90.0666i −0.429752 0.744352i
\(122\) −234.000 135.100i −1.91803 1.10738i
\(123\) −9.00000 + 15.5885i −0.0731707 + 0.126735i
\(124\) 52.5000 30.3109i 0.423387 0.244443i
\(125\) 119.512i 0.956092i
\(126\) 49.5000 38.9711i 0.392857 0.309295i
\(127\) 35.0000 0.275591 0.137795 0.990461i \(-0.455998\pi\)
0.137795 + 0.990461i \(0.455998\pi\)
\(128\) 46.5000 + 80.5404i 0.363281 + 0.629222i
\(129\) 111.000 + 64.0859i 0.860465 + 0.496790i
\(130\) −108.000 + 187.061i −0.830769 + 1.43893i
\(131\) 148.500 85.7365i 1.13359 0.654477i 0.188753 0.982025i \(-0.439555\pi\)
0.944835 + 0.327547i \(0.106222\pi\)
\(132\) 129.904i 0.984120i
\(133\) −72.0000 + 10.3923i −0.541353 + 0.0781376i
\(134\) −228.000 −1.70149
\(135\) −13.5000 23.3827i −0.100000 0.173205i
\(136\) 27.0000 + 15.5885i 0.198529 + 0.114621i
\(137\) 48.0000 83.1384i 0.350365 0.606850i −0.635948 0.771732i \(-0.719391\pi\)
0.986313 + 0.164882i \(0.0527242\pi\)
\(138\) 0 0
\(139\) 183.597i 1.32084i −0.750894 0.660422i \(-0.770377\pi\)
0.750894 0.660422i \(-0.229623\pi\)
\(140\) −67.5000 + 168.875i −0.482143 + 1.20625i
\(141\) 0 0
\(142\) −126.000 218.238i −0.887324 1.53689i
\(143\) 180.000 + 103.923i 1.25874 + 0.726735i
\(144\) −16.5000 + 28.5788i −0.114583 + 0.198464i
\(145\) −40.5000 + 23.3827i −0.279310 + 0.161260i
\(146\) 187.061i 1.28124i
\(147\) −24.0000 81.4064i −0.163265 0.553785i
\(148\) 50.0000 0.337838
\(149\) 93.0000 + 161.081i 0.624161 + 1.08108i 0.988702 + 0.149892i \(0.0478924\pi\)
−0.364541 + 0.931187i \(0.618774\pi\)
\(150\) 9.00000 + 5.19615i 0.0600000 + 0.0346410i
\(151\) −39.5000 + 68.4160i −0.261589 + 0.453086i −0.966664 0.256047i \(-0.917580\pi\)
0.705075 + 0.709133i \(0.250913\pi\)
\(152\) −27.0000 + 15.5885i −0.177632 + 0.102556i
\(153\) 31.1769i 0.203771i
\(154\) 292.500 + 116.913i 1.89935 + 0.759178i
\(155\) −63.0000 −0.406452
\(156\) −60.0000 103.923i −0.384615 0.666173i
\(157\) −18.0000 10.3923i −0.114650 0.0661930i 0.441579 0.897223i \(-0.354419\pi\)
−0.556228 + 0.831030i \(0.687752\pi\)
\(158\) 64.5000 111.717i 0.408228 0.707071i
\(159\) 49.5000 28.5788i 0.311321 0.179741i
\(160\) 233.827i 1.46142i
\(161\) 0 0
\(162\) 27.0000 0.166667
\(163\) 104.000 + 180.133i 0.638037 + 1.10511i 0.985863 + 0.167553i \(0.0535866\pi\)
−0.347826 + 0.937559i \(0.613080\pi\)
\(164\) 45.0000 + 25.9808i 0.274390 + 0.158419i
\(165\) 67.5000 116.913i 0.409091 0.708566i
\(166\) −310.500 + 179.267i −1.87048 + 1.07992i
\(167\) 249.415i 1.49350i −0.665102 0.746752i \(-0.731612\pi\)
0.665102 0.746752i \(-0.268388\pi\)
\(168\) −22.5000 28.5788i −0.133929 0.170112i
\(169\) −23.0000 −0.136095
\(170\) −81.0000 140.296i −0.476471 0.825271i
\(171\) −27.0000 15.5885i −0.157895 0.0911606i
\(172\) 185.000 320.429i 1.07558 1.86296i
\(173\) −198.000 + 114.315i −1.14451 + 0.660782i −0.947543 0.319628i \(-0.896442\pi\)
−0.196966 + 0.980410i \(0.563109\pi\)
\(174\) 46.7654i 0.268767i
\(175\) 11.0000 8.66025i 0.0628571 0.0494872i
\(176\) −165.000 −0.937500
\(177\) −13.5000 23.3827i −0.0762712 0.132106i
\(178\) 189.000 + 109.119i 1.06180 + 0.613029i
\(179\) −45.0000 + 77.9423i −0.251397 + 0.435432i −0.963911 0.266226i \(-0.914223\pi\)
0.712514 + 0.701658i \(0.247557\pi\)
\(180\) −67.5000 + 38.9711i −0.375000 + 0.216506i
\(181\) 10.3923i 0.0574160i −0.999588 0.0287080i \(-0.990861\pi\)
0.999588 0.0287080i \(-0.00913930\pi\)
\(182\) −288.000 + 41.5692i −1.58242 + 0.228402i
\(183\) −156.000 −0.852459
\(184\) 0 0
\(185\) −45.0000 25.9808i −0.243243 0.140437i
\(186\) 31.5000 54.5596i 0.169355 0.293331i
\(187\) −135.000 + 77.9423i −0.721925 + 0.416804i
\(188\) 0 0
\(189\) 13.5000 33.7750i 0.0714286 0.178704i
\(190\) 162.000 0.852632
\(191\) 156.000 + 270.200i 0.816754 + 1.41466i 0.908062 + 0.418837i \(0.137562\pi\)
−0.0913077 + 0.995823i \(0.529105\pi\)
\(192\) 136.500 + 78.8083i 0.710938 + 0.410460i
\(193\) 92.5000 160.215i 0.479275 0.830128i −0.520443 0.853896i \(-0.674233\pi\)
0.999717 + 0.0237685i \(0.00756646\pi\)
\(194\) 481.500 277.994i 2.48196 1.43296i
\(195\) 124.708i 0.639526i
\(196\) −235.000 + 69.2820i −1.19898 + 0.353480i
\(197\) 330.000 1.67513 0.837563 0.546340i \(-0.183979\pi\)
0.837563 + 0.546340i \(0.183979\pi\)
\(198\) 67.5000 + 116.913i 0.340909 + 0.590472i
\(199\) 6.00000 + 3.46410i 0.0301508 + 0.0174075i 0.515000 0.857190i \(-0.327792\pi\)
−0.484849 + 0.874598i \(0.661125\pi\)
\(200\) 3.00000 5.19615i 0.0150000 0.0259808i
\(201\) −114.000 + 65.8179i −0.567164 + 0.327452i
\(202\) 436.477i 2.16078i
\(203\) −58.5000 23.3827i −0.288177 0.115186i
\(204\) 90.0000 0.441176
\(205\) −27.0000 46.7654i −0.131707 0.228124i
\(206\) 180.000 + 103.923i 0.873786 + 0.504481i
\(207\) 0 0
\(208\) 132.000 76.2102i 0.634615 0.366395i
\(209\) 155.885i 0.745859i
\(210\) 27.0000 + 187.061i 0.128571 + 0.890769i
\(211\) −248.000 −1.17536 −0.587678 0.809095i \(-0.699958\pi\)
−0.587678 + 0.809095i \(0.699958\pi\)
\(212\) −82.5000 142.894i −0.389151 0.674029i
\(213\) −126.000 72.7461i −0.591549 0.341531i
\(214\) −139.500 + 241.621i −0.651869 + 1.12907i
\(215\) −333.000 + 192.258i −1.54884 + 0.894222i
\(216\) 15.5885i 0.0721688i
\(217\) −52.5000 66.6840i −0.241935 0.307299i
\(218\) −24.0000 −0.110092
\(219\) 54.0000 + 93.5307i 0.246575 + 0.427081i
\(220\) −337.500 194.856i −1.53409 0.885708i
\(221\) 72.0000 124.708i 0.325792 0.564288i
\(222\) 45.0000 25.9808i 0.202703 0.117030i
\(223\) 192.258i 0.862142i −0.902318 0.431071i \(-0.858136\pi\)
0.902318 0.431071i \(-0.141864\pi\)
\(224\) 247.500 194.856i 1.10491 0.869892i
\(225\) 6.00000 0.0266667
\(226\) −63.0000 109.119i −0.278761 0.482828i
\(227\) −76.5000 44.1673i −0.337004 0.194570i 0.321942 0.946759i \(-0.395664\pi\)
−0.658947 + 0.752190i \(0.728998\pi\)
\(228\) −45.0000 + 77.9423i −0.197368 + 0.341852i
\(229\) 285.000 164.545i 1.24454 0.718536i 0.274526 0.961580i \(-0.411479\pi\)
0.970015 + 0.243043i \(0.0781457\pi\)
\(230\) 0 0
\(231\) 180.000 25.9808i 0.779221 0.112471i
\(232\) −27.0000 −0.116379
\(233\) −135.000 233.827i −0.579399 1.00355i −0.995548 0.0942524i \(-0.969954\pi\)
0.416149 0.909296i \(-0.363379\pi\)
\(234\) −108.000 62.3538i −0.461538 0.266469i
\(235\) 0 0
\(236\) −67.5000 + 38.9711i −0.286017 + 0.165132i
\(237\) 74.4782i 0.314254i
\(238\) 81.0000 202.650i 0.340336 0.851470i
\(239\) −228.000 −0.953975 −0.476987 0.878910i \(-0.658271\pi\)
−0.476987 + 0.878910i \(0.658271\pi\)
\(240\) −49.5000 85.7365i −0.206250 0.357235i
\(241\) 385.500 + 222.569i 1.59959 + 0.923521i 0.991567 + 0.129598i \(0.0413687\pi\)
0.608018 + 0.793923i \(0.291965\pi\)
\(242\) −156.000 + 270.200i −0.644628 + 1.11653i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 450.333i 1.84563i
\(245\) 247.500 + 59.7558i 1.01020 + 0.243901i
\(246\) 54.0000 0.219512
\(247\) 72.0000 + 124.708i 0.291498 + 0.504889i
\(248\) −31.5000 18.1865i −0.127016 0.0733328i
\(249\) −103.500 + 179.267i −0.415663 + 0.719949i
\(250\) 310.500 179.267i 1.24200 0.717069i
\(251\) 5.19615i 0.0207018i −0.999946 0.0103509i \(-0.996705\pi\)
0.999946 0.0103509i \(-0.00329485\pi\)
\(252\) −97.5000 38.9711i −0.386905 0.154647i
\(253\) 0 0
\(254\) −52.5000 90.9327i −0.206693 0.358003i
\(255\) −81.0000 46.7654i −0.317647 0.183394i
\(256\) −42.5000 + 73.6122i −0.166016 + 0.287547i
\(257\) 99.0000 57.1577i 0.385214 0.222403i −0.294870 0.955537i \(-0.595276\pi\)
0.680084 + 0.733134i \(0.261943\pi\)
\(258\) 384.515i 1.49037i
\(259\) −10.0000 69.2820i −0.0386100 0.267498i
\(260\) 360.000 1.38462
\(261\) −13.5000 23.3827i −0.0517241 0.0895888i
\(262\) −445.500 257.210i −1.70038 0.981716i
\(263\) −93.0000 + 161.081i −0.353612 + 0.612474i −0.986879 0.161459i \(-0.948380\pi\)
0.633267 + 0.773933i \(0.281713\pi\)
\(264\) 67.5000 38.9711i 0.255682 0.147618i
\(265\) 171.473i 0.647068i
\(266\) 135.000 + 171.473i 0.507519 + 0.644635i
\(267\) 126.000 0.471910
\(268\) 190.000 + 329.090i 0.708955 + 1.22795i
\(269\) −292.500 168.875i −1.08736 0.627788i −0.154488 0.987995i \(-0.549373\pi\)
−0.932873 + 0.360207i \(0.882706\pi\)
\(270\) −40.5000 + 70.1481i −0.150000 + 0.259808i
\(271\) 79.5000 45.8993i 0.293358 0.169370i −0.346097 0.938199i \(-0.612493\pi\)
0.639455 + 0.768828i \(0.279160\pi\)
\(272\) 114.315i 0.420277i
\(273\) −132.000 + 103.923i −0.483516 + 0.380671i
\(274\) −288.000 −1.05109
\(275\) 15.0000 + 25.9808i 0.0545455 + 0.0944755i
\(276\) 0 0
\(277\) −190.000 + 329.090i −0.685921 + 1.18805i 0.287226 + 0.957863i \(0.407267\pi\)
−0.973147 + 0.230186i \(0.926066\pi\)
\(278\) −477.000 + 275.396i −1.71583 + 0.990633i
\(279\) 36.3731i 0.130369i
\(280\) 108.000 15.5885i 0.385714 0.0556731i
\(281\) 300.000 1.06762 0.533808 0.845606i \(-0.320761\pi\)
0.533808 + 0.845606i \(0.320761\pi\)
\(282\) 0 0
\(283\) 177.000 + 102.191i 0.625442 + 0.361099i 0.778985 0.627043i \(-0.215735\pi\)
−0.153543 + 0.988142i \(0.549068\pi\)
\(284\) −210.000 + 363.731i −0.739437 + 1.28074i
\(285\) 81.0000 46.7654i 0.284211 0.164089i
\(286\) 623.538i 2.18020i
\(287\) 27.0000 67.5500i 0.0940767 0.235366i
\(288\) 135.000 0.468750
\(289\) −90.5000 156.751i −0.313149 0.542390i
\(290\) 121.500 + 70.1481i 0.418966 + 0.241890i
\(291\) 160.500 277.994i 0.551546 0.955306i
\(292\) 270.000 155.885i 0.924658 0.533851i
\(293\) 545.596i 1.86210i 0.364889 + 0.931051i \(0.381107\pi\)
−0.364889 + 0.931051i \(0.618893\pi\)
\(294\) −175.500 + 184.463i −0.596939 + 0.627427i
\(295\) 81.0000 0.274576
\(296\) −15.0000 25.9808i −0.0506757 0.0877728i
\(297\) 67.5000 + 38.9711i 0.227273 + 0.131216i
\(298\) 279.000 483.242i 0.936242 1.62162i
\(299\) 0 0
\(300\) 17.3205i 0.0577350i
\(301\) −481.000 192.258i −1.59801 0.638730i
\(302\) 237.000 0.784768
\(303\) 126.000 + 218.238i 0.415842 + 0.720259i
\(304\) −99.0000 57.1577i −0.325658 0.188019i
\(305\) 234.000 405.300i 0.767213 1.32885i
\(306\) 81.0000 46.7654i 0.264706 0.152828i
\(307\) 173.205i 0.564186i 0.959387 + 0.282093i \(0.0910287\pi\)
−0.959387 + 0.282093i \(0.908971\pi\)
\(308\) −75.0000 519.615i −0.243506 1.68706i
\(309\) 120.000 0.388350
\(310\) 94.5000 + 163.679i 0.304839 + 0.527996i
\(311\) −153.000 88.3346i −0.491961 0.284034i 0.233426 0.972374i \(-0.425006\pi\)
−0.725388 + 0.688340i \(0.758340\pi\)
\(312\) −36.0000 + 62.3538i −0.115385 + 0.199852i
\(313\) −184.500 + 106.521i −0.589457 + 0.340323i −0.764883 0.644170i \(-0.777203\pi\)
0.175426 + 0.984493i \(0.443870\pi\)
\(314\) 62.3538i 0.198579i
\(315\) 67.5000 + 85.7365i 0.214286 + 0.272179i
\(316\) −215.000 −0.680380
\(317\) −58.5000 101.325i −0.184543 0.319637i 0.758880 0.651231i \(-0.225747\pi\)
−0.943422 + 0.331594i \(0.892414\pi\)
\(318\) −148.500 85.7365i −0.466981 0.269612i
\(319\) 67.5000 116.913i 0.211599 0.366500i
\(320\) −409.500 + 236.425i −1.27969 + 0.738828i
\(321\) 161.081i 0.501809i
\(322\) 0 0
\(323\) −108.000 −0.334365
\(324\) −22.5000 38.9711i −0.0694444 0.120281i
\(325\) −24.0000 13.8564i −0.0738462 0.0426351i
\(326\) 312.000 540.400i 0.957055 1.65767i
\(327\) −12.0000 + 6.92820i −0.0366972 + 0.0211872i
\(328\) 31.1769i 0.0950516i
\(329\) 0 0
\(330\) −405.000 −1.22727
\(331\) −20.0000 34.6410i −0.0604230 0.104656i 0.834232 0.551414i \(-0.185912\pi\)
−0.894655 + 0.446759i \(0.852578\pi\)
\(332\) 517.500 + 298.779i 1.55873 + 0.899936i
\(333\) 15.0000 25.9808i 0.0450450 0.0780203i
\(334\) −648.000 + 374.123i −1.94012 + 1.12013i
\(335\) 394.908i 1.17883i
\(336\) 49.5000 123.842i 0.147321 0.368576i
\(337\) 91.0000 0.270030 0.135015 0.990844i \(-0.456892\pi\)
0.135015 + 0.990844i \(0.456892\pi\)
\(338\) 34.5000 + 59.7558i 0.102071 + 0.176792i
\(339\) −63.0000 36.3731i −0.185841 0.107295i
\(340\) −135.000 + 233.827i −0.397059 + 0.687726i
\(341\) 157.500 90.9327i 0.461877 0.266665i
\(342\) 93.5307i 0.273482i
\(343\) 143.000 + 311.769i 0.416910 + 0.908948i
\(344\) −222.000 −0.645349
\(345\) 0 0
\(346\) 594.000 + 342.946i 1.71676 + 0.991174i
\(347\) −105.000 + 181.865i −0.302594 + 0.524108i −0.976723 0.214506i \(-0.931186\pi\)
0.674129 + 0.738614i \(0.264519\pi\)
\(348\) −67.5000 + 38.9711i −0.193966 + 0.111986i
\(349\) 304.841i 0.873470i −0.899590 0.436735i \(-0.856135\pi\)
0.899590 0.436735i \(-0.143865\pi\)
\(350\) −39.0000 15.5885i −0.111429 0.0445384i
\(351\) −72.0000 −0.205128
\(352\) 337.500 + 584.567i 0.958807 + 1.66070i
\(353\) 342.000 + 197.454i 0.968839 + 0.559359i 0.898882 0.438191i \(-0.144381\pi\)
0.0699566 + 0.997550i \(0.477714\pi\)
\(354\) −40.5000 + 70.1481i −0.114407 + 0.198158i
\(355\) 378.000 218.238i 1.06479 0.614756i
\(356\) 363.731i 1.02172i
\(357\) −18.0000 124.708i −0.0504202 0.349321i
\(358\) 270.000 0.754190
\(359\) −246.000 426.084i −0.685237 1.18686i −0.973362 0.229272i \(-0.926365\pi\)
0.288126 0.957593i \(-0.406968\pi\)
\(360\) 40.5000 + 23.3827i 0.112500 + 0.0649519i
\(361\) −126.500 + 219.104i −0.350416 + 0.606937i
\(362\) −27.0000 + 15.5885i −0.0745856 + 0.0430620i
\(363\) 180.133i 0.496235i
\(364\) 300.000 + 381.051i 0.824176 + 1.04684i
\(365\) −324.000 −0.887671
\(366\) 234.000 + 405.300i 0.639344 + 1.10738i
\(367\) −283.500 163.679i −0.772480 0.445991i 0.0612789 0.998121i \(-0.480482\pi\)
−0.833758 + 0.552129i \(0.813815\pi\)
\(368\) 0 0
\(369\) 27.0000 15.5885i 0.0731707 0.0422451i
\(370\) 155.885i 0.421310i
\(371\) −181.500 + 142.894i −0.489218 + 0.385160i
\(372\) −105.000 −0.282258
\(373\) −85.0000 147.224i −0.227882 0.394703i 0.729298 0.684196i \(-0.239847\pi\)
−0.957180 + 0.289493i \(0.906513\pi\)
\(374\) 405.000 + 233.827i 1.08289 + 0.625206i
\(375\) 103.500 179.267i 0.276000 0.478046i
\(376\) 0 0
\(377\) 124.708i 0.330790i
\(378\) −108.000 + 15.5885i −0.285714 + 0.0412393i
\(379\) 82.0000 0.216359 0.108179 0.994131i \(-0.465498\pi\)
0.108179 + 0.994131i \(0.465498\pi\)
\(380\) −135.000 233.827i −0.355263 0.615334i
\(381\) −52.5000 30.3109i −0.137795 0.0795561i
\(382\) 468.000 810.600i 1.22513 2.12199i
\(383\) 189.000 109.119i 0.493473 0.284907i −0.232541 0.972587i \(-0.574704\pi\)
0.726014 + 0.687680i \(0.241371\pi\)
\(384\) 161.081i 0.419481i
\(385\) −202.500 + 506.625i −0.525974 + 1.31591i
\(386\) −555.000 −1.43782
\(387\) −111.000 192.258i −0.286822 0.496790i
\(388\) −802.500 463.324i −2.06830 1.19413i
\(389\) −153.000 + 265.004i −0.393316 + 0.681244i −0.992885 0.119080i \(-0.962006\pi\)
0.599568 + 0.800323i \(0.295339\pi\)
\(390\) 324.000 187.061i 0.830769 0.479645i
\(391\) 0 0
\(392\) 106.500 + 101.325i 0.271684 + 0.258482i
\(393\) −297.000 −0.755725
\(394\) −495.000 857.365i −1.25635 2.17605i
\(395\) 193.500 + 111.717i 0.489873 + 0.282829i
\(396\) 112.500 194.856i 0.284091 0.492060i
\(397\) −222.000 + 128.172i −0.559194 + 0.322851i −0.752822 0.658224i \(-0.771308\pi\)
0.193628 + 0.981075i \(0.437975\pi\)
\(398\) 20.7846i 0.0522226i
\(399\) 117.000 + 46.7654i 0.293233 + 0.117206i
\(400\) 22.0000 0.0550000
\(401\) −66.0000 114.315i −0.164589 0.285076i 0.771921 0.635719i \(-0.219296\pi\)
−0.936509 + 0.350643i \(0.885963\pi\)
\(402\) 342.000 + 197.454i 0.850746 + 0.491179i
\(403\) −84.0000 + 145.492i −0.208437 + 0.361023i
\(404\) 630.000 363.731i 1.55941 0.900323i
\(405\) 46.7654i 0.115470i
\(406\) 27.0000 + 187.061i 0.0665025 + 0.460743i
\(407\) 150.000 0.368550
\(408\) −27.0000 46.7654i −0.0661765 0.114621i
\(409\) −313.500 180.999i −0.766504 0.442541i 0.0651223 0.997877i \(-0.479256\pi\)
−0.831626 + 0.555336i \(0.812590\pi\)
\(410\) −81.0000 + 140.296i −0.197561 + 0.342186i
\(411\) −144.000 + 83.1384i −0.350365 + 0.202283i
\(412\) 346.410i 0.840801i
\(413\) 67.5000 + 85.7365i 0.163438 + 0.207594i
\(414\) 0 0
\(415\) −310.500 537.802i −0.748193 1.29591i
\(416\) −540.000 311.769i −1.29808 0.749445i
\(417\) −159.000 + 275.396i −0.381295 + 0.660422i
\(418\) −405.000 + 233.827i −0.968900 + 0.559394i
\(419\) 644.323i 1.53776i 0.639391 + 0.768882i \(0.279187\pi\)
−0.639391 + 0.768882i \(0.720813\pi\)
\(420\) 247.500 194.856i 0.589286 0.463942i
\(421\) 752.000 1.78622 0.893112 0.449835i \(-0.148517\pi\)
0.893112 + 0.449835i \(0.148517\pi\)
\(422\) 372.000 + 644.323i 0.881517 + 1.52683i
\(423\) 0 0
\(424\) −49.5000 + 85.7365i −0.116745 + 0.202209i
\(425\) 18.0000 10.3923i 0.0423529 0.0244525i
\(426\) 436.477i 1.02459i
\(427\) 624.000 90.0666i 1.46136 0.210929i
\(428\) 465.000 1.08645
\(429\) −180.000 311.769i −0.419580 0.726735i
\(430\) 999.000 + 576.773i 2.32326 + 1.34133i
\(431\) −81.0000 + 140.296i −0.187935 + 0.325513i −0.944562 0.328334i \(-0.893513\pi\)
0.756627 + 0.653847i \(0.226846\pi\)
\(432\) 49.5000 28.5788i 0.114583 0.0661547i
\(433\) 339.482i 0.784023i −0.919960 0.392011i \(-0.871779\pi\)
0.919960 0.392011i \(-0.128221\pi\)
\(434\) −94.5000 + 236.425i −0.217742 + 0.544758i
\(435\) 81.0000 0.186207
\(436\) 20.0000 + 34.6410i 0.0458716 + 0.0794519i
\(437\) 0 0
\(438\) 162.000 280.592i 0.369863 0.640622i
\(439\) 337.500 194.856i 0.768793 0.443863i −0.0636511 0.997972i \(-0.520274\pi\)
0.832444 + 0.554110i \(0.186941\pi\)
\(440\) 233.827i 0.531425i
\(441\) −34.5000 + 142.894i −0.0782313 + 0.324023i
\(442\) −432.000 −0.977376
\(443\) 148.500 + 257.210i 0.335214 + 0.580608i 0.983526 0.180767i \(-0.0578579\pi\)
−0.648312 + 0.761375i \(0.724525\pi\)
\(444\) −75.0000 43.3013i −0.168919 0.0975254i
\(445\) −189.000 + 327.358i −0.424719 + 0.735635i
\(446\) −499.500 + 288.386i −1.11996 + 0.646606i
\(447\) 322.161i 0.720719i
\(448\) −591.500 236.425i −1.32031 0.527734i
\(449\) −492.000 −1.09577 −0.547884 0.836554i \(-0.684567\pi\)
−0.547884 + 0.836554i \(0.684567\pi\)
\(450\) −9.00000 15.5885i −0.0200000 0.0346410i
\(451\) 135.000 + 77.9423i 0.299335 + 0.172821i
\(452\) −105.000 + 181.865i −0.232301 + 0.402357i
\(453\) 118.500 68.4160i 0.261589 0.151029i
\(454\) 265.004i 0.583709i
\(455\) −72.0000 498.831i −0.158242 1.09633i
\(456\) 54.0000 0.118421
\(457\) 221.500 + 383.649i 0.484683 + 0.839495i 0.999845 0.0175975i \(-0.00560174\pi\)
−0.515162 + 0.857093i \(0.672268\pi\)
\(458\) −855.000 493.634i −1.86681 1.07780i
\(459\) 27.0000 46.7654i 0.0588235 0.101885i
\(460\) 0 0
\(461\) 415.692i 0.901718i 0.892595 + 0.450859i \(0.148882\pi\)
−0.892595 + 0.450859i \(0.851118\pi\)
\(462\) −337.500 428.683i −0.730519 0.927884i
\(463\) −82.0000 −0.177106 −0.0885529 0.996071i \(-0.528224\pi\)
−0.0885529 + 0.996071i \(0.528224\pi\)
\(464\) −49.5000 85.7365i −0.106681 0.184777i
\(465\) 94.5000 + 54.5596i 0.203226 + 0.117332i
\(466\) −405.000 + 701.481i −0.869099 + 1.50532i
\(467\) 234.000 135.100i 0.501071 0.289293i −0.228085 0.973641i \(-0.573246\pi\)
0.729156 + 0.684348i \(0.239913\pi\)
\(468\) 207.846i 0.444116i
\(469\) 418.000 329.090i 0.891258 0.701684i
\(470\) 0 0
\(471\) 18.0000 + 31.1769i 0.0382166 + 0.0661930i
\(472\) 40.5000 + 23.3827i 0.0858051 + 0.0495396i
\(473\) 555.000 961.288i 1.17336 2.03232i
\(474\) −193.500 + 111.717i −0.408228 + 0.235690i
\(475\) 20.7846i 0.0437571i
\(476\) −360.000 + 51.9615i −0.756303 + 0.109163i
\(477\) −99.0000 −0.207547
\(478\) 342.000 + 592.361i 0.715481 + 1.23925i
\(479\) 297.000 + 171.473i 0.620042 + 0.357981i 0.776885 0.629642i \(-0.216798\pi\)
−0.156844 + 0.987623i \(0.550132\pi\)
\(480\) −202.500 + 350.740i −0.421875 + 0.730709i
\(481\) −120.000 + 69.2820i −0.249480 + 0.144037i
\(482\) 1335.41i 2.77056i
\(483\) 0 0
\(484\) 520.000 1.07438
\(485\) 481.500 + 833.982i 0.992784 + 1.71955i
\(486\) −40.5000 23.3827i −0.0833333 0.0481125i
\(487\) 158.500 274.530i 0.325462 0.563717i −0.656144 0.754636i \(-0.727814\pi\)
0.981606 + 0.190919i \(0.0611468\pi\)
\(488\) 234.000 135.100i 0.479508 0.276844i
\(489\) 360.267i 0.736741i
\(490\) −216.000 732.657i −0.440816 1.49522i
\(491\) 27.0000 0.0549898 0.0274949 0.999622i \(-0.491247\pi\)
0.0274949 + 0.999622i \(0.491247\pi\)
\(492\) −45.0000 77.9423i −0.0914634 0.158419i
\(493\) −81.0000 46.7654i −0.164300 0.0948588i
\(494\) 216.000 374.123i 0.437247 0.757334i
\(495\) −202.500 + 116.913i −0.409091 + 0.236189i
\(496\) 133.368i 0.268887i
\(497\) 546.000 + 218.238i 1.09859 + 0.439111i
\(498\) 621.000 1.24699
\(499\) 223.000 + 386.247i 0.446894 + 0.774043i 0.998182 0.0602721i \(-0.0191969\pi\)
−0.551288 + 0.834315i \(0.685864\pi\)
\(500\) −517.500 298.779i −1.03500 0.597558i
\(501\) −216.000 + 374.123i −0.431138 + 0.746752i
\(502\) −13.5000 + 7.79423i −0.0268924 + 0.0155264i
\(503\) 488.438i 0.971050i −0.874223 0.485525i \(-0.838628\pi\)
0.874223 0.485525i \(-0.161372\pi\)
\(504\) 9.00000 + 62.3538i 0.0178571 + 0.123718i
\(505\) −756.000 −1.49703
\(506\) 0 0
\(507\) 34.5000 + 19.9186i 0.0680473 + 0.0392871i
\(508\) −87.5000 + 151.554i −0.172244 + 0.298336i
\(509\) 85.5000 49.3634i 0.167976 0.0969812i −0.413655 0.910434i \(-0.635748\pi\)
0.581631 + 0.813453i \(0.302415\pi\)
\(510\) 280.592i 0.550181i
\(511\) −270.000 342.946i −0.528376 0.671127i
\(512\) 627.000 1.22461
\(513\) 27.0000 + 46.7654i 0.0526316 + 0.0911606i
\(514\) −297.000 171.473i −0.577821 0.333605i
\(515\) −180.000 + 311.769i −0.349515 + 0.605377i
\(516\) −555.000 + 320.429i −1.07558 + 0.620987i
\(517\) 0 0
\(518\) −165.000 + 129.904i −0.318533 + 0.250780i
\(519\) 396.000 0.763006
\(520\) −108.000 187.061i −0.207692 0.359734i
\(521\) −783.000 452.065i −1.50288 0.867688i −0.999994 0.00333410i \(-0.998939\pi\)
−0.502885 0.864354i \(-0.667728\pi\)
\(522\) −40.5000 + 70.1481i −0.0775862 + 0.134383i
\(523\) −606.000 + 349.874i −1.15870 + 0.668976i −0.950992 0.309215i \(-0.899934\pi\)
−0.207708 + 0.978191i \(0.566600\pi\)
\(524\) 857.365i 1.63619i
\(525\) −24.0000 + 3.46410i −0.0457143 + 0.00659829i
\(526\) 558.000 1.06084
\(527\) −63.0000 109.119i −0.119545 0.207057i
\(528\) 247.500 + 142.894i 0.468750 + 0.270633i
\(529\) 264.500 458.127i 0.500000 0.866025i
\(530\) 445.500 257.210i 0.840566 0.485301i
\(531\) 46.7654i 0.0880704i
\(532\) 135.000 337.750i 0.253759 0.634868i
\(533\) −144.000 −0.270169
\(534\) −189.000 327.358i −0.353933 0.613029i
\(535\) −418.500 241.621i −0.782243 0.451628i
\(536\) 114.000 197.454i 0.212687 0.368384i
\(537\) 135.000 77.9423i 0.251397 0.145144i
\(538\) 1013.25i 1.88336i
\(539\) −705.000 + 207.846i −1.30798 + 0.385614i
\(540\) 135.000 0.250000
\(541\) −37.0000 64.0859i −0.0683919 0.118458i 0.829802 0.558058i \(-0.188453\pi\)
−0.898194 + 0.439600i \(0.855120\pi\)
\(542\) −238.500 137.698i −0.440037 0.254055i
\(543\) −9.00000 + 15.5885i −0.0165746 + 0.0287080i
\(544\) 405.000 233.827i 0.744485 0.429829i
\(545\) 41.5692i 0.0762738i
\(546\) 468.000 + 187.061i 0.857143 + 0.342603i
\(547\) −934.000 −1.70750 −0.853748 0.520687i \(-0.825676\pi\)
−0.853748 + 0.520687i \(0.825676\pi\)
\(548\) 240.000 + 415.692i 0.437956 + 0.758562i
\(549\) 234.000 + 135.100i 0.426230 + 0.246084i
\(550\) 45.0000 77.9423i 0.0818182 0.141713i
\(551\) 81.0000 46.7654i 0.147005 0.0848736i
\(552\) 0 0
\(553\) 43.0000 + 297.913i 0.0777577 + 0.538721i
\(554\) 1140.00 2.05776
\(555\) 45.0000 + 77.9423i 0.0810811 + 0.140437i
\(556\) 795.000 + 458.993i 1.42986 + 0.825528i
\(557\) −421.500 + 730.059i −0.756732 + 1.31070i 0.187776 + 0.982212i \(0.439872\pi\)
−0.944508 + 0.328487i \(0.893461\pi\)
\(558\) −94.5000 + 54.5596i −0.169355 + 0.0977771i
\(559\) 1025.37i 1.83430i
\(560\) 247.500 + 314.367i 0.441964 + 0.561370i
\(561\) 270.000 0.481283
\(562\) −450.000 779.423i −0.800712 1.38687i
\(563\) 823.500 + 475.448i 1.46270 + 0.844490i 0.999135 0.0415731i \(-0.0132369\pi\)
0.463564 + 0.886063i \(0.346570\pi\)
\(564\) 0 0
\(565\) 189.000 109.119i 0.334513 0.193131i
\(566\) 613.146i 1.08330i
\(567\) −49.5000 + 38.9711i −0.0873016 + 0.0687322i
\(568\) 252.000 0.443662
\(569\) −111.000 192.258i −0.195079 0.337887i 0.751847 0.659337i \(-0.229163\pi\)
−0.946926 + 0.321450i \(0.895830\pi\)
\(570\) −243.000 140.296i −0.426316 0.246134i
\(571\) −220.000 + 381.051i −0.385289 + 0.667340i −0.991809 0.127728i \(-0.959232\pi\)
0.606520 + 0.795068i \(0.292565\pi\)
\(572\) −900.000 + 519.615i −1.57343 + 0.908418i
\(573\) 540.400i 0.943106i
\(574\) −216.000 + 31.1769i −0.376307 + 0.0543152i
\(575\) 0 0
\(576\) −136.500 236.425i −0.236979 0.410460i
\(577\) 568.500 + 328.224i 0.985269 + 0.568845i 0.903857 0.427835i \(-0.140724\pi\)
0.0814120 + 0.996681i \(0.474057\pi\)
\(578\) −271.500 + 470.252i −0.469723 + 0.813584i
\(579\) −277.500 + 160.215i −0.479275 + 0.276709i
\(580\) 233.827i 0.403150i
\(581\) 310.500 776.825i 0.534423 1.33705i
\(582\) −963.000 −1.65464
\(583\) −247.500 428.683i −0.424528 0.735305i
\(584\) −162.000 93.5307i −0.277397 0.160155i
\(585\) 108.000 187.061i 0.184615 0.319763i
\(586\) 1417.50 818.394i 2.41894 1.39658i
\(587\) 1054.82i 1.79697i −0.439008 0.898483i \(-0.644670\pi\)
0.439008 0.898483i \(-0.355330\pi\)
\(588\) 412.500 + 99.5929i 0.701531 + 0.169376i
\(589\) 126.000 0.213922
\(590\) −121.500 210.444i −0.205932 0.356685i
\(591\) −495.000 285.788i −0.837563 0.483567i
\(592\) 55.0000 95.2628i 0.0929054 0.160917i
\(593\) 612.000 353.338i 1.03204 0.595849i 0.114472 0.993426i \(-0.463482\pi\)
0.917569 + 0.397578i \(0.130149\pi\)
\(594\) 233.827i 0.393648i
\(595\) 351.000 + 140.296i 0.589916 + 0.235792i
\(596\) −930.000 −1.56040
\(597\) −6.00000 10.3923i −0.0100503 0.0174075i
\(598\) 0 0
\(599\) −258.000 + 446.869i −0.430718 + 0.746025i −0.996935 0.0782307i \(-0.975073\pi\)
0.566217 + 0.824256i \(0.308406\pi\)
\(600\) −9.00000 + 5.19615i −0.0150000 + 0.00866025i
\(601\) 247.683i 0.412119i −0.978540 0.206059i \(-0.933936\pi\)
0.978540 0.206059i \(-0.0660640\pi\)
\(602\) 222.000 + 1538.06i 0.368771 + 2.55492i
\(603\) 228.000 0.378109
\(604\) −197.500 342.080i −0.326987 0.566358i
\(605\) −468.000 270.200i −0.773554 0.446611i
\(606\) 378.000 654.715i 0.623762 1.08039i
\(607\) −562.500 + 324.760i −0.926689 + 0.535024i −0.885763 0.464138i \(-0.846364\pi\)
−0.0409259 + 0.999162i \(0.513031\pi\)
\(608\) 467.654i 0.769167i
\(609\) 67.5000 + 85.7365i 0.110837 + 0.140782i
\(610\) −1404.00 −2.30164
\(611\) 0 0
\(612\) −135.000 77.9423i −0.220588 0.127357i
\(613\) 446.000 772.495i 0.727569 1.26019i −0.230338 0.973111i \(-0.573983\pi\)
0.957908 0.287076i \(-0.0926834\pi\)
\(614\) 450.000 259.808i 0.732899 0.423139i
\(615\) 93.5307i 0.152083i
\(616\) −247.500 + 194.856i −0.401786 + 0.316324i
\(617\) −1224.00 −1.98379 −0.991896 0.127050i \(-0.959449\pi\)
−0.991896 + 0.127050i \(0.959449\pi\)
\(618\) −180.000 311.769i −0.291262 0.504481i
\(619\) −348.000 200.918i −0.562197 0.324585i 0.191830 0.981428i \(-0.438558\pi\)
−0.754027 + 0.656844i \(0.771891\pi\)
\(620\) 157.500 272.798i 0.254032 0.439997i
\(621\) 0 0
\(622\) 530.008i 0.852102i
\(623\) −504.000 + 72.7461i −0.808989 + 0.116767i
\(624\) −264.000 −0.423077
\(625\) 335.500 + 581.103i 0.536800 + 0.929765i
\(626\) 553.500 + 319.563i 0.884185 + 0.510485i
\(627\) −135.000 + 233.827i −0.215311 + 0.372930i
\(628\) 90.0000 51.9615i 0.143312 0.0827413i
\(629\) 103.923i 0.165219i
\(630\) 121.500 303.975i 0.192857 0.482500i
\(631\) 1115.00 1.76704 0.883518 0.468397i \(-0.155168\pi\)
0.883518 + 0.468397i \(0.155168\pi\)
\(632\) 64.5000 + 111.717i 0.102057 + 0.176768i
\(633\) 372.000 + 214.774i 0.587678 + 0.339296i
\(634\) −175.500 + 303.975i −0.276814 + 0.479456i
\(635\) 157.500 90.9327i 0.248031 0.143201i
\(636\) 285.788i 0.449353i
\(637\) 468.000 491.902i 0.734694 0.772217i
\(638\) −405.000 −0.634796
\(639\) 126.000 + 218.238i 0.197183 + 0.341531i
\(640\) 418.500 + 241.621i 0.653906 + 0.377533i
\(641\) 192.000 332.554i 0.299532 0.518805i −0.676497 0.736445i \(-0.736503\pi\)
0.976029 + 0.217641i \(0.0698361\pi\)
\(642\) 418.500 241.621i 0.651869 0.376357i
\(643\) 6.92820i 0.0107748i −0.999985 0.00538741i \(-0.998285\pi\)
0.999985 0.00538741i \(-0.00171487\pi\)
\(644\) 0 0
\(645\) 666.000 1.03256
\(646\) 162.000 + 280.592i 0.250774 + 0.434353i
\(647\) 774.000 + 446.869i 1.19629 + 0.690679i 0.959726 0.280937i \(-0.0906452\pi\)
0.236564 + 0.971616i \(0.423979\pi\)
\(648\) −13.5000 + 23.3827i −0.0208333 + 0.0360844i
\(649\) −202.500 + 116.913i −0.312018 + 0.180144i
\(650\) 83.1384i 0.127905i
\(651\) 21.0000 + 145.492i 0.0322581 + 0.223490i
\(652\) −1040.00 −1.59509
\(653\) −37.5000 64.9519i −0.0574273 0.0994669i 0.835883 0.548908i \(-0.184956\pi\)
−0.893310 + 0.449441i \(0.851623\pi\)
\(654\) 36.0000 + 20.7846i 0.0550459 + 0.0317807i
\(655\) 445.500 771.629i 0.680153 1.17806i
\(656\) 99.0000 57.1577i 0.150915 0.0871306i
\(657\) 187.061i 0.284721i
\(658\) 0 0
\(659\) 642.000 0.974203 0.487102 0.873345i \(-0.338054\pi\)
0.487102 + 0.873345i \(0.338054\pi\)
\(660\) 337.500 + 584.567i 0.511364 + 0.885708i
\(661\) −243.000 140.296i −0.367625 0.212248i 0.304795 0.952418i \(-0.401412\pi\)
−0.672420 + 0.740170i \(0.734745\pi\)
\(662\) −60.0000 + 103.923i −0.0906344 + 0.156983i
\(663\) −216.000 + 124.708i −0.325792 + 0.188096i
\(664\) 358.535i 0.539962i
\(665\) −297.000 + 233.827i −0.446617 + 0.351619i
\(666\) −90.0000 −0.135135
\(667\) 0 0
\(668\) 1080.00 + 623.538i 1.61677 + 0.933441i
\(669\) −166.500 + 288.386i −0.248879 + 0.431071i
\(670\) −1026.00 + 592.361i −1.53134 + 0.884121i
\(671\) 1351.00i 2.01341i
\(672\) −540.000 + 77.9423i −0.803571 + 0.115986i
\(673\) 13.0000 0.0193165 0.00965825 0.999953i \(-0.496926\pi\)
0.00965825 + 0.999953i \(0.496926\pi\)
\(674\) −136.500 236.425i −0.202522 0.350779i
\(675\) −9.00000 5.19615i −0.0133333 0.00769800i
\(676\) 57.5000 99.5929i 0.0850592 0.147327i
\(677\) −1093.50 + 631.333i −1.61521 + 0.932544i −0.627079 + 0.778955i \(0.715750\pi\)
−0.988135 + 0.153589i \(0.950917\pi\)
\(678\) 218.238i 0.321886i
\(679\) −481.500 + 1204.64i −0.709131 + 1.77414i
\(680\) 162.000 0.238235
\(681\) 76.5000 + 132.502i 0.112335 + 0.194570i
\(682\) −472.500 272.798i −0.692815 0.399997i
\(683\) 484.500 839.179i 0.709370 1.22867i −0.255721 0.966751i \(-0.582313\pi\)
0.965091 0.261915i \(-0.0843540\pi\)
\(684\) 135.000 77.9423i 0.197368 0.113951i
\(685\) 498.831i 0.728220i
\(686\) 595.500 839.179i 0.868076 1.22329i
\(687\) −570.000 −0.829694
\(688\) −407.000 704.945i −0.591570 1.02463i
\(689\) 396.000 + 228.631i 0.574746 + 0.331830i
\(690\) 0 0
\(691\) −87.0000 + 50.2295i −0.125904 + 0.0726910i −0.561629 0.827389i \(-0.689825\pi\)
0.435725 + 0.900080i \(0.356492\pi\)
\(692\) 1143.15i 1.65196i
\(693\) −292.500 116.913i −0.422078 0.168706i
\(694\) 630.000 0.907781
\(695\) −477.000 826.188i −0.686331 1.18876i
\(696\) 40.5000 + 23.3827i 0.0581897 + 0.0335958i
\(697\) 54.0000 93.5307i 0.0774749 0.134190i
\(698\) −792.000 + 457.261i −1.13467 + 0.655102i
\(699\) 467.654i 0.669033i
\(700\) 10.0000 + 69.2820i 0.0142857 + 0.0989743i
\(701\) 597.000 0.851641 0.425820 0.904808i \(-0.359986\pi\)
0.425820 + 0.904808i \(0.359986\pi\)
\(702\) 108.000 + 187.061i 0.153846 + 0.266469i
\(703\) 90.0000 + 51.9615i 0.128023 + 0.0739140i
\(704\) 682.500 1182.12i 0.969460 1.67915i
\(705\) 0 0
\(706\) 1184.72i 1.67808i
\(707\) −630.000 800.207i −0.891089 1.13184i
\(708\) 135.000 0.190678
\(709\) 415.000 + 718.801i 0.585331 + 1.01382i 0.994834 + 0.101515i \(0.0323689\pi\)
−0.409503 + 0.912309i \(0.634298\pi\)
\(710\) −1134.00 654.715i −1.59718 0.922134i
\(711\) −64.5000 + 111.717i −0.0907173 + 0.157127i
\(712\) −189.000 + 109.119i −0.265449 + 0.153257i
\(713\) 0 0
\(714\) −297.000 + 233.827i −0.415966 + 0.327489i
\(715\) 1080.00 1.51049
\(716\) −225.000 389.711i −0.314246 0.544290i
\(717\) 342.000 + 197.454i 0.476987 + 0.275389i
\(718\) −738.000 + 1278.25i −1.02786 + 1.78030i
\(719\) 297.000 171.473i 0.413074 0.238488i −0.279036 0.960281i \(-0.590015\pi\)
0.692110 + 0.721792i \(0.256681\pi\)
\(720\) 171.473i 0.238157i
\(721\) −480.000 + 69.2820i −0.665742 + 0.0960916i
\(722\) 759.000 1.05125
\(723\) −385.500 667.706i −0.533195 0.923521i
\(724\) 45.0000 + 25.9808i 0.0621547 + 0.0358850i
\(725\) −9.00000 + 15.5885i −0.0124138 + 0.0215013i
\(726\) 468.000 270.200i 0.644628 0.372176i
\(727\) 50.2295i 0.0690914i 0.999403 + 0.0345457i \(0.0109984\pi\)
−0.999403 + 0.0345457i \(0.989002\pi\)
\(728\) 108.000 270.200i 0.148352 0.371154i
\(729\) −27.0000 −0.0370370
\(730\) 486.000 + 841.777i 0.665753 + 1.15312i
\(731\) −666.000 384.515i −0.911081 0.526013i
\(732\) 390.000 675.500i 0.532787 0.922814i
\(733\) −159.000 + 91.7987i −0.216917 + 0.125237i −0.604522 0.796589i \(-0.706636\pi\)
0.387605 + 0.921826i \(0.373302\pi\)
\(734\) 982.073i 1.33797i
\(735\) −319.500 303.975i −0.434694 0.413571i
\(736\) 0 0
\(737\) 570.000 + 987.269i 0.773406 + 1.33958i
\(738\) −81.0000 46.7654i −0.109756 0.0633677i
\(739\) 167.000 289.252i 0.225981 0.391411i −0.730632 0.682771i \(-0.760775\pi\)
0.956613 + 0.291361i \(0.0941079\pi\)
\(740\) 225.000 129.904i 0.304054 0.175546i
\(741\) 249.415i 0.336593i
\(742\) 643.500 + 257.210i 0.867251 + 0.346644i
\(743\) 84.0000 0.113055 0.0565276 0.998401i \(-0.481997\pi\)
0.0565276 + 0.998401i \(0.481997\pi\)
\(744\) 31.5000 + 54.5596i 0.0423387 + 0.0733328i
\(745\) 837.000 + 483.242i 1.12349 + 0.648647i
\(746\) −255.000 + 441.673i −0.341823 + 0.592055i
\(747\) 310.500 179.267i 0.415663 0.239983i
\(748\) 779.423i 1.04201i
\(749\) −93.0000 644.323i −0.124166 0.860244i
\(750\) −621.000 −0.828000
\(751\) 179.500 + 310.903i 0.239015 + 0.413986i 0.960432 0.278515i \(-0.0898423\pi\)
−0.721417 + 0.692501i \(0.756509\pi\)
\(752\) 0 0
\(753\) −4.50000 + 7.79423i −0.00597610 + 0.0103509i
\(754\) 324.000 187.061i 0.429708 0.248092i
\(755\) 410.496i 0.543703i
\(756\) 112.500 + 142.894i 0.148810 + 0.189013i
\(757\) −80.0000 −0.105680 −0.0528402 0.998603i \(-0.516827\pi\)
−0.0528402 + 0.998603i \(0.516827\pi\)
\(758\) −123.000 213.042i −0.162269 0.281058i
\(759\) 0 0
\(760\) −81.0000 + 140.296i −0.106579 + 0.184600i
\(761\) −702.000 + 405.300i −0.922470 + 0.532589i −0.884422 0.466687i \(-0.845447\pi\)
−0.0380481 + 0.999276i \(0.512114\pi\)
\(762\) 181.865i 0.238668i
\(763\) 44.0000 34.6410i 0.0576671 0.0454011i
\(764\) −1560.00 −2.04188
\(765\) 81.0000 + 140.296i 0.105882 + 0.183394i
\(766\) −567.000 327.358i −0.740209 0.427360i
\(767\) 108.000 187.061i 0.140808 0.243887i
\(768\) 127.500 73.6122i 0.166016 0.0958492i
\(769\) 774.227i 1.00680i −0.864054 0.503398i \(-0.832083\pi\)
0.864054 0.503398i \(-0.167917\pi\)
\(770\) 1620.00 233.827i 2.10390 0.303671i
\(771\) −198.000 −0.256809
\(772\) 462.500 + 801.073i 0.599093 + 1.03766i
\(773\) −630.000 363.731i −0.815006 0.470544i 0.0336850 0.999433i \(-0.489276\pi\)
−0.848691 + 0.528888i \(0.822609\pi\)
\(774\) −333.000 + 576.773i −0.430233 + 0.745185i
\(775\) −21.0000 + 12.1244i −0.0270968 + 0.0156443i
\(776\) 555.988i 0.716480i
\(777\) −45.0000 + 112.583i −0.0579151 + 0.144895i
\(778\) 918.000 1.17995
\(779\) 54.0000 + 93.5307i 0.0693196 + 0.120065i
\(780\) −540.000 311.769i −0.692308 0.399704i
\(781\) −630.000 + 1091.19i −0.806658 + 1.39717i
\(782\) 0 0
\(783\) 46.7654i 0.0597259i
\(784\) −126.500 + 523.945i −0.161352 + 0.668298i
\(785\) −108.000 −0.137580
\(786\) 445.500 + 771.629i 0.566794 + 0.981716i
\(787\) −1236.00 713.605i −1.57052 0.906741i −0.996105 0.0881773i \(-0.971896\pi\)
−0.574416 0.818563i \(-0.694771\pi\)
\(788\) −825.000 + 1428.94i −1.04695 + 1.81338i
\(789\) 279.000 161.081i 0.353612 0.204158i
\(790\) 670.304i 0.848486i
\(791\) 273.000 + 109.119i 0.345133 + 0.137951i
\(792\) −135.000 −0.170455
\(793\) −624.000 1080.80i −0.786885 1.36293i
\(794\) 666.000 + 384.515i 0.838791 + 0.484276i
\(795\) 148.500 257.210i 0.186792 0.323534i
\(796\) −30.0000 + 17.3205i −0.0376884 + 0.0217594i
\(797\) 607.950i 0.762798i 0.924411 + 0.381399i \(0.124558\pi\)
−0.924411 + 0.381399i \(0.875442\pi\)
\(798\) −54.0000 374.123i −0.0676692 0.468826i
\(799\) 0 0
\(800\) −45.0000 77.9423i −0.0562500 0.0974279i
\(801\) −189.000 109.119i −0.235955 0.136229i
\(802\) −198.000 + 342.946i −0.246883 + 0.427614i
\(803\) 810.000 467.654i 1.00872 0.582383i
\(804\) 658.179i 0.818631i
\(805\) 0 0
\(806\) 504.000 0.625310
\(807\) 292.500 + 506.625i 0.362454 + 0.627788i
\(808\) −378.000 218.238i −0.467822 0.270097i
\(809\) 84.0000 145.492i 0.103832 0.179842i −0.809428 0.587218i \(-0.800223\pi\)
0.913260 + 0.407376i \(0.133556\pi\)
\(810\) 121.500 70.1481i 0.150000 0.0866025i
\(811\) 353.338i 0.435682i 0.975984 + 0.217841i \(0.0699015\pi\)
−0.975984 + 0.217841i \(0.930099\pi\)
\(812\) 247.500 194.856i 0.304803 0.239970i
\(813\) −159.000 −0.195572
\(814\) −225.000 389.711i −0.276413 0.478761i
\(815\) 936.000 + 540.400i 1.14847 + 0.663067i
\(816\) 99.0000 171.473i 0.121324 0.210139i
\(817\) 666.000 384.515i 0.815177 0.470643i
\(818\) 1086.00i 1.32762i
\(819\) 288.000 41.5692i 0.351648 0.0507561i
\(820\) 270.000 0.329268
\(821\) −142.500 246.817i −0.173569 0.300630i 0.766096 0.642726i \(-0.222197\pi\)
−0.939665 + 0.342096i \(0.888863\pi\)
\(822\) 432.000 + 249.415i 0.525547 + 0.303425i
\(823\) 137.000 237.291i 0.166464 0.288324i −0.770710 0.637186i \(-0.780098\pi\)
0.937174 + 0.348862i \(0.113432\pi\)
\(824\) −180.000 + 103.923i −0.218447 + 0.126120i
\(825\) 51.9615i 0.0629837i
\(826\) 121.500 303.975i 0.147094 0.368008i
\(827\) 429.000 0.518742 0.259371 0.965778i \(-0.416485\pi\)
0.259371 + 0.965778i \(0.416485\pi\)
\(828\) 0 0
\(829\) −819.000 472.850i −0.987937 0.570386i −0.0832802 0.996526i \(-0.526540\pi\)
−0.904657 + 0.426140i \(0.859873\pi\)
\(830\) −931.500 + 1613.41i −1.12229 + 1.94386i
\(831\) 570.000 329.090i 0.685921 0.396016i
\(832\) 1260.93i 1.51554i
\(833\) 144.000 + 488.438i 0.172869 + 0.586361i
\(834\) 954.000 1.14388
\(835\) −648.000 1122.37i −0.776048 1.34415i
\(836\) 675.000 + 389.711i 0.807416 + 0.466162i
\(837\) −31.5000 + 54.5596i −0.0376344 + 0.0651847i
\(838\) 1674.00 966.484i 1.99761 1.15332i
\(839\) 259.808i 0.309663i 0.987941 + 0.154832i \(0.0494835\pi\)
−0.987941 + 0.154832i \(0.950516\pi\)
\(840\) −175.500 70.1481i −0.208929 0.0835096i
\(841\) −760.000 −0.903686
\(842\) −1128.00 1953.75i −1.33967 2.32037i
\(843\) −450.000 259.808i −0.533808 0.308194i
\(844\) 620.000 1073.87i 0.734597 1.27236i
\(845\) −103.500 + 59.7558i −0.122485 + 0.0707169i
\(846\) 0 0
\(847\) −104.000 720.533i −0.122786 0.850688i
\(848\) −363.000 −0.428066
\(849\) −177.000 306.573i −0.208481 0.361099i
\(850\) −54.0000 31.1769i −0.0635294 0.0366787i
\(851\) 0 0
\(852\) 630.000 363.731i 0.739437 0.426914i
\(853\) 997.661i 1.16959i 0.811181 + 0.584796i \(0.198825\pi\)
−0.811181 + 0.584796i \(0.801175\pi\)
\(854\) −1170.00 1486.10i −1.37002 1.74016i
\(855\) −162.000 −0.189474
\(856\) −139.500 241.621i −0.162967 0.282268i
\(857\) 378.000 + 218.238i 0.441074 + 0.254654i 0.704053 0.710148i \(-0.251372\pi\)
−0.262979 + 0.964801i \(0.584705\pi\)
\(858\) −540.000 + 935.307i −0.629371 + 1.09010i
\(859\) −393.000 + 226.899i −0.457509 + 0.264143i −0.710996 0.703196i \(-0.751756\pi\)
0.253487 + 0.967339i \(0.418422\pi\)
\(860\) 1922.58i 2.23555i
\(861\) −99.0000 + 77.9423i −0.114983 + 0.0905253i
\(862\) 486.000 0.563805
\(863\) 195.000 + 337.750i 0.225956 + 0.391367i 0.956606 0.291385i \(-0.0941161\pi\)
−0.730650 + 0.682752i \(0.760783\pi\)
\(864\) −202.500 116.913i −0.234375 0.135316i
\(865\) −594.000 + 1028.84i −0.686705 + 1.18941i
\(866\) −882.000 + 509.223i −1.01848 + 0.588017i
\(867\) 313.501i 0.361593i
\(868\) 420.000 60.6218i 0.483871 0.0698408i
\(869\) −645.000 −0.742232
\(870\) −121.500 210.444i −0.139655 0.241890i
\(871\) −912.000 526.543i −1.04707 0.604527i
\(872\) 12.0000 20.7846i 0.0137615 0.0238356i
\(873\) −481.500 + 277.994i −0.551546 + 0.318435i
\(874\) 0 0
\(875\) −310.500 + 776.825i −0.354857 + 0.887800i
\(876\) −540.000 −0.616438
\(877\) 272.000 + 471.118i 0.310148 + 0.537192i 0.978394 0.206748i \(-0.0662880\pi\)
−0.668246 + 0.743940i \(0.732955\pi\)
\(878\) −1012.50 584.567i −1.15319 0.665794i
\(879\) 472.500 818.394i 0.537543 0.931051i
\(880\) −742.500 + 428.683i −0.843750 + 0.487139i
\(881\) 187.061i 0.212329i −0.994349 0.106164i \(-0.966143\pi\)
0.994349 0.106164i \(-0.0338569\pi\)
\(882\) 423.000 124.708i 0.479592 0.141392i
\(883\) 322.000 0.364666 0.182333 0.983237i \(-0.441635\pi\)
0.182333 + 0.983237i \(0.441635\pi\)
\(884\) 360.000 + 623.538i 0.407240 + 0.705360i
\(885\) −121.500 70.1481i −0.137288 0.0792633i
\(886\) 445.500 771.629i 0.502822 0.870913i
\(887\) 612.000 353.338i 0.689966 0.398352i −0.113633 0.993523i \(-0.536249\pi\)
0.803599 + 0.595171i \(0.202916\pi\)
\(888\) 51.9615i 0.0585152i
\(889\) 227.500 + 90.9327i 0.255906 + 0.102286i
\(890\) 1134.00 1.27416
\(891\) −67.5000 116.913i −0.0757576 0.131216i
\(892\) 832.500 + 480.644i 0.933296 + 0.538839i
\(893\) 0 0
\(894\) −837.000 + 483.242i −0.936242 + 0.540539i
\(895\) 467.654i 0.522518i
\(896\) 93.0000 + 644.323i 0.103795 + 0.719110i
\(897\) 0 0
\(898\) 738.000 + 1278.25i 0.821826 + 1.42344i
\(899\) 94.5000 + 54.5596i 0.105117 + 0.0606892i
\(900\) −15.0000 + 25.9808i −0.0166667 + 0.0288675i
\(901\) −297.000 + 171.473i −0.329634 + 0.190314i
\(902\) 467.654i 0.518463i
\(903\) 555.000 + 704.945i 0.614618 + 0.780670i
\(904\) 126.000 0.139381
\(905\) −27.0000 46.7654i −0.0298343 0.0516744i
\(906\) −355.500 205.248i −0.392384 0.226543i
\(907\) 550.000 952.628i 0.606395 1.05031i −0.385435 0.922735i \(-0.625948\pi\)
0.991829 0.127571i \(-0.0407182\pi\)
\(908\) 382.500 220.836i 0.421256 0.243212i
\(909\) 436.477i 0.480173i
\(910\) −1188.00 + 935.307i −1.30549 + 1.02781i
\(911\) 900.000 0.987925 0.493963 0.869483i \(-0.335548\pi\)
0.493963 + 0.869483i \(0.335548\pi\)
\(912\) 99.0000 + 171.473i 0.108553 + 0.188019i
\(913\) 1552.50 + 896.336i 1.70044 + 0.981748i
\(914\) 664.500 1150.95i 0.727024 1.25924i
\(915\) −702.000 + 405.300i −0.767213 + 0.442951i
\(916\) 1645.45i 1.79634i
\(917\) 1188.00 171.473i 1.29553 0.186993i
\(918\) −162.000 −0.176471
\(919\) 859.000 + 1487.83i 0.934712 + 1.61897i 0.775147 + 0.631781i \(0.217676\pi\)
0.159564 + 0.987188i \(0.448991\pi\)
\(920\) 0 0
\(921\) 150.000 259.808i 0.162866 0.282093i
\(922\) 1080.00 623.538i 1.17137 0.676289i
\(923\) 1163.94i 1.26104i
\(924\) −337.500 + 844.375i −0.365260 + 0.913826i
\(925\) −20.0000 −0.0216216
\(926\) 123.000 + 213.042i 0.132829 + 0.230067i
\(927\) −180.000 103.923i −0.194175 0.112107i
\(928\) −202.500 + 350.740i −0.218211 + 0.377953i
\(929\) −1287.00 + 743.050i −1.38536 + 0.799838i −0.992788 0.119883i \(-0.961748\pi\)
−0.392573 + 0.919721i \(0.628415\pi\)
\(930\) 327.358i 0.351997i
\(931\) −495.000 119.512i −0.531686 0.128369i
\(932\) 1350.00 1.44850
\(933\) 153.000 + 265.004i 0.163987 + 0.284034i
\(934\) −702.000 405.300i −0.751606 0.433940i
\(935\) −405.000 + 701.481i −0.433155 + 0.750247i
\(936\) 108.000 62.3538i 0.115385 0.0666173i
\(937\) 957.824i 1.02222i −0.859514 0.511112i \(-0.829234\pi\)
0.859514 0.511112i \(-0.170766\pi\)
\(938\) −1482.00 592.361i −1.57996 0.631515i
\(939\) 369.000 0.392971
\(940\) 0 0
\(941\) 310.500 + 179.267i 0.329968 + 0.190507i 0.655827 0.754911i \(-0.272320\pi\)
−0.325859 + 0.945418i \(0.605653\pi\)
\(942\) 54.0000 93.5307i 0.0573248 0.0992895i
\(943\) 0 0
\(944\) 171.473i 0.181645i
\(945\) −27.0000 187.061i −0.0285714 0.197949i
\(946\) −3330.00 −3.52008
\(947\) −81.0000 140.296i −0.0855333 0.148148i 0.820085 0.572242i \(-0.193926\pi\)
−0.905618 + 0.424094i \(0.860593\pi\)
\(948\) 322.500 + 186.195i 0.340190 + 0.196409i
\(949\) −432.000 + 748.246i −0.455216 + 0.788457i
\(950\) 54.0000 31.1769i 0.0568421 0.0328178i
\(951\) 202.650i 0.213091i
\(952\) 135.000 + 171.473i 0.141807 + 0.180119i
\(953\) −954.000 −1.00105 −0.500525 0.865722i \(-0.666860\pi\)
−0.500525 + 0.865722i \(0.666860\pi\)
\(954\) 148.500 + 257.210i 0.155660 + 0.269612i
\(955\) 1404.00 + 810.600i 1.47016 + 0.848796i
\(956\) 570.000 987.269i 0.596234 1.03271i
\(957\) −202.500 + 116.913i −0.211599 + 0.122167i
\(958\) 1028.84i 1.07394i
\(959\) 528.000 415.692i 0.550574 0.433464i
\(960\) 819.000 0.853125
\(961\) −407.000 704.945i −0.423517 0.733553i
\(962\) 360.000 + 207.846i 0.374220 + 0.216056i
\(963\) 139.500 241.621i 0.144860 0.250905i
\(964\) −1927.50 + 1112.84i −1.99948 + 1.15440i
\(965\) 961.288i 0.996154i
\(966\) 0 0
\(967\) −751.000 −0.776629 −0.388314 0.921527i \(-0.626943\pi\)
−0.388314 + 0.921527i \(0.626943\pi\)
\(968\) −156.000 270.200i −0.161157 0.279132i
\(969\) 162.000 + 93.5307i 0.167183 + 0.0965230i
\(970\) 1444.50 2501.95i 1.48918 2.57933i
\(971\) −247.500 + 142.894i −0.254892 + 0.147162i −0.622002 0.783016i \(-0.713680\pi\)
0.367110 + 0.930177i \(0.380347\pi\)
\(972\) 77.9423i 0.0801875i
\(973\) 477.000 1193.38i 0.490236 1.22650i
\(974\) −951.000 −0.976386
\(975\) 24.0000 + 41.5692i 0.0246154 + 0.0426351i
\(976\) 858.000 + 495.367i 0.879098 + 0.507548i
\(977\) 9.00000 15.5885i 0.00921187 0.0159554i −0.861383 0.507957i \(-0.830401\pi\)
0.870595 + 0.492001i \(0.163734\pi\)
\(978\) −936.000 + 540.400i −0.957055 + 0.552556i
\(979\) 1091.19i 1.11460i
\(980\) −877.500 + 922.317i −0.895408 + 0.941140i
\(981\) 24.0000 0.0244648
\(982\) −40.5000 70.1481i −0.0412424 0.0714339i
\(983\) −855.000 493.634i −0.869786 0.502171i −0.00250913 0.999997i \(-0.500799\pi\)
−0.867277 + 0.497825i \(0.834132\pi\)
\(984\) −27.0000 + 46.7654i −0.0274390 + 0.0475258i
\(985\) 1485.00 857.365i 1.50761 0.870421i
\(986\) 280.592i 0.284576i
\(987\) 0 0
\(988\) −720.000 −0.728745
\(989\) 0 0
\(990\) 607.500 + 350.740i 0.613636 + 0.354283i
\(991\) −351.500 + 608.816i −0.354692 + 0.614345i −0.987065 0.160319i \(-0.948748\pi\)
0.632373 + 0.774664i \(0.282081\pi\)
\(992\) −472.500 + 272.798i −0.476310 + 0.274998i
\(993\) 69.2820i 0.0697704i
\(994\) −252.000 1745.91i −0.253521 1.75645i
\(995\) 36.0000 0.0361809
\(996\) −517.500 896.336i −0.519578 0.899936i
\(997\) 186.000 + 107.387i 0.186560 + 0.107710i 0.590371 0.807132i \(-0.298981\pi\)
−0.403811 + 0.914842i \(0.632315\pi\)
\(998\) 669.000 1158.74i 0.670341 1.16106i
\(999\) −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 21.3.f.a.10.1 2
3.2 odd 2 63.3.m.d.10.1 2
4.3 odd 2 336.3.bh.d.241.1 2
5.2 odd 4 525.3.s.e.199.2 4
5.3 odd 4 525.3.s.e.199.1 4
5.4 even 2 525.3.o.h.451.1 2
7.2 even 3 147.3.f.a.19.1 2
7.3 odd 6 147.3.d.c.97.1 2
7.4 even 3 147.3.d.c.97.2 2
7.5 odd 6 inner 21.3.f.a.19.1 yes 2
7.6 odd 2 147.3.f.a.31.1 2
12.11 even 2 1008.3.cg.a.577.1 2
21.2 odd 6 441.3.m.g.19.1 2
21.5 even 6 63.3.m.d.19.1 2
21.11 odd 6 441.3.d.a.244.1 2
21.17 even 6 441.3.d.a.244.2 2
21.20 even 2 441.3.m.g.325.1 2
28.3 even 6 2352.3.f.a.97.2 2
28.11 odd 6 2352.3.f.a.97.1 2
28.19 even 6 336.3.bh.d.145.1 2
35.12 even 12 525.3.s.e.124.1 4
35.19 odd 6 525.3.o.h.376.1 2
35.33 even 12 525.3.s.e.124.2 4
84.47 odd 6 1008.3.cg.a.145.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.3.f.a.10.1 2 1.1 even 1 trivial
21.3.f.a.19.1 yes 2 7.5 odd 6 inner
63.3.m.d.10.1 2 3.2 odd 2
63.3.m.d.19.1 2 21.5 even 6
147.3.d.c.97.1 2 7.3 odd 6
147.3.d.c.97.2 2 7.4 even 3
147.3.f.a.19.1 2 7.2 even 3
147.3.f.a.31.1 2 7.6 odd 2
336.3.bh.d.145.1 2 28.19 even 6
336.3.bh.d.241.1 2 4.3 odd 2
441.3.d.a.244.1 2 21.11 odd 6
441.3.d.a.244.2 2 21.17 even 6
441.3.m.g.19.1 2 21.2 odd 6
441.3.m.g.325.1 2 21.20 even 2
525.3.o.h.376.1 2 35.19 odd 6
525.3.o.h.451.1 2 5.4 even 2
525.3.s.e.124.1 4 35.12 even 12
525.3.s.e.124.2 4 35.33 even 12
525.3.s.e.199.1 4 5.3 odd 4
525.3.s.e.199.2 4 5.2 odd 4
1008.3.cg.a.145.1 2 84.47 odd 6
1008.3.cg.a.577.1 2 12.11 even 2
2352.3.f.a.97.1 2 28.11 odd 6
2352.3.f.a.97.2 2 28.3 even 6