Properties

Label 1014.3.f.d.775.2
Level $1014$
Weight $3$
Character 1014.775
Analytic conductor $27.629$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,3,Mod(577,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.577");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1014.f (of order \(4\), 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: \(27.6294988061\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
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: \( 2 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 775.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.775
Dual form 1014.3.f.d.577.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(1.26795 + 1.26795i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(6.83013 - 6.83013i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -2.53590i q^{10} +(7.26795 - 7.26795i) q^{11} +3.46410i q^{12} -13.6603 q^{14} +(2.19615 + 2.19615i) q^{15} -4.00000 q^{16} -18.9282i q^{17} +(-3.00000 - 3.00000i) q^{18} +(23.3923 + 23.3923i) q^{19} +(-2.53590 + 2.53590i) q^{20} +(11.8301 - 11.8301i) q^{21} -14.5359 q^{22} -4.14359i q^{23} +(3.46410 - 3.46410i) q^{24} -21.7846i q^{25} +5.19615 q^{27} +(13.6603 + 13.6603i) q^{28} -17.3205 q^{29} -4.39230i q^{30} +(-22.1699 - 22.1699i) q^{31} +(4.00000 + 4.00000i) q^{32} +(12.5885 - 12.5885i) q^{33} +(-18.9282 + 18.9282i) q^{34} +17.3205 q^{35} +6.00000i q^{36} +(-26.1769 + 26.1769i) q^{37} -46.7846i q^{38} +5.07180 q^{40} +(18.2487 + 18.2487i) q^{41} -23.6603 q^{42} +15.3397i q^{43} +(14.5359 + 14.5359i) q^{44} +(3.80385 + 3.80385i) q^{45} +(-4.14359 + 4.14359i) q^{46} +(-7.01924 + 7.01924i) q^{47} -6.92820 q^{48} -44.3013i q^{49} +(-21.7846 + 21.7846i) q^{50} -32.7846i q^{51} -61.6743 q^{53} +(-5.19615 - 5.19615i) q^{54} +18.4308 q^{55} -27.3205i q^{56} +(40.5167 + 40.5167i) q^{57} +(17.3205 + 17.3205i) q^{58} +(46.7321 - 46.7321i) q^{59} +(-4.39230 + 4.39230i) q^{60} -7.30127 q^{61} +44.3397i q^{62} +(20.4904 - 20.4904i) q^{63} -8.00000i q^{64} -25.1769 q^{66} +(27.7391 + 27.7391i) q^{67} +37.8564 q^{68} -7.17691i q^{69} +(-17.3205 - 17.3205i) q^{70} +(76.0526 + 76.0526i) q^{71} +(6.00000 - 6.00000i) q^{72} +(67.4186 - 67.4186i) q^{73} +52.3538 q^{74} -37.7321i q^{75} +(-46.7846 + 46.7846i) q^{76} -99.2820i q^{77} +11.8756 q^{79} +(-5.07180 - 5.07180i) q^{80} +9.00000 q^{81} -36.4974i q^{82} +(-111.033 - 111.033i) q^{83} +(23.6603 + 23.6603i) q^{84} +(24.0000 - 24.0000i) q^{85} +(15.3397 - 15.3397i) q^{86} -30.0000 q^{87} -29.0718i q^{88} +(118.641 - 118.641i) q^{89} -7.60770i q^{90} +8.28719 q^{92} +(-38.3993 - 38.3993i) q^{93} +14.0385 q^{94} +59.3205i q^{95} +(6.92820 + 6.92820i) q^{96} +(109.988 + 109.988i) q^{97} +(-44.3013 + 44.3013i) q^{98} +(21.8038 - 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 12 q^{5} + 10 q^{7} + 8 q^{8} + 12 q^{9} + 36 q^{11} - 20 q^{14} - 12 q^{15} - 16 q^{16} - 12 q^{18} + 52 q^{19} - 24 q^{20} + 30 q^{21} - 72 q^{22} + 20 q^{28} - 106 q^{31} + 16 q^{32}+ \cdots + 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.73205 0.577350
\(4\) 2.00000i 0.500000i
\(5\) 1.26795 + 1.26795i 0.253590 + 0.253590i 0.822441 0.568851i \(-0.192612\pi\)
−0.568851 + 0.822441i \(0.692612\pi\)
\(6\) −1.73205 1.73205i −0.288675 0.288675i
\(7\) 6.83013 6.83013i 0.975732 0.975732i −0.0239800 0.999712i \(-0.507634\pi\)
0.999712 + 0.0239800i \(0.00763381\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000 0.333333
\(10\) 2.53590i 0.253590i
\(11\) 7.26795 7.26795i 0.660723 0.660723i −0.294828 0.955550i \(-0.595262\pi\)
0.955550 + 0.294828i \(0.0952623\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 0 0
\(14\) −13.6603 −0.975732
\(15\) 2.19615 + 2.19615i 0.146410 + 0.146410i
\(16\) −4.00000 −0.250000
\(17\) 18.9282i 1.11342i −0.830706 0.556712i \(-0.812063\pi\)
0.830706 0.556712i \(-0.187937\pi\)
\(18\) −3.00000 3.00000i −0.166667 0.166667i
\(19\) 23.3923 + 23.3923i 1.23117 + 1.23117i 0.963513 + 0.267661i \(0.0862506\pi\)
0.267661 + 0.963513i \(0.413749\pi\)
\(20\) −2.53590 + 2.53590i −0.126795 + 0.126795i
\(21\) 11.8301 11.8301i 0.563339 0.563339i
\(22\) −14.5359 −0.660723
\(23\) 4.14359i 0.180156i −0.995935 0.0900781i \(-0.971288\pi\)
0.995935 0.0900781i \(-0.0287117\pi\)
\(24\) 3.46410 3.46410i 0.144338 0.144338i
\(25\) 21.7846i 0.871384i
\(26\) 0 0
\(27\) 5.19615 0.192450
\(28\) 13.6603 + 13.6603i 0.487866 + 0.487866i
\(29\) −17.3205 −0.597259 −0.298629 0.954369i \(-0.596529\pi\)
−0.298629 + 0.954369i \(0.596529\pi\)
\(30\) 4.39230i 0.146410i
\(31\) −22.1699 22.1699i −0.715157 0.715157i 0.252452 0.967609i \(-0.418763\pi\)
−0.967609 + 0.252452i \(0.918763\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 12.5885 12.5885i 0.381468 0.381468i
\(34\) −18.9282 + 18.9282i −0.556712 + 0.556712i
\(35\) 17.3205 0.494872
\(36\) 6.00000i 0.166667i
\(37\) −26.1769 + 26.1769i −0.707484 + 0.707484i −0.966006 0.258521i \(-0.916765\pi\)
0.258521 + 0.966006i \(0.416765\pi\)
\(38\) 46.7846i 1.23117i
\(39\) 0 0
\(40\) 5.07180 0.126795
\(41\) 18.2487 + 18.2487i 0.445091 + 0.445091i 0.893719 0.448628i \(-0.148087\pi\)
−0.448628 + 0.893719i \(0.648087\pi\)
\(42\) −23.6603 −0.563339
\(43\) 15.3397i 0.356738i 0.983964 + 0.178369i \(0.0570821\pi\)
−0.983964 + 0.178369i \(0.942918\pi\)
\(44\) 14.5359 + 14.5359i 0.330361 + 0.330361i
\(45\) 3.80385 + 3.80385i 0.0845299 + 0.0845299i
\(46\) −4.14359 + 4.14359i −0.0900781 + 0.0900781i
\(47\) −7.01924 + 7.01924i −0.149345 + 0.149345i −0.777826 0.628480i \(-0.783677\pi\)
0.628480 + 0.777826i \(0.283677\pi\)
\(48\) −6.92820 −0.144338
\(49\) 44.3013i 0.904108i
\(50\) −21.7846 + 21.7846i −0.435692 + 0.435692i
\(51\) 32.7846i 0.642835i
\(52\) 0 0
\(53\) −61.6743 −1.16367 −0.581833 0.813308i \(-0.697664\pi\)
−0.581833 + 0.813308i \(0.697664\pi\)
\(54\) −5.19615 5.19615i −0.0962250 0.0962250i
\(55\) 18.4308 0.335105
\(56\) 27.3205i 0.487866i
\(57\) 40.5167 + 40.5167i 0.710819 + 0.710819i
\(58\) 17.3205 + 17.3205i 0.298629 + 0.298629i
\(59\) 46.7321 46.7321i 0.792069 0.792069i −0.189762 0.981830i \(-0.560771\pi\)
0.981830 + 0.189762i \(0.0607715\pi\)
\(60\) −4.39230 + 4.39230i −0.0732051 + 0.0732051i
\(61\) −7.30127 −0.119693 −0.0598465 0.998208i \(-0.519061\pi\)
−0.0598465 + 0.998208i \(0.519061\pi\)
\(62\) 44.3397i 0.715157i
\(63\) 20.4904 20.4904i 0.325244 0.325244i
\(64\) 8.00000i 0.125000i
\(65\) 0 0
\(66\) −25.1769 −0.381468
\(67\) 27.7391 + 27.7391i 0.414016 + 0.414016i 0.883135 0.469119i \(-0.155428\pi\)
−0.469119 + 0.883135i \(0.655428\pi\)
\(68\) 37.8564 0.556712
\(69\) 7.17691i 0.104013i
\(70\) −17.3205 17.3205i −0.247436 0.247436i
\(71\) 76.0526 + 76.0526i 1.07116 + 1.07116i 0.997266 + 0.0738969i \(0.0235436\pi\)
0.0738969 + 0.997266i \(0.476456\pi\)
\(72\) 6.00000 6.00000i 0.0833333 0.0833333i
\(73\) 67.4186 67.4186i 0.923542 0.923542i −0.0737356 0.997278i \(-0.523492\pi\)
0.997278 + 0.0737356i \(0.0234921\pi\)
\(74\) 52.3538 0.707484
\(75\) 37.7321i 0.503094i
\(76\) −46.7846 + 46.7846i −0.615587 + 0.615587i
\(77\) 99.2820i 1.28938i
\(78\) 0 0
\(79\) 11.8756 0.150325 0.0751623 0.997171i \(-0.476053\pi\)
0.0751623 + 0.997171i \(0.476053\pi\)
\(80\) −5.07180 5.07180i −0.0633975 0.0633975i
\(81\) 9.00000 0.111111
\(82\) 36.4974i 0.445091i
\(83\) −111.033 111.033i −1.33775 1.33775i −0.898235 0.439516i \(-0.855150\pi\)
−0.439516 0.898235i \(-0.644850\pi\)
\(84\) 23.6603 + 23.6603i 0.281670 + 0.281670i
\(85\) 24.0000 24.0000i 0.282353 0.282353i
\(86\) 15.3397 15.3397i 0.178369 0.178369i
\(87\) −30.0000 −0.344828
\(88\) 29.0718i 0.330361i
\(89\) 118.641 118.641i 1.33305 1.33305i 0.430413 0.902632i \(-0.358368\pi\)
0.902632 0.430413i \(-0.141632\pi\)
\(90\) 7.60770i 0.0845299i
\(91\) 0 0
\(92\) 8.28719 0.0900781
\(93\) −38.3993 38.3993i −0.412896 0.412896i
\(94\) 14.0385 0.149345
\(95\) 59.3205i 0.624426i
\(96\) 6.92820 + 6.92820i 0.0721688 + 0.0721688i
\(97\) 109.988 + 109.988i 1.13389 + 1.13389i 0.989524 + 0.144371i \(0.0461160\pi\)
0.144371 + 0.989524i \(0.453884\pi\)
\(98\) −44.3013 + 44.3013i −0.452054 + 0.452054i
\(99\) 21.8038 21.8038i 0.220241 0.220241i
\(100\) 43.5692 0.435692
\(101\) 186.813i 1.84963i −0.380415 0.924816i \(-0.624219\pi\)
0.380415 0.924816i \(-0.375781\pi\)
\(102\) −32.7846 + 32.7846i −0.321418 + 0.321418i
\(103\) 83.2628i 0.808377i 0.914676 + 0.404188i \(0.132446\pi\)
−0.914676 + 0.404188i \(0.867554\pi\)
\(104\) 0 0
\(105\) 30.0000 0.285714
\(106\) 61.6743 + 61.6743i 0.581833 + 0.581833i
\(107\) 102.497 0.957920 0.478960 0.877837i \(-0.341014\pi\)
0.478960 + 0.877837i \(0.341014\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −48.1891 48.1891i −0.442102 0.442102i 0.450616 0.892718i \(-0.351204\pi\)
−0.892718 + 0.450616i \(0.851204\pi\)
\(110\) −18.4308 18.4308i −0.167553 0.167553i
\(111\) −45.3397 + 45.3397i −0.408466 + 0.408466i
\(112\) −27.3205 + 27.3205i −0.243933 + 0.243933i
\(113\) −45.2154 −0.400136 −0.200068 0.979782i \(-0.564116\pi\)
−0.200068 + 0.979782i \(0.564116\pi\)
\(114\) 81.0333i 0.710819i
\(115\) 5.25387 5.25387i 0.0456858 0.0456858i
\(116\) 34.6410i 0.298629i
\(117\) 0 0
\(118\) −93.4641 −0.792069
\(119\) −129.282 129.282i −1.08640 1.08640i
\(120\) 8.78461 0.0732051
\(121\) 15.3538i 0.126891i
\(122\) 7.30127 + 7.30127i 0.0598465 + 0.0598465i
\(123\) 31.6077 + 31.6077i 0.256973 + 0.256973i
\(124\) 44.3397 44.3397i 0.357579 0.357579i
\(125\) 59.3205 59.3205i 0.474564 0.474564i
\(126\) −40.9808 −0.325244
\(127\) 236.846i 1.86493i 0.361260 + 0.932465i \(0.382347\pi\)
−0.361260 + 0.932465i \(0.617653\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 26.5692i 0.205963i
\(130\) 0 0
\(131\) −209.636 −1.60027 −0.800137 0.599817i \(-0.795240\pi\)
−0.800137 + 0.599817i \(0.795240\pi\)
\(132\) 25.1769 + 25.1769i 0.190734 + 0.190734i
\(133\) 319.545 2.40259
\(134\) 55.4782i 0.414016i
\(135\) 6.58846 + 6.58846i 0.0488034 + 0.0488034i
\(136\) −37.8564 37.8564i −0.278356 0.278356i
\(137\) −80.5359 + 80.5359i −0.587853 + 0.587853i −0.937050 0.349196i \(-0.886455\pi\)
0.349196 + 0.937050i \(0.386455\pi\)
\(138\) −7.17691 + 7.17691i −0.0520066 + 0.0520066i
\(139\) −95.7077 −0.688544 −0.344272 0.938870i \(-0.611874\pi\)
−0.344272 + 0.938870i \(0.611874\pi\)
\(140\) 34.6410i 0.247436i
\(141\) −12.1577 + 12.1577i −0.0862247 + 0.0862247i
\(142\) 152.105i 1.07116i
\(143\) 0 0
\(144\) −12.0000 −0.0833333
\(145\) −21.9615 21.9615i −0.151459 0.151459i
\(146\) −134.837 −0.923542
\(147\) 76.7321i 0.521987i
\(148\) −52.3538 52.3538i −0.353742 0.353742i
\(149\) −40.2102 40.2102i −0.269867 0.269867i 0.559179 0.829047i \(-0.311116\pi\)
−0.829047 + 0.559179i \(0.811116\pi\)
\(150\) −37.7321 + 37.7321i −0.251547 + 0.251547i
\(151\) 55.0385 55.0385i 0.364493 0.364493i −0.500971 0.865464i \(-0.667024\pi\)
0.865464 + 0.500971i \(0.167024\pi\)
\(152\) 93.5692 0.615587
\(153\) 56.7846i 0.371141i
\(154\) −99.2820 + 99.2820i −0.644689 + 0.644689i
\(155\) 56.2205i 0.362713i
\(156\) 0 0
\(157\) 55.4308 0.353062 0.176531 0.984295i \(-0.443512\pi\)
0.176531 + 0.984295i \(0.443512\pi\)
\(158\) −11.8756 11.8756i −0.0751623 0.0751623i
\(159\) −106.823 −0.671843
\(160\) 10.1436i 0.0633975i
\(161\) −28.3013 28.3013i −0.175784 0.175784i
\(162\) −9.00000 9.00000i −0.0555556 0.0555556i
\(163\) 144.653 144.653i 0.887443 0.887443i −0.106834 0.994277i \(-0.534071\pi\)
0.994277 + 0.106834i \(0.0340713\pi\)
\(164\) −36.4974 + 36.4974i −0.222545 + 0.222545i
\(165\) 31.9230 0.193473
\(166\) 222.067i 1.33775i
\(167\) −114.431 + 114.431i −0.685214 + 0.685214i −0.961170 0.275956i \(-0.911006\pi\)
0.275956 + 0.961170i \(0.411006\pi\)
\(168\) 47.3205i 0.281670i
\(169\) 0 0
\(170\) −48.0000 −0.282353
\(171\) 70.1769 + 70.1769i 0.410391 + 0.410391i
\(172\) −30.6795 −0.178369
\(173\) 268.459i 1.55179i −0.630865 0.775893i \(-0.717300\pi\)
0.630865 0.775893i \(-0.282700\pi\)
\(174\) 30.0000 + 30.0000i 0.172414 + 0.172414i
\(175\) −148.792 148.792i −0.850238 0.850238i
\(176\) −29.0718 + 29.0718i −0.165181 + 0.165181i
\(177\) 80.9423 80.9423i 0.457301 0.457301i
\(178\) −237.282 −1.33305
\(179\) 285.779i 1.59653i −0.602304 0.798267i \(-0.705751\pi\)
0.602304 0.798267i \(-0.294249\pi\)
\(180\) −7.60770 + 7.60770i −0.0422650 + 0.0422650i
\(181\) 177.646i 0.981471i 0.871309 + 0.490735i \(0.163272\pi\)
−0.871309 + 0.490735i \(0.836728\pi\)
\(182\) 0 0
\(183\) −12.6462 −0.0691048
\(184\) −8.28719 8.28719i −0.0450391 0.0450391i
\(185\) −66.3820 −0.358822
\(186\) 76.7987i 0.412896i
\(187\) −137.569 137.569i −0.735664 0.735664i
\(188\) −14.0385 14.0385i −0.0746727 0.0746727i
\(189\) 35.4904 35.4904i 0.187780 0.187780i
\(190\) 59.3205 59.3205i 0.312213 0.312213i
\(191\) 197.321 1.03309 0.516546 0.856260i \(-0.327218\pi\)
0.516546 + 0.856260i \(0.327218\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −14.8494 + 14.8494i −0.0769397 + 0.0769397i −0.744529 0.667590i \(-0.767326\pi\)
0.667590 + 0.744529i \(0.267326\pi\)
\(194\) 219.976i 1.13389i
\(195\) 0 0
\(196\) 88.6025 0.452054
\(197\) −106.956 106.956i −0.542926 0.542926i 0.381460 0.924385i \(-0.375421\pi\)
−0.924385 + 0.381460i \(0.875421\pi\)
\(198\) −43.6077 −0.220241
\(199\) 22.2154i 0.111635i −0.998441 0.0558176i \(-0.982223\pi\)
0.998441 0.0558176i \(-0.0177765\pi\)
\(200\) −43.5692 43.5692i −0.217846 0.217846i
\(201\) 48.0455 + 48.0455i 0.239032 + 0.239032i
\(202\) −186.813 + 186.813i −0.924816 + 0.924816i
\(203\) −118.301 + 118.301i −0.582765 + 0.582765i
\(204\) 65.5692 0.321418
\(205\) 46.2769i 0.225741i
\(206\) 83.2628 83.2628i 0.404188 0.404188i
\(207\) 12.4308i 0.0600521i
\(208\) 0 0
\(209\) 340.028 1.62693
\(210\) −30.0000 30.0000i −0.142857 0.142857i
\(211\) 64.2013 0.304272 0.152136 0.988360i \(-0.451385\pi\)
0.152136 + 0.988360i \(0.451385\pi\)
\(212\) 123.349i 0.581833i
\(213\) 131.727 + 131.727i 0.618436 + 0.618436i
\(214\) −102.497 102.497i −0.478960 0.478960i
\(215\) −19.4500 + 19.4500i −0.0904652 + 0.0904652i
\(216\) 10.3923 10.3923i 0.0481125 0.0481125i
\(217\) −302.846 −1.39560
\(218\) 96.3782i 0.442102i
\(219\) 116.772 116.772i 0.533207 0.533207i
\(220\) 36.8616i 0.167553i
\(221\) 0 0
\(222\) 90.6795 0.408466
\(223\) 154.531 + 154.531i 0.692963 + 0.692963i 0.962883 0.269920i \(-0.0869972\pi\)
−0.269920 + 0.962883i \(0.586997\pi\)
\(224\) 54.6410 0.243933
\(225\) 65.3538i 0.290461i
\(226\) 45.2154 + 45.2154i 0.200068 + 0.200068i
\(227\) 45.7128 + 45.7128i 0.201378 + 0.201378i 0.800590 0.599212i \(-0.204519\pi\)
−0.599212 + 0.800590i \(0.704519\pi\)
\(228\) −81.0333 + 81.0333i −0.355409 + 0.355409i
\(229\) −58.6846 + 58.6846i −0.256265 + 0.256265i −0.823533 0.567268i \(-0.808000\pi\)
0.567268 + 0.823533i \(0.308000\pi\)
\(230\) −10.5077 −0.0456858
\(231\) 171.962i 0.744422i
\(232\) −34.6410 + 34.6410i −0.149315 + 0.149315i
\(233\) 380.669i 1.63377i 0.576798 + 0.816887i \(0.304302\pi\)
−0.576798 + 0.816887i \(0.695698\pi\)
\(234\) 0 0
\(235\) −17.8001 −0.0757450
\(236\) 93.4641 + 93.4641i 0.396034 + 0.396034i
\(237\) 20.5692 0.0867900
\(238\) 258.564i 1.08640i
\(239\) 167.138 + 167.138i 0.699324 + 0.699324i 0.964265 0.264941i \(-0.0853524\pi\)
−0.264941 + 0.964265i \(0.585352\pi\)
\(240\) −8.78461 8.78461i −0.0366025 0.0366025i
\(241\) −2.17691 + 2.17691i −0.00903284 + 0.00903284i −0.711609 0.702576i \(-0.752033\pi\)
0.702576 + 0.711609i \(0.252033\pi\)
\(242\) 15.3538 15.3538i 0.0634456 0.0634456i
\(243\) 15.5885 0.0641500
\(244\) 14.6025i 0.0598465i
\(245\) 56.1718 56.1718i 0.229272 0.229272i
\(246\) 63.2154i 0.256973i
\(247\) 0 0
\(248\) −88.6795 −0.357579
\(249\) −192.315 192.315i −0.772351 0.772351i
\(250\) −118.641 −0.474564
\(251\) 208.708i 0.831505i 0.909478 + 0.415752i \(0.136482\pi\)
−0.909478 + 0.415752i \(0.863518\pi\)
\(252\) 40.9808 + 40.9808i 0.162622 + 0.162622i
\(253\) −30.1154 30.1154i −0.119033 0.119033i
\(254\) 236.846 236.846i 0.932465 0.932465i
\(255\) 41.5692 41.5692i 0.163017 0.163017i
\(256\) 16.0000 0.0625000
\(257\) 74.2205i 0.288796i 0.989520 + 0.144398i \(0.0461245\pi\)
−0.989520 + 0.144398i \(0.953875\pi\)
\(258\) 26.5692 26.5692i 0.102981 0.102981i
\(259\) 357.583i 1.38063i
\(260\) 0 0
\(261\) −51.9615 −0.199086
\(262\) 209.636 + 209.636i 0.800137 + 0.800137i
\(263\) −24.3641 −0.0926393 −0.0463197 0.998927i \(-0.514749\pi\)
−0.0463197 + 0.998927i \(0.514749\pi\)
\(264\) 50.3538i 0.190734i
\(265\) −78.1999 78.1999i −0.295094 0.295094i
\(266\) −319.545 319.545i −1.20130 1.20130i
\(267\) 205.492 205.492i 0.769634 0.769634i
\(268\) −55.4782 + 55.4782i −0.207008 + 0.207008i
\(269\) −175.741 −0.653312 −0.326656 0.945143i \(-0.605922\pi\)
−0.326656 + 0.945143i \(0.605922\pi\)
\(270\) 13.1769i 0.0488034i
\(271\) 197.046 197.046i 0.727105 0.727105i −0.242937 0.970042i \(-0.578111\pi\)
0.970042 + 0.242937i \(0.0781108\pi\)
\(272\) 75.7128i 0.278356i
\(273\) 0 0
\(274\) 161.072 0.587853
\(275\) −158.329 158.329i −0.575743 0.575743i
\(276\) 14.3538 0.0520066
\(277\) 446.985i 1.61366i 0.590782 + 0.806831i \(0.298819\pi\)
−0.590782 + 0.806831i \(0.701181\pi\)
\(278\) 95.7077 + 95.7077i 0.344272 + 0.344272i
\(279\) −66.5096 66.5096i −0.238386 0.238386i
\(280\) 34.6410 34.6410i 0.123718 0.123718i
\(281\) 5.54483 5.54483i 0.0197325 0.0197325i −0.697172 0.716904i \(-0.745558\pi\)
0.716904 + 0.697172i \(0.245558\pi\)
\(282\) 24.3154 0.0862247
\(283\) 16.6462i 0.0588204i 0.999567 + 0.0294102i \(0.00936291\pi\)
−0.999567 + 0.0294102i \(0.990637\pi\)
\(284\) −152.105 + 152.105i −0.535581 + 0.535581i
\(285\) 102.746i 0.360513i
\(286\) 0 0
\(287\) 249.282 0.868579
\(288\) 12.0000 + 12.0000i 0.0416667 + 0.0416667i
\(289\) −69.2769 −0.239712
\(290\) 43.9230i 0.151459i
\(291\) 190.504 + 190.504i 0.654655 + 0.654655i
\(292\) 134.837 + 134.837i 0.461771 + 0.461771i
\(293\) −132.473 + 132.473i −0.452126 + 0.452126i −0.896060 0.443933i \(-0.853583\pi\)
0.443933 + 0.896060i \(0.353583\pi\)
\(294\) −76.7321 + 76.7321i −0.260993 + 0.260993i
\(295\) 118.508 0.401721
\(296\) 104.708i 0.353742i
\(297\) 37.7654 37.7654i 0.127156 0.127156i
\(298\) 80.4205i 0.269867i
\(299\) 0 0
\(300\) 75.4641 0.251547
\(301\) 104.772 + 104.772i 0.348081 + 0.348081i
\(302\) −110.077 −0.364493
\(303\) 323.569i 1.06789i
\(304\) −93.5692 93.5692i −0.307793 0.307793i
\(305\) −9.25764 9.25764i −0.0303529 0.0303529i
\(306\) −56.7846 + 56.7846i −0.185571 + 0.185571i
\(307\) −375.069 + 375.069i −1.22172 + 1.22172i −0.254702 + 0.967020i \(0.581977\pi\)
−0.967020 + 0.254702i \(0.918023\pi\)
\(308\) 198.564 0.644689
\(309\) 144.215i 0.466716i
\(310\) −56.2205 + 56.2205i −0.181357 + 0.181357i
\(311\) 296.238i 0.952535i −0.879300 0.476268i \(-0.841989\pi\)
0.879300 0.476268i \(-0.158011\pi\)
\(312\) 0 0
\(313\) 118.286 0.377910 0.188955 0.981986i \(-0.439490\pi\)
0.188955 + 0.981986i \(0.439490\pi\)
\(314\) −55.4308 55.4308i −0.176531 0.176531i
\(315\) 51.9615 0.164957
\(316\) 23.7513i 0.0751623i
\(317\) 280.708 + 280.708i 0.885513 + 0.885513i 0.994088 0.108575i \(-0.0346288\pi\)
−0.108575 + 0.994088i \(0.534629\pi\)
\(318\) 106.823 + 106.823i 0.335922 + 0.335922i
\(319\) −125.885 + 125.885i −0.394622 + 0.394622i
\(320\) 10.1436 10.1436i 0.0316987 0.0316987i
\(321\) 177.531 0.553055
\(322\) 56.6025i 0.175784i
\(323\) 442.774 442.774i 1.37082 1.37082i
\(324\) 18.0000i 0.0555556i
\(325\) 0 0
\(326\) −289.306 −0.887443
\(327\) −83.4660 83.4660i −0.255248 0.255248i
\(328\) 72.9948 0.222545
\(329\) 95.8846i 0.291442i
\(330\) −31.9230 31.9230i −0.0967365 0.0967365i
\(331\) −100.624 100.624i −0.303999 0.303999i 0.538577 0.842576i \(-0.318962\pi\)
−0.842576 + 0.538577i \(0.818962\pi\)
\(332\) 222.067 222.067i 0.668875 0.668875i
\(333\) −78.5307 + 78.5307i −0.235828 + 0.235828i
\(334\) 228.862 0.685214
\(335\) 70.3435i 0.209981i
\(336\) −47.3205 + 47.3205i −0.140835 + 0.140835i
\(337\) 347.508i 1.03118i 0.856835 + 0.515590i \(0.172427\pi\)
−0.856835 + 0.515590i \(0.827573\pi\)
\(338\) 0 0
\(339\) −78.3154 −0.231019
\(340\) 48.0000 + 48.0000i 0.141176 + 0.141176i
\(341\) −322.259 −0.945041
\(342\) 140.354i 0.410391i
\(343\) 32.0929 + 32.0929i 0.0935654 + 0.0935654i
\(344\) 30.6795 + 30.6795i 0.0891846 + 0.0891846i
\(345\) 9.09996 9.09996i 0.0263767 0.0263767i
\(346\) −268.459 + 268.459i −0.775893 + 0.775893i
\(347\) 437.703 1.26139 0.630695 0.776031i \(-0.282770\pi\)
0.630695 + 0.776031i \(0.282770\pi\)
\(348\) 60.0000i 0.172414i
\(349\) −316.897 + 316.897i −0.908014 + 0.908014i −0.996112 0.0880981i \(-0.971921\pi\)
0.0880981 + 0.996112i \(0.471921\pi\)
\(350\) 297.583i 0.850238i
\(351\) 0 0
\(352\) 58.1436 0.165181
\(353\) 415.037 + 415.037i 1.17574 + 1.17574i 0.980818 + 0.194924i \(0.0624461\pi\)
0.194924 + 0.980818i \(0.437554\pi\)
\(354\) −161.885 −0.457301
\(355\) 192.862i 0.543272i
\(356\) 237.282 + 237.282i 0.666523 + 0.666523i
\(357\) −223.923 223.923i −0.627235 0.627235i
\(358\) −285.779 + 285.779i −0.798267 + 0.798267i
\(359\) −64.2769 + 64.2769i −0.179044 + 0.179044i −0.790939 0.611895i \(-0.790408\pi\)
0.611895 + 0.790939i \(0.290408\pi\)
\(360\) 15.2154 0.0422650
\(361\) 733.400i 2.03158i
\(362\) 177.646 177.646i 0.490735 0.490735i
\(363\) 26.5936i 0.0732606i
\(364\) 0 0
\(365\) 170.967 0.468402
\(366\) 12.6462 + 12.6462i 0.0345524 + 0.0345524i
\(367\) −217.785 −0.593419 −0.296709 0.954968i \(-0.595889\pi\)
−0.296709 + 0.954968i \(0.595889\pi\)
\(368\) 16.5744i 0.0450391i
\(369\) 54.7461 + 54.7461i 0.148364 + 0.148364i
\(370\) 66.3820 + 66.3820i 0.179411 + 0.179411i
\(371\) −421.244 + 421.244i −1.13543 + 1.13543i
\(372\) 76.7987 76.7987i 0.206448 0.206448i
\(373\) −219.606 −0.588757 −0.294378 0.955689i \(-0.595113\pi\)
−0.294378 + 0.955689i \(0.595113\pi\)
\(374\) 275.138i 0.735664i
\(375\) 102.746 102.746i 0.273990 0.273990i
\(376\) 28.0770i 0.0746727i
\(377\) 0 0
\(378\) −70.9808 −0.187780
\(379\) −137.107 137.107i −0.361760 0.361760i 0.502701 0.864461i \(-0.332340\pi\)
−0.864461 + 0.502701i \(0.832340\pi\)
\(380\) −118.641 −0.312213
\(381\) 410.229i 1.07672i
\(382\) −197.321 197.321i −0.516546 0.516546i
\(383\) 137.751 + 137.751i 0.359664 + 0.359664i 0.863689 0.504025i \(-0.168148\pi\)
−0.504025 + 0.863689i \(0.668148\pi\)
\(384\) −13.8564 + 13.8564i −0.0360844 + 0.0360844i
\(385\) 125.885 125.885i 0.326973 0.326973i
\(386\) 29.6987 0.0769397
\(387\) 46.0192i 0.118913i
\(388\) −219.976 + 219.976i −0.566947 + 0.566947i
\(389\) 17.7513i 0.0456331i −0.999740 0.0228166i \(-0.992737\pi\)
0.999740 0.0228166i \(-0.00726337\pi\)
\(390\) 0 0
\(391\) −78.4308 −0.200590
\(392\) −88.6025 88.6025i −0.226027 0.226027i
\(393\) −363.100 −0.923918
\(394\) 213.913i 0.542926i
\(395\) 15.0577 + 15.0577i 0.0381208 + 0.0381208i
\(396\) 43.6077 + 43.6077i 0.110120 + 0.110120i
\(397\) 238.643 238.643i 0.601116 0.601116i −0.339493 0.940609i \(-0.610255\pi\)
0.940609 + 0.339493i \(0.110255\pi\)
\(398\) −22.2154 + 22.2154i −0.0558176 + 0.0558176i
\(399\) 553.468 1.38714
\(400\) 87.1384i 0.217846i
\(401\) −363.415 + 363.415i −0.906273 + 0.906273i −0.995969 0.0896965i \(-0.971410\pi\)
0.0896965 + 0.995969i \(0.471410\pi\)
\(402\) 96.0910i 0.239032i
\(403\) 0 0
\(404\) 373.626 0.924816
\(405\) 11.4115 + 11.4115i 0.0281766 + 0.0281766i
\(406\) 236.603 0.582765
\(407\) 380.505i 0.934902i
\(408\) −65.5692 65.5692i −0.160709 0.160709i
\(409\) −412.026 412.026i −1.00740 1.00740i −0.999972 0.00742680i \(-0.997636\pi\)
−0.00742680 0.999972i \(-0.502364\pi\)
\(410\) 46.2769 46.2769i 0.112870 0.112870i
\(411\) −139.492 + 139.492i −0.339397 + 0.339397i
\(412\) −166.526 −0.404188
\(413\) 638.372i 1.54569i
\(414\) −12.4308 + 12.4308i −0.0300260 + 0.0300260i
\(415\) 281.569i 0.678480i
\(416\) 0 0
\(417\) −165.771 −0.397531
\(418\) −340.028 340.028i −0.813465 0.813465i
\(419\) −782.354 −1.86719 −0.933596 0.358326i \(-0.883348\pi\)
−0.933596 + 0.358326i \(0.883348\pi\)
\(420\) 60.0000i 0.142857i
\(421\) 27.0352 + 27.0352i 0.0642166 + 0.0642166i 0.738486 0.674269i \(-0.235541\pi\)
−0.674269 + 0.738486i \(0.735541\pi\)
\(422\) −64.2013 64.2013i −0.152136 0.152136i
\(423\) −21.0577 + 21.0577i −0.0497818 + 0.0497818i
\(424\) −123.349 + 123.349i −0.290917 + 0.290917i
\(425\) −412.344 −0.970220
\(426\) 263.454i 0.618436i
\(427\) −49.8686 + 49.8686i −0.116788 + 0.116788i
\(428\) 204.995i 0.478960i
\(429\) 0 0
\(430\) 38.9000 0.0904652
\(431\) −445.310 445.310i −1.03320 1.03320i −0.999430 0.0337728i \(-0.989248\pi\)
−0.0337728 0.999430i \(-0.510752\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 237.785i 0.549156i 0.961565 + 0.274578i \(0.0885382\pi\)
−0.961565 + 0.274578i \(0.911462\pi\)
\(434\) 302.846 + 302.846i 0.697802 + 0.697802i
\(435\) −38.0385 38.0385i −0.0874448 0.0874448i
\(436\) 96.3782 96.3782i 0.221051 0.221051i
\(437\) 96.9282 96.9282i 0.221804 0.221804i
\(438\) −233.545 −0.533207
\(439\) 689.463i 1.57053i 0.619160 + 0.785265i \(0.287473\pi\)
−0.619160 + 0.785265i \(0.712527\pi\)
\(440\) 36.8616 36.8616i 0.0837763 0.0837763i
\(441\) 132.904i 0.301369i
\(442\) 0 0
\(443\) −304.028 −0.686294 −0.343147 0.939282i \(-0.611493\pi\)
−0.343147 + 0.939282i \(0.611493\pi\)
\(444\) −90.6795 90.6795i −0.204233 0.204233i
\(445\) 300.862 0.676093
\(446\) 309.061i 0.692963i
\(447\) −69.6462 69.6462i −0.155808 0.155808i
\(448\) −54.6410 54.6410i −0.121967 0.121967i
\(449\) 200.694 200.694i 0.446979 0.446979i −0.447370 0.894349i \(-0.647639\pi\)
0.894349 + 0.447370i \(0.147639\pi\)
\(450\) −65.3538 + 65.3538i −0.145231 + 0.145231i
\(451\) 265.261 0.588163
\(452\) 90.4308i 0.200068i
\(453\) 95.3294 95.3294i 0.210440 0.210440i
\(454\) 91.4256i 0.201378i
\(455\) 0 0
\(456\) 162.067 0.355409
\(457\) 101.519 + 101.519i 0.222141 + 0.222141i 0.809400 0.587258i \(-0.199793\pi\)
−0.587258 + 0.809400i \(0.699793\pi\)
\(458\) 117.369 0.256265
\(459\) 98.3538i 0.214278i
\(460\) 10.5077 + 10.5077i 0.0228429 + 0.0228429i
\(461\) 416.123 + 416.123i 0.902653 + 0.902653i 0.995665 0.0930121i \(-0.0296495\pi\)
−0.0930121 + 0.995665i \(0.529650\pi\)
\(462\) −171.962 + 171.962i −0.372211 + 0.372211i
\(463\) 169.599 169.599i 0.366305 0.366305i −0.499823 0.866128i \(-0.666601\pi\)
0.866128 + 0.499823i \(0.166601\pi\)
\(464\) 69.2820 0.149315
\(465\) 97.3768i 0.209413i
\(466\) 380.669 380.669i 0.816887 0.816887i
\(467\) 732.649i 1.56884i 0.620230 + 0.784420i \(0.287039\pi\)
−0.620230 + 0.784420i \(0.712961\pi\)
\(468\) 0 0
\(469\) 378.923 0.807938
\(470\) 17.8001 + 17.8001i 0.0378725 + 0.0378725i
\(471\) 96.0089 0.203841
\(472\) 186.928i 0.396034i
\(473\) 111.488 + 111.488i 0.235705 + 0.235705i
\(474\) −20.5692 20.5692i −0.0433950 0.0433950i
\(475\) 509.592 509.592i 1.07283 1.07283i
\(476\) 258.564 258.564i 0.543202 0.543202i
\(477\) −185.023 −0.387889
\(478\) 334.277i 0.699324i
\(479\) −261.464 + 261.464i −0.545854 + 0.545854i −0.925239 0.379385i \(-0.876136\pi\)
0.379385 + 0.925239i \(0.376136\pi\)
\(480\) 17.5692i 0.0366025i
\(481\) 0 0
\(482\) 4.35383 0.00903284
\(483\) −49.0192 49.0192i −0.101489 0.101489i
\(484\) −30.7077 −0.0634456
\(485\) 278.918i 0.575088i
\(486\) −15.5885 15.5885i −0.0320750 0.0320750i
\(487\) 137.000 + 137.000i 0.281314 + 0.281314i 0.833633 0.552319i \(-0.186257\pi\)
−0.552319 + 0.833633i \(0.686257\pi\)
\(488\) −14.6025 + 14.6025i −0.0299232 + 0.0299232i
\(489\) 250.547 250.547i 0.512365 0.512365i
\(490\) −112.344 −0.229272
\(491\) 36.9282i 0.0752102i −0.999293 0.0376051i \(-0.988027\pi\)
0.999293 0.0376051i \(-0.0119729\pi\)
\(492\) −63.2154 + 63.2154i −0.128487 + 0.128487i
\(493\) 327.846i 0.665002i
\(494\) 0 0
\(495\) 55.2923 0.111702
\(496\) 88.6795 + 88.6795i 0.178789 + 0.178789i
\(497\) 1038.90 2.09034
\(498\) 384.631i 0.772351i
\(499\) −462.769 462.769i −0.927393 0.927393i 0.0701438 0.997537i \(-0.477654\pi\)
−0.997537 + 0.0701438i \(0.977654\pi\)
\(500\) 118.641 + 118.641i 0.237282 + 0.237282i
\(501\) −198.200 + 198.200i −0.395609 + 0.395609i
\(502\) 208.708 208.708i 0.415752 0.415752i
\(503\) −358.756 −0.713233 −0.356617 0.934251i \(-0.616070\pi\)
−0.356617 + 0.934251i \(0.616070\pi\)
\(504\) 81.9615i 0.162622i
\(505\) 236.869 236.869i 0.469048 0.469048i
\(506\) 60.2309i 0.119033i
\(507\) 0 0
\(508\) −473.692 −0.932465
\(509\) 521.745 + 521.745i 1.02504 + 1.02504i 0.999678 + 0.0253604i \(0.00807334\pi\)
0.0253604 + 0.999678i \(0.491927\pi\)
\(510\) −83.1384 −0.163017
\(511\) 920.955i 1.80226i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 121.550 + 121.550i 0.236940 + 0.236940i
\(514\) 74.2205 74.2205i 0.144398 0.144398i
\(515\) −105.573 + 105.573i −0.204996 + 0.204996i
\(516\) −53.1384 −0.102981
\(517\) 102.031i 0.197352i
\(518\) 357.583 357.583i 0.690315 0.690315i
\(519\) 464.985i 0.895924i
\(520\) 0 0
\(521\) 156.049 0.299518 0.149759 0.988723i \(-0.452150\pi\)
0.149759 + 0.988723i \(0.452150\pi\)
\(522\) 51.9615 + 51.9615i 0.0995431 + 0.0995431i
\(523\) 41.9230 0.0801588 0.0400794 0.999196i \(-0.487239\pi\)
0.0400794 + 0.999196i \(0.487239\pi\)
\(524\) 419.272i 0.800137i
\(525\) −257.715 257.715i −0.490885 0.490885i
\(526\) 24.3641 + 24.3641i 0.0463197 + 0.0463197i
\(527\) −419.636 + 419.636i −0.796273 + 0.796273i
\(528\) −50.3538 + 50.3538i −0.0953671 + 0.0953671i
\(529\) 511.831 0.967544
\(530\) 156.400i 0.295094i
\(531\) 140.196 140.196i 0.264023 0.264023i
\(532\) 639.090i 1.20130i
\(533\) 0 0
\(534\) −410.985 −0.769634
\(535\) 129.962 + 129.962i 0.242919 + 0.242919i
\(536\) 110.956 0.207008
\(537\) 494.985i 0.921759i
\(538\) 175.741 + 175.741i 0.326656 + 0.326656i
\(539\) −321.979 321.979i −0.597364 0.597364i
\(540\) −13.1769 + 13.1769i −0.0244017 + 0.0244017i
\(541\) 4.44298 4.44298i 0.00821253 0.00821253i −0.702989 0.711201i \(-0.748152\pi\)
0.711201 + 0.702989i \(0.248152\pi\)
\(542\) −394.091 −0.727105
\(543\) 307.692i 0.566652i
\(544\) 75.7128 75.7128i 0.139178 0.139178i
\(545\) 122.203i 0.224225i
\(546\) 0 0
\(547\) −101.508 −0.185572 −0.0927859 0.995686i \(-0.529577\pi\)
−0.0927859 + 0.995686i \(0.529577\pi\)
\(548\) −161.072 161.072i −0.293927 0.293927i
\(549\) −21.9038 −0.0398977
\(550\) 316.659i 0.575743i
\(551\) −405.167 405.167i −0.735330 0.735330i
\(552\) −14.3538 14.3538i −0.0260033 0.0260033i
\(553\) 81.1122 81.1122i 0.146677 0.146677i
\(554\) 446.985 446.985i 0.806831 0.806831i
\(555\) −114.977 −0.207166
\(556\) 191.415i 0.344272i
\(557\) −465.846 + 465.846i −0.836348 + 0.836348i −0.988376 0.152028i \(-0.951420\pi\)
0.152028 + 0.988376i \(0.451420\pi\)
\(558\) 133.019i 0.238386i
\(559\) 0 0
\(560\) −69.2820 −0.123718
\(561\) −238.277 238.277i −0.424736 0.424736i
\(562\) −11.0897 −0.0197325
\(563\) 88.7255i 0.157594i −0.996891 0.0787971i \(-0.974892\pi\)
0.996891 0.0787971i \(-0.0251079\pi\)
\(564\) −24.3154 24.3154i −0.0431123 0.0431123i
\(565\) −57.3308 57.3308i −0.101470 0.101470i
\(566\) 16.6462 16.6462i 0.0294102 0.0294102i
\(567\) 61.4711 61.4711i 0.108415 0.108415i
\(568\) 304.210 0.535581
\(569\) 431.569i 0.758470i −0.925300 0.379235i \(-0.876187\pi\)
0.925300 0.379235i \(-0.123813\pi\)
\(570\) 102.746 102.746i 0.180256 0.180256i
\(571\) 959.892i 1.68107i −0.541756 0.840536i \(-0.682240\pi\)
0.541756 0.840536i \(-0.317760\pi\)
\(572\) 0 0
\(573\) 341.769 0.596456
\(574\) −249.282 249.282i −0.434289 0.434289i
\(575\) −90.2666 −0.156985
\(576\) 24.0000i 0.0416667i
\(577\) 313.669 + 313.669i 0.543621 + 0.543621i 0.924588 0.380968i \(-0.124409\pi\)
−0.380968 + 0.924588i \(0.624409\pi\)
\(578\) 69.2769 + 69.2769i 0.119856 + 0.119856i
\(579\) −25.7199 + 25.7199i −0.0444212 + 0.0444212i
\(580\) 43.9230 43.9230i 0.0757294 0.0757294i
\(581\) −1516.74 −2.61057
\(582\) 381.009i 0.654655i
\(583\) −448.246 + 448.246i −0.768861 + 0.768861i
\(584\) 269.674i 0.461771i
\(585\) 0 0
\(586\) 264.946 0.452126
\(587\) 160.004 + 160.004i 0.272579 + 0.272579i 0.830138 0.557559i \(-0.188262\pi\)
−0.557559 + 0.830138i \(0.688262\pi\)
\(588\) 153.464 0.260993
\(589\) 1037.21i 1.76097i
\(590\) −118.508 118.508i −0.200861 0.200861i
\(591\) −185.254 185.254i −0.313458 0.313458i
\(592\) 104.708 104.708i 0.176871 0.176871i
\(593\) −335.229 + 335.229i −0.565311 + 0.565311i −0.930811 0.365500i \(-0.880898\pi\)
0.365500 + 0.930811i \(0.380898\pi\)
\(594\) −75.5307 −0.127156
\(595\) 327.846i 0.551002i
\(596\) 80.4205 80.4205i 0.134934 0.134934i
\(597\) 38.4782i 0.0644526i
\(598\) 0 0
\(599\) 136.908 0.228560 0.114280 0.993449i \(-0.463544\pi\)
0.114280 + 0.993449i \(0.463544\pi\)
\(600\) −75.4641 75.4641i −0.125774 0.125774i
\(601\) −17.5692 −0.0292333 −0.0146167 0.999893i \(-0.504653\pi\)
−0.0146167 + 0.999893i \(0.504653\pi\)
\(602\) 209.545i 0.348081i
\(603\) 83.2173 + 83.2173i 0.138005 + 0.138005i
\(604\) 110.077 + 110.077i 0.182247 + 0.182247i
\(605\) −19.4679 + 19.4679i −0.0321783 + 0.0321783i
\(606\) −323.569 + 323.569i −0.533943 + 0.533943i
\(607\) 844.600 1.39143 0.695716 0.718317i \(-0.255087\pi\)
0.695716 + 0.718317i \(0.255087\pi\)
\(608\) 187.138i 0.307793i
\(609\) −204.904 + 204.904i −0.336459 + 0.336459i
\(610\) 18.5153i 0.0303529i
\(611\) 0 0
\(612\) 113.569 0.185571
\(613\) 445.757 + 445.757i 0.727173 + 0.727173i 0.970056 0.242883i \(-0.0780930\pi\)
−0.242883 + 0.970056i \(0.578093\pi\)
\(614\) 750.137 1.22172
\(615\) 80.1539i 0.130332i
\(616\) −198.564 198.564i −0.322344 0.322344i
\(617\) 78.3397 + 78.3397i 0.126969 + 0.126969i 0.767736 0.640767i \(-0.221383\pi\)
−0.640767 + 0.767736i \(0.721383\pi\)
\(618\) 144.215 144.215i 0.233358 0.233358i
\(619\) 111.970 111.970i 0.180888 0.180888i −0.610854 0.791743i \(-0.709174\pi\)
0.791743 + 0.610854i \(0.209174\pi\)
\(620\) 112.441 0.181357
\(621\) 21.5307i 0.0346711i
\(622\) −296.238 + 296.238i −0.476268 + 0.476268i
\(623\) 1620.67i 2.60139i
\(624\) 0 0
\(625\) −394.184 −0.630695
\(626\) −118.286 118.286i −0.188955 0.188955i
\(627\) 588.946 0.939308
\(628\) 110.862i 0.176531i
\(629\) 495.482 + 495.482i 0.787730 + 0.787730i
\(630\) −51.9615 51.9615i −0.0824786 0.0824786i
\(631\) −773.445 + 773.445i −1.22575 + 1.22575i −0.260187 + 0.965558i \(0.583784\pi\)
−0.965558 + 0.260187i \(0.916216\pi\)
\(632\) 23.7513 23.7513i 0.0375812 0.0375812i
\(633\) 111.200 0.175671
\(634\) 561.415i 0.885513i
\(635\) −300.309 + 300.309i −0.472927 + 0.472927i
\(636\) 213.646i 0.335922i
\(637\) 0 0
\(638\) 251.769 0.394622
\(639\) 228.158 + 228.158i 0.357054 + 0.357054i
\(640\) −20.2872 −0.0316987
\(641\) 408.613i 0.637462i 0.947845 + 0.318731i \(0.103257\pi\)
−0.947845 + 0.318731i \(0.896743\pi\)
\(642\) −177.531 177.531i −0.276528 0.276528i
\(643\) −316.730 316.730i −0.492582 0.492582i 0.416537 0.909119i \(-0.363244\pi\)
−0.909119 + 0.416537i \(0.863244\pi\)
\(644\) 56.6025 56.6025i 0.0878921 0.0878921i
\(645\) −33.6884 + 33.6884i −0.0522301 + 0.0522301i
\(646\) −885.549 −1.37082
\(647\) 322.841i 0.498981i −0.968377 0.249491i \(-0.919737\pi\)
0.968377 0.249491i \(-0.0802632\pi\)
\(648\) 18.0000 18.0000i 0.0277778 0.0277778i
\(649\) 679.292i 1.04668i
\(650\) 0 0
\(651\) −524.545 −0.805752
\(652\) 289.306 + 289.306i 0.443722 + 0.443722i
\(653\) −1020.85 −1.56332 −0.781660 0.623704i \(-0.785627\pi\)
−0.781660 + 0.623704i \(0.785627\pi\)
\(654\) 166.932i 0.255248i
\(655\) −265.808 265.808i −0.405813 0.405813i
\(656\) −72.9948 72.9948i −0.111273 0.111273i
\(657\) 202.256 202.256i 0.307847 0.307847i
\(658\) 95.8846 95.8846i 0.145721 0.145721i
\(659\) 227.685 0.345500 0.172750 0.984966i \(-0.444735\pi\)
0.172750 + 0.984966i \(0.444735\pi\)
\(660\) 63.8461i 0.0967365i
\(661\) 107.012 107.012i 0.161894 0.161894i −0.621511 0.783405i \(-0.713481\pi\)
0.783405 + 0.621511i \(0.213481\pi\)
\(662\) 201.247i 0.303999i
\(663\) 0 0
\(664\) −444.133 −0.668875
\(665\) 405.167 + 405.167i 0.609273 + 0.609273i
\(666\) 157.061 0.235828
\(667\) 71.7691i 0.107600i
\(668\) −228.862 228.862i −0.342607 0.342607i
\(669\) 267.655 + 267.655i 0.400082 + 0.400082i
\(670\) 70.3435 70.3435i 0.104990 0.104990i
\(671\) −53.0653 + 53.0653i −0.0790838 + 0.0790838i
\(672\) 94.6410 0.140835
\(673\) 707.991i 1.05199i −0.850487 0.525996i \(-0.823693\pi\)
0.850487 0.525996i \(-0.176307\pi\)
\(674\) 347.508 347.508i 0.515590 0.515590i
\(675\) 113.196i 0.167698i
\(676\) 0 0
\(677\) −754.592 −1.11461 −0.557306 0.830307i \(-0.688165\pi\)
−0.557306 + 0.830307i \(0.688165\pi\)
\(678\) 78.3154 + 78.3154i 0.115509 + 0.115509i
\(679\) 1502.46 2.21276
\(680\) 96.0000i 0.141176i
\(681\) 79.1769 + 79.1769i 0.116266 + 0.116266i
\(682\) 322.259 + 322.259i 0.472521 + 0.472521i
\(683\) 101.678 101.678i 0.148870 0.148870i −0.628743 0.777613i \(-0.716430\pi\)
0.777613 + 0.628743i \(0.216430\pi\)
\(684\) −140.354 + 140.354i −0.205196 + 0.205196i
\(685\) −204.231 −0.298147
\(686\) 64.1858i 0.0935654i
\(687\) −101.645 + 101.645i −0.147955 + 0.147955i
\(688\) 61.3590i 0.0891846i
\(689\) 0 0
\(690\) −18.1999 −0.0263767
\(691\) −385.030 385.030i −0.557207 0.557207i 0.371304 0.928511i \(-0.378911\pi\)
−0.928511 + 0.371304i \(0.878911\pi\)
\(692\) 536.918 0.775893
\(693\) 297.846i 0.429792i
\(694\) −437.703 437.703i −0.630695 0.630695i
\(695\) −121.352 121.352i −0.174608 0.174608i
\(696\) −60.0000 + 60.0000i −0.0862069 + 0.0862069i
\(697\) 345.415 345.415i 0.495574 0.495574i
\(698\) 633.794 0.908014
\(699\) 659.338i 0.943259i
\(700\) 297.583 297.583i 0.425119 0.425119i
\(701\) 568.344i 0.810761i −0.914148 0.405381i \(-0.867139\pi\)
0.914148 0.405381i \(-0.132861\pi\)
\(702\) 0 0
\(703\) −1224.68 −1.74207
\(704\) −58.1436 58.1436i −0.0825903 0.0825903i
\(705\) −30.8306 −0.0437314
\(706\) 830.074i 1.17574i
\(707\) −1275.95 1275.95i −1.80475 1.80475i
\(708\) 161.885 + 161.885i 0.228651 + 0.228651i
\(709\) −259.419 + 259.419i −0.365894 + 0.365894i −0.865977 0.500084i \(-0.833303\pi\)
0.500084 + 0.865977i \(0.333303\pi\)
\(710\) 192.862 192.862i 0.271636 0.271636i
\(711\) 35.6269 0.0501082
\(712\) 474.564i 0.666523i
\(713\) −91.8629 + 91.8629i −0.128840 + 0.128840i
\(714\) 447.846i 0.627235i
\(715\) 0 0
\(716\) 571.559 0.798267
\(717\) 289.492 + 289.492i 0.403755 + 0.403755i
\(718\) 128.554 0.179044
\(719\) 263.520i 0.366510i −0.983065 0.183255i \(-0.941337\pi\)
0.983065 0.183255i \(-0.0586633\pi\)
\(720\) −15.2154 15.2154i −0.0211325 0.0211325i
\(721\) 568.695 + 568.695i 0.788759 + 0.788759i
\(722\) 733.400 733.400i 1.01579 1.01579i
\(723\) −3.77053 + 3.77053i −0.00521511 + 0.00521511i
\(724\) −355.292 −0.490735
\(725\) 377.321i 0.520442i
\(726\) 26.5936 26.5936i 0.0366303 0.0366303i
\(727\) 878.415i 1.20827i −0.796880 0.604137i \(-0.793518\pi\)
0.796880 0.604137i \(-0.206482\pi\)
\(728\) 0 0
\(729\) 27.0000 0.0370370
\(730\) −170.967 170.967i −0.234201 0.234201i
\(731\) 290.354 0.397201
\(732\) 25.2923i 0.0345524i
\(733\) 146.627 + 146.627i 0.200037 + 0.200037i 0.800016 0.599979i \(-0.204824\pi\)
−0.599979 + 0.800016i \(0.704824\pi\)
\(734\) 217.785 + 217.785i 0.296709 + 0.296709i
\(735\) 97.2923 97.2923i 0.132371 0.132371i
\(736\) 16.5744 16.5744i 0.0225195 0.0225195i
\(737\) 403.213 0.547100
\(738\) 109.492i 0.148364i
\(739\) 455.161 455.161i 0.615915 0.615915i −0.328566 0.944481i \(-0.606565\pi\)
0.944481 + 0.328566i \(0.106565\pi\)
\(740\) 132.764i 0.179411i
\(741\) 0 0
\(742\) 842.487 1.13543
\(743\) 9.63963 + 9.63963i 0.0129739 + 0.0129739i 0.713564 0.700590i \(-0.247080\pi\)
−0.700590 + 0.713564i \(0.747080\pi\)
\(744\) −153.597 −0.206448
\(745\) 101.969i 0.136871i
\(746\) 219.606 + 219.606i 0.294378 + 0.294378i
\(747\) −333.100 333.100i −0.445917 0.445917i
\(748\) 275.138 275.138i 0.367832 0.367832i
\(749\) 700.070 700.070i 0.934673 0.934673i
\(750\) −205.492 −0.273990
\(751\) 160.077i 0.213152i −0.994305 0.106576i \(-0.966011\pi\)
0.994305 0.106576i \(-0.0339887\pi\)
\(752\) 28.0770 28.0770i 0.0373364 0.0373364i
\(753\) 361.492i 0.480069i
\(754\) 0 0
\(755\) 139.572 0.184864
\(756\) 70.9808 + 70.9808i 0.0938899 + 0.0938899i
\(757\) −1467.38 −1.93842 −0.969210 0.246234i \(-0.920807\pi\)
−0.969210 + 0.246234i \(0.920807\pi\)
\(758\) 274.214i 0.361760i
\(759\) −52.1615 52.1615i −0.0687239 0.0687239i
\(760\) 118.641 + 118.641i 0.156107 + 0.156107i
\(761\) −129.367 + 129.367i −0.169995 + 0.169995i −0.786977 0.616982i \(-0.788355\pi\)
0.616982 + 0.786977i \(0.288355\pi\)
\(762\) 410.229 410.229i 0.538359 0.538359i
\(763\) −658.275 −0.862746
\(764\) 394.641i 0.516546i
\(765\) 72.0000 72.0000i 0.0941176 0.0941176i
\(766\) 275.503i 0.359664i
\(767\) 0 0
\(768\) 27.7128 0.0360844
\(769\) −961.315 961.315i −1.25008 1.25008i −0.955681 0.294404i \(-0.904879\pi\)
−0.294404 0.955681i \(-0.595121\pi\)
\(770\) −251.769 −0.326973
\(771\) 128.554i 0.166736i
\(772\) −29.6987 29.6987i −0.0384699 0.0384699i
\(773\) 692.232 + 692.232i 0.895513 + 0.895513i 0.995035 0.0995220i \(-0.0317314\pi\)
−0.0995220 + 0.995035i \(0.531731\pi\)
\(774\) 46.0192 46.0192i 0.0594564 0.0594564i
\(775\) −482.962 + 482.962i −0.623177 + 0.623177i
\(776\) 439.951 0.566947
\(777\) 619.352i 0.797107i
\(778\) −17.7513 + 17.7513i −0.0228166 + 0.0228166i
\(779\) 853.759i 1.09597i
\(780\) 0 0
\(781\) 1105.49 1.41548
\(782\) 78.4308 + 78.4308i 0.100295 + 0.100295i
\(783\) −90.0000 −0.114943
\(784\) 177.205i 0.226027i
\(785\) 70.2834 + 70.2834i 0.0895330 + 0.0895330i
\(786\) 363.100 + 363.100i 0.461959 + 0.461959i
\(787\) −83.4533 + 83.4533i −0.106040 + 0.106040i −0.758136 0.652096i \(-0.773890\pi\)
0.652096 + 0.758136i \(0.273890\pi\)
\(788\) 213.913 213.913i 0.271463 0.271463i
\(789\) −42.1999 −0.0534853
\(790\) 30.1154i 0.0381208i
\(791\) −308.827 + 308.827i −0.390426 + 0.390426i
\(792\) 87.2154i 0.110120i
\(793\) 0 0
\(794\) −477.286 −0.601116
\(795\) −135.446 135.446i −0.170373 0.170373i
\(796\) 44.4308 0.0558176
\(797\) 567.118i 0.711566i −0.934569 0.355783i \(-0.884214\pi\)
0.934569 0.355783i \(-0.115786\pi\)
\(798\) −553.468 553.468i −0.693569 0.693569i
\(799\) 132.862 + 132.862i 0.166285 + 0.166285i
\(800\) 87.1384 87.1384i 0.108923 0.108923i
\(801\) 355.923 355.923i 0.444348 0.444348i
\(802\) 726.831 0.906273
\(803\) 979.990i 1.22041i
\(804\) −96.0910 + 96.0910i −0.119516 + 0.119516i
\(805\) 71.7691i 0.0891542i
\(806\) 0 0
\(807\) −304.392 −0.377190
\(808\) −373.626 373.626i −0.462408 0.462408i
\(809\) 87.4462 0.108092 0.0540459 0.998538i \(-0.482788\pi\)
0.0540459 + 0.998538i \(0.482788\pi\)
\(810\) 22.8231i 0.0281766i
\(811\) 519.193 + 519.193i 0.640189 + 0.640189i 0.950602 0.310413i \(-0.100467\pi\)
−0.310413 + 0.950602i \(0.600467\pi\)
\(812\) −236.603 236.603i −0.291382 0.291382i
\(813\) 341.293 341.293i 0.419794 0.419794i
\(814\) 380.505 380.505i 0.467451 0.467451i
\(815\) 366.826 0.450093
\(816\) 131.138i 0.160709i
\(817\) −358.832 + 358.832i −0.439207 + 0.439207i
\(818\) 824.053i 1.00740i
\(819\) 0 0
\(820\) −92.5538 −0.112870
\(821\) −406.750 406.750i −0.495432 0.495432i 0.414580 0.910013i \(-0.363928\pi\)
−0.910013 + 0.414580i \(0.863928\pi\)
\(822\) 278.985 0.339397
\(823\) 329.169i 0.399963i 0.979800 + 0.199981i \(0.0640882\pi\)
−0.979800 + 0.199981i \(0.935912\pi\)
\(824\) 166.526 + 166.526i 0.202094 + 0.202094i
\(825\) −274.235 274.235i −0.332406 0.332406i
\(826\) −638.372 + 638.372i −0.772847 + 0.772847i
\(827\) −514.410 + 514.410i −0.622020 + 0.622020i −0.946048 0.324028i \(-0.894963\pi\)
0.324028 + 0.946048i \(0.394963\pi\)
\(828\) 24.8616 0.0300260
\(829\) 943.092i 1.13763i −0.822467 0.568813i \(-0.807403\pi\)
0.822467 0.568813i \(-0.192597\pi\)
\(830\) −281.569 + 281.569i −0.339240 + 0.339240i
\(831\) 774.200i 0.931649i
\(832\) 0 0
\(833\) −838.543 −1.00665
\(834\) 165.771 + 165.771i 0.198766 + 0.198766i
\(835\) −290.185 −0.347527
\(836\) 680.056i 0.813465i
\(837\) −115.198 115.198i −0.137632 0.137632i
\(838\) 782.354 + 782.354i 0.933596 + 0.933596i
\(839\) 556.070 556.070i 0.662778 0.662778i −0.293256 0.956034i \(-0.594739\pi\)
0.956034 + 0.293256i \(0.0947389\pi\)
\(840\) 60.0000 60.0000i 0.0714286 0.0714286i
\(841\) −541.000 −0.643282
\(842\) 54.0704i 0.0642166i
\(843\) 9.60392 9.60392i 0.0113926 0.0113926i
\(844\) 128.403i 0.152136i
\(845\) 0 0
\(846\) 42.1154 0.0497818
\(847\) 104.869 + 104.869i 0.123812 + 0.123812i
\(848\) 246.697 0.290917
\(849\) 28.8320i 0.0339600i
\(850\) 412.344 + 412.344i 0.485110 + 0.485110i
\(851\) 108.466 + 108.466i 0.127458 + 0.127458i
\(852\) −263.454 + 263.454i −0.309218 + 0.309218i
\(853\) −472.527 + 472.527i −0.553960 + 0.553960i −0.927581 0.373622i \(-0.878116\pi\)
0.373622 + 0.927581i \(0.378116\pi\)
\(854\) 99.7372 0.116788
\(855\) 177.962i 0.208142i
\(856\) 204.995 204.995i 0.239480 0.239480i
\(857\) 436.543i 0.509386i −0.967022 0.254693i \(-0.918026\pi\)
0.967022 0.254693i \(-0.0819743\pi\)
\(858\) 0 0
\(859\) −1238.40 −1.44167 −0.720837 0.693104i \(-0.756243\pi\)
−0.720837 + 0.693104i \(0.756243\pi\)
\(860\) −38.9000 38.9000i −0.0452326 0.0452326i
\(861\) 431.769 0.501474
\(862\) 890.620i 1.03320i
\(863\) −729.373 729.373i −0.845160 0.845160i 0.144365 0.989525i \(-0.453886\pi\)
−0.989525 + 0.144365i \(0.953886\pi\)
\(864\) 20.7846 + 20.7846i 0.0240563 + 0.0240563i
\(865\) 340.392 340.392i 0.393517 0.393517i
\(866\) 237.785 237.785i 0.274578 0.274578i
\(867\) −119.991 −0.138398
\(868\) 605.692i 0.697802i
\(869\) 86.3116 86.3116i 0.0993229 0.0993229i
\(870\) 76.0770i 0.0874448i
\(871\) 0 0
\(872\) −192.756 −0.221051
\(873\) 329.963 + 329.963i 0.377965 + 0.377965i
\(874\) −193.856 −0.221804
\(875\) 810.333i 0.926095i
\(876\) 233.545 + 233.545i 0.266604 + 0.266604i
\(877\) 962.069 + 962.069i 1.09700 + 1.09700i 0.994760 + 0.102240i \(0.0326011\pi\)
0.102240 + 0.994760i \(0.467399\pi\)
\(878\) 689.463 689.463i 0.785265 0.785265i
\(879\) −229.450 + 229.450i −0.261035 + 0.261035i
\(880\) −73.7231 −0.0837763
\(881\) 1563.66i 1.77487i 0.460929 + 0.887437i \(0.347516\pi\)
−0.460929 + 0.887437i \(0.652484\pi\)
\(882\) −132.904 + 132.904i −0.150685 + 0.150685i
\(883\) 452.723i 0.512710i −0.966583 0.256355i \(-0.917478\pi\)
0.966583 0.256355i \(-0.0825216\pi\)
\(884\) 0 0
\(885\) 205.261 0.231934
\(886\) 304.028 + 304.028i 0.343147 + 0.343147i
\(887\) 910.939 1.02699 0.513494 0.858093i \(-0.328351\pi\)
0.513494 + 0.858093i \(0.328351\pi\)
\(888\) 181.359i 0.204233i
\(889\) 1617.69 + 1617.69i 1.81967 + 1.81967i
\(890\) −300.862 300.862i −0.338047 0.338047i
\(891\) 65.4115 65.4115i 0.0734136 0.0734136i
\(892\) −309.061 + 309.061i −0.346481 + 0.346481i
\(893\) −328.392 −0.367741
\(894\) 139.292i 0.155808i
\(895\) 362.354 362.354i 0.404865 0.404865i
\(896\) 109.282i 0.121967i
\(897\) 0 0
\(898\) −401.387 −0.446979
\(899\) 383.993 + 383.993i 0.427134 + 0.427134i
\(900\) 130.708 0.145231
\(901\) 1167.38i 1.29565i
\(902\) −265.261 265.261i −0.294081 0.294081i
\(903\) 181.471 + 181.471i 0.200965 + 0.200965i
\(904\) −90.4308 + 90.4308i −0.100034 + 0.100034i
\(905\) −225.246 + 225.246i −0.248891 + 0.248891i
\(906\) −190.659 −0.210440
\(907\) 445.138i 0.490781i 0.969424 + 0.245391i \(0.0789162\pi\)
−0.969424 + 0.245391i \(0.921084\pi\)
\(908\) −91.4256 + 91.4256i −0.100689 + 0.100689i
\(909\) 560.438i 0.616544i
\(910\) 0 0
\(911\) 717.233 0.787303 0.393652 0.919260i \(-0.371212\pi\)
0.393652 + 0.919260i \(0.371212\pi\)
\(912\) −162.067 162.067i −0.177705 0.177705i
\(913\) −1613.97 −1.76776
\(914\) 203.037i 0.222141i
\(915\) −16.0347 16.0347i −0.0175243 0.0175243i
\(916\) −117.369 117.369i −0.128132 0.128132i
\(917\) −1431.84 + 1431.84i −1.56144 + 1.56144i
\(918\) −98.3538 + 98.3538i −0.107139 + 0.107139i
\(919\) 743.138 0.808638 0.404319 0.914618i \(-0.367509\pi\)
0.404319 + 0.914618i \(0.367509\pi\)
\(920\) 21.0155i 0.0228429i
\(921\) −649.638 + 649.638i −0.705361 + 0.705361i
\(922\) 832.246i 0.902653i
\(923\) 0 0
\(924\) 343.923 0.372211
\(925\) 570.254 + 570.254i 0.616491 + 0.616491i
\(926\) −339.199 −0.366305
\(927\) 249.788i 0.269459i
\(928\) −69.2820 69.2820i −0.0746574 0.0746574i
\(929\) 1042.54 + 1042.54i 1.12222 + 1.12222i 0.991407 + 0.130814i \(0.0417592\pi\)
0.130814 + 0.991407i \(0.458241\pi\)
\(930\) −97.3768 + 97.3768i −0.104706 + 0.104706i
\(931\) 1036.31 1036.31i 1.11311 1.11311i
\(932\) −761.338 −0.816887
\(933\) 513.100i 0.549946i
\(934\) 732.649 732.649i 0.784420 0.784420i
\(935\) 348.862i 0.373114i
\(936\) 0 0
\(937\) −172.477 −0.184073 −0.0920367 0.995756i \(-0.529338\pi\)
−0.0920367 + 0.995756i \(0.529338\pi\)
\(938\) −378.923 378.923i −0.403969 0.403969i
\(939\) 204.877 0.218186
\(940\) 35.6001i 0.0378725i
\(941\) −145.055 145.055i −0.154150 0.154150i 0.625819 0.779969i \(-0.284765\pi\)
−0.779969 + 0.625819i \(0.784765\pi\)
\(942\) −96.0089 96.0089i −0.101920 0.101920i
\(943\) 75.6152 75.6152i 0.0801858 0.0801858i
\(944\) −186.928 + 186.928i −0.198017 + 0.198017i
\(945\) 90.0000 0.0952381
\(946\) 222.977i 0.235705i
\(947\) −487.474 + 487.474i −0.514757 + 0.514757i −0.915980 0.401224i \(-0.868585\pi\)
0.401224 + 0.915980i \(0.368585\pi\)
\(948\) 41.1384i 0.0433950i
\(949\) 0 0
\(950\) −1019.18 −1.07283
\(951\) 486.200 + 486.200i 0.511251 + 0.511251i
\(952\) −517.128 −0.543202
\(953\) 1206.62i 1.26613i 0.774100 + 0.633063i \(0.218203\pi\)
−0.774100 + 0.633063i \(0.781797\pi\)
\(954\) 185.023 + 185.023i 0.193944 + 0.193944i
\(955\) 250.192 + 250.192i 0.261982 + 0.261982i
\(956\) −334.277 + 334.277i −0.349662 + 0.349662i
\(957\) −218.038 + 218.038i −0.227835 + 0.227835i
\(958\) 522.928 0.545854
\(959\) 1100.14i 1.14718i
\(960\) 17.5692 17.5692i 0.0183013 0.0183013i
\(961\) 22.0065i 0.0228996i
\(962\) 0 0
\(963\) 307.492 0.319307
\(964\) −4.35383 4.35383i −0.00451642 0.00451642i
\(965\) −37.6565 −0.0390223
\(966\) 98.0385i 0.101489i
\(967\) 169.831 + 169.831i 0.175626 + 0.175626i 0.789446 0.613820i \(-0.210368\pi\)
−0.613820 + 0.789446i \(0.710368\pi\)
\(968\) 30.7077 + 30.7077i 0.0317228 + 0.0317228i
\(969\) 766.908 766.908i 0.791442 0.791442i
\(970\) 278.918 278.918i 0.287544 0.287544i
\(971\) 747.700 0.770031 0.385015 0.922910i \(-0.374196\pi\)
0.385015 + 0.922910i \(0.374196\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) −653.695 + 653.695i −0.671835 + 0.671835i
\(974\) 274.000i 0.281314i
\(975\) 0 0
\(976\) 29.2051 0.0299232
\(977\) 152.967 + 152.967i 0.156568 + 0.156568i 0.781044 0.624476i \(-0.214687\pi\)
−0.624476 + 0.781044i \(0.714687\pi\)
\(978\) −501.093 −0.512365
\(979\) 1724.55i 1.76155i
\(980\) 112.344 + 112.344i 0.114636 + 0.114636i
\(981\) −144.567 144.567i −0.147367 0.147367i
\(982\) −36.9282 + 36.9282i −0.0376051 + 0.0376051i
\(983\) −1367.93 + 1367.93i −1.39158 + 1.39158i −0.569801 + 0.821783i \(0.692980\pi\)
−0.821783 + 0.569801i \(0.807020\pi\)
\(984\) 126.431 0.128487
\(985\) 271.230i 0.275361i
\(986\) 327.846 327.846i 0.332501 0.332501i
\(987\) 166.077i 0.168264i
\(988\) 0 0
\(989\) 63.5617 0.0642686
\(990\) −55.2923 55.2923i −0.0558509 0.0558509i
\(991\) −1871.26 −1.88826 −0.944128 0.329579i \(-0.893093\pi\)
−0.944128 + 0.329579i \(0.893093\pi\)
\(992\) 177.359i 0.178789i
\(993\) −174.285 174.285i −0.175514 0.175514i
\(994\) −1038.90 1038.90i −1.04517 1.04517i
\(995\) 28.1680 28.1680i 0.0283095 0.0283095i
\(996\) 384.631 384.631i 0.386175 0.386175i
\(997\) 1537.17 1.54179 0.770897 0.636960i \(-0.219808\pi\)
0.770897 + 0.636960i \(0.219808\pi\)
\(998\) 925.538i 0.927393i
\(999\) −136.019 + 136.019i −0.136155 + 0.136155i
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 1014.3.f.d.775.2 4
13.4 even 6 78.3.l.a.37.1 yes 4
13.5 odd 4 inner 1014.3.f.d.577.2 4
13.8 odd 4 1014.3.f.e.577.2 4
13.11 odd 12 78.3.l.a.19.1 4
13.12 even 2 1014.3.f.e.775.2 4
39.11 even 12 234.3.bb.c.19.1 4
39.17 odd 6 234.3.bb.c.37.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.l.a.19.1 4 13.11 odd 12
78.3.l.a.37.1 yes 4 13.4 even 6
234.3.bb.c.19.1 4 39.11 even 12
234.3.bb.c.37.1 4 39.17 odd 6
1014.3.f.d.577.2 4 13.5 odd 4 inner
1014.3.f.d.775.2 4 1.1 even 1 trivial
1014.3.f.e.577.2 4 13.8 odd 4
1014.3.f.e.775.2 4 13.12 even 2