Properties

Label 1155.2.k.a.769.3
Level $1155$
Weight $2$
Character 1155.769
Analytic conductor $9.223$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(769,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.769");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.k (of order \(2\), degree \(1\), 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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 769.3
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.a.769.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.52930 q^{2} -1.00000 q^{3} +4.39737 q^{4} +(1.63381 - 1.52665i) q^{5} +2.52930 q^{6} +(-2.48590 - 0.905718i) q^{7} -6.06368 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.52930 q^{2} -1.00000 q^{3} +4.39737 q^{4} +(1.63381 - 1.52665i) q^{5} +2.52930 q^{6} +(-2.48590 - 0.905718i) q^{7} -6.06368 q^{8} +1.00000 q^{9} +(-4.13240 + 3.86136i) q^{10} +(-2.13976 + 2.53405i) q^{11} -4.39737 q^{12} +5.27466i q^{13} +(6.28758 + 2.29084i) q^{14} +(-1.63381 + 1.52665i) q^{15} +6.54214 q^{16} -5.11968i q^{17} -2.52930 q^{18} +4.28158 q^{19} +(7.18448 - 6.71325i) q^{20} +(2.48590 + 0.905718i) q^{21} +(5.41211 - 6.40938i) q^{22} +1.22635i q^{23} +6.06368 q^{24} +(0.338675 - 4.98852i) q^{25} -13.3412i q^{26} -1.00000 q^{27} +(-10.9314 - 3.98278i) q^{28} -8.66218i q^{29} +(4.13240 - 3.86136i) q^{30} +3.16260i q^{31} -4.41970 q^{32} +(2.13976 - 2.53405i) q^{33} +12.9492i q^{34} +(-5.44420 + 2.31532i) q^{35} +4.39737 q^{36} +3.79008i q^{37} -10.8294 q^{38} -5.27466i q^{39} +(-9.90691 + 9.25713i) q^{40} -5.95804 q^{41} +(-6.28758 - 2.29084i) q^{42} +7.87280 q^{43} +(-9.40934 + 11.1432i) q^{44} +(1.63381 - 1.52665i) q^{45} -3.10180i q^{46} +6.85157 q^{47} -6.54214 q^{48} +(5.35935 + 4.50304i) q^{49} +(-0.856613 + 12.6175i) q^{50} +5.11968i q^{51} +23.1947i q^{52} -12.4608i q^{53} +2.52930 q^{54} +(0.372642 + 7.40683i) q^{55} +(15.0737 + 5.49199i) q^{56} -4.28158 q^{57} +21.9093i q^{58} -1.69675i q^{59} +(-7.18448 + 6.71325i) q^{60} -7.32231 q^{61} -7.99918i q^{62} +(-2.48590 - 0.905718i) q^{63} -1.90553 q^{64} +(8.05257 + 8.61780i) q^{65} +(-5.41211 + 6.40938i) q^{66} +1.64438i q^{67} -22.5131i q^{68} -1.22635i q^{69} +(13.7700 - 5.85615i) q^{70} -4.95049 q^{71} -6.06368 q^{72} -13.6548i q^{73} -9.58626i q^{74} +(-0.338675 + 4.98852i) q^{75} +18.8277 q^{76} +(7.61436 - 4.36136i) q^{77} +13.3412i q^{78} -2.01901i q^{79} +(10.6886 - 9.98757i) q^{80} +1.00000 q^{81} +15.0697 q^{82} +3.14880i q^{83} +(10.9314 + 3.98278i) q^{84} +(-7.81596 - 8.36459i) q^{85} -19.9127 q^{86} +8.66218i q^{87} +(12.9748 - 15.3657i) q^{88} +4.88199i q^{89} +(-4.13240 + 3.86136i) q^{90} +(4.77736 - 13.1123i) q^{91} +5.39270i q^{92} -3.16260i q^{93} -17.3297 q^{94} +(6.99530 - 6.53648i) q^{95} +4.41970 q^{96} -15.6959 q^{97} +(-13.5554 - 11.3896i) q^{98} +(-2.13976 + 2.53405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52930 −1.78849 −0.894244 0.447581i \(-0.852286\pi\)
−0.894244 + 0.447581i \(0.852286\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.39737 2.19869
\(5\) 1.63381 1.52665i 0.730662 0.682739i
\(6\) 2.52930 1.03258
\(7\) −2.48590 0.905718i −0.939580 0.342329i
\(8\) −6.06368 −2.14384
\(9\) 1.00000 0.333333
\(10\) −4.13240 + 3.86136i −1.30678 + 1.22107i
\(11\) −2.13976 + 2.53405i −0.645163 + 0.764045i
\(12\) −4.39737 −1.26941
\(13\) 5.27466i 1.46293i 0.681880 + 0.731464i \(0.261163\pi\)
−0.681880 + 0.731464i \(0.738837\pi\)
\(14\) 6.28758 + 2.29084i 1.68043 + 0.612251i
\(15\) −1.63381 + 1.52665i −0.421848 + 0.394180i
\(16\) 6.54214 1.63554
\(17\) 5.11968i 1.24171i −0.783927 0.620853i \(-0.786787\pi\)
0.783927 0.620853i \(-0.213213\pi\)
\(18\) −2.52930 −0.596162
\(19\) 4.28158 0.982263 0.491131 0.871085i \(-0.336583\pi\)
0.491131 + 0.871085i \(0.336583\pi\)
\(20\) 7.18448 6.71325i 1.60650 1.50113i
\(21\) 2.48590 + 0.905718i 0.542467 + 0.197644i
\(22\) 5.41211 6.40938i 1.15387 1.36648i
\(23\) 1.22635i 0.255711i 0.991793 + 0.127855i \(0.0408093\pi\)
−0.991793 + 0.127855i \(0.959191\pi\)
\(24\) 6.06368 1.23774
\(25\) 0.338675 4.98852i 0.0677351 0.997703i
\(26\) 13.3412i 2.61643i
\(27\) −1.00000 −0.192450
\(28\) −10.9314 3.98278i −2.06584 0.752675i
\(29\) 8.66218i 1.60853i −0.594274 0.804263i \(-0.702560\pi\)
0.594274 0.804263i \(-0.297440\pi\)
\(30\) 4.13240 3.86136i 0.754470 0.704985i
\(31\) 3.16260i 0.568020i 0.958821 + 0.284010i \(0.0916649\pi\)
−0.958821 + 0.284010i \(0.908335\pi\)
\(32\) −4.41970 −0.781300
\(33\) 2.13976 2.53405i 0.372485 0.441122i
\(34\) 12.9492i 2.22077i
\(35\) −5.44420 + 2.31532i −0.920237 + 0.391361i
\(36\) 4.39737 0.732896
\(37\) 3.79008i 0.623085i 0.950232 + 0.311543i \(0.100846\pi\)
−0.950232 + 0.311543i \(0.899154\pi\)
\(38\) −10.8294 −1.75676
\(39\) 5.27466i 0.844622i
\(40\) −9.90691 + 9.25713i −1.56642 + 1.46368i
\(41\) −5.95804 −0.930489 −0.465245 0.885182i \(-0.654034\pi\)
−0.465245 + 0.885182i \(0.654034\pi\)
\(42\) −6.28758 2.29084i −0.970195 0.353484i
\(43\) 7.87280 1.20059 0.600296 0.799778i \(-0.295050\pi\)
0.600296 + 0.799778i \(0.295050\pi\)
\(44\) −9.40934 + 11.1432i −1.41851 + 1.67990i
\(45\) 1.63381 1.52665i 0.243554 0.227580i
\(46\) 3.10180i 0.457335i
\(47\) 6.85157 0.999404 0.499702 0.866198i \(-0.333443\pi\)
0.499702 + 0.866198i \(0.333443\pi\)
\(48\) −6.54214 −0.944277
\(49\) 5.35935 + 4.50304i 0.765621 + 0.643291i
\(50\) −0.856613 + 12.6175i −0.121143 + 1.78438i
\(51\) 5.11968i 0.716899i
\(52\) 23.1947i 3.21652i
\(53\) 12.4608i 1.71162i −0.517289 0.855811i \(-0.673059\pi\)
0.517289 0.855811i \(-0.326941\pi\)
\(54\) 2.52930 0.344195
\(55\) 0.372642 + 7.40683i 0.0502470 + 0.998737i
\(56\) 15.0737 + 5.49199i 2.01431 + 0.733898i
\(57\) −4.28158 −0.567110
\(58\) 21.9093i 2.87683i
\(59\) 1.69675i 0.220898i −0.993882 0.110449i \(-0.964771\pi\)
0.993882 0.110449i \(-0.0352289\pi\)
\(60\) −7.18448 + 6.71325i −0.927512 + 0.866677i
\(61\) −7.32231 −0.937525 −0.468763 0.883324i \(-0.655300\pi\)
−0.468763 + 0.883324i \(0.655300\pi\)
\(62\) 7.99918i 1.01590i
\(63\) −2.48590 0.905718i −0.313193 0.114110i
\(64\) −1.90553 −0.238191
\(65\) 8.05257 + 8.61780i 0.998798 + 1.06891i
\(66\) −5.41211 + 6.40938i −0.666185 + 0.788940i
\(67\) 1.64438i 0.200893i 0.994942 + 0.100446i \(0.0320271\pi\)
−0.994942 + 0.100446i \(0.967973\pi\)
\(68\) 22.5131i 2.73012i
\(69\) 1.22635i 0.147635i
\(70\) 13.7700 5.85615i 1.64583 0.699944i
\(71\) −4.95049 −0.587515 −0.293758 0.955880i \(-0.594906\pi\)
−0.293758 + 0.955880i \(0.594906\pi\)
\(72\) −6.06368 −0.714612
\(73\) 13.6548i 1.59817i −0.601218 0.799085i \(-0.705318\pi\)
0.601218 0.799085i \(-0.294682\pi\)
\(74\) 9.58626i 1.11438i
\(75\) −0.338675 + 4.98852i −0.0391069 + 0.576024i
\(76\) 18.8277 2.15969
\(77\) 7.61436 4.36136i 0.867737 0.497023i
\(78\) 13.3412i 1.51060i
\(79\) 2.01901i 0.227157i −0.993529 0.113578i \(-0.963769\pi\)
0.993529 0.113578i \(-0.0362313\pi\)
\(80\) 10.6886 9.98757i 1.19502 1.11664i
\(81\) 1.00000 0.111111
\(82\) 15.0697 1.66417
\(83\) 3.14880i 0.345626i 0.984955 + 0.172813i \(0.0552856\pi\)
−0.984955 + 0.172813i \(0.944714\pi\)
\(84\) 10.9314 + 3.98278i 1.19271 + 0.434557i
\(85\) −7.81596 8.36459i −0.847760 0.907267i
\(86\) −19.9127 −2.14724
\(87\) 8.66218i 0.928683i
\(88\) 12.9748 15.3657i 1.38312 1.63799i
\(89\) 4.88199i 0.517489i 0.965946 + 0.258745i \(0.0833088\pi\)
−0.965946 + 0.258745i \(0.916691\pi\)
\(90\) −4.13240 + 3.86136i −0.435593 + 0.407023i
\(91\) 4.77736 13.1123i 0.500803 1.37454i
\(92\) 5.39270i 0.562228i
\(93\) 3.16260i 0.327947i
\(94\) −17.3297 −1.78742
\(95\) 6.99530 6.53648i 0.717703 0.670629i
\(96\) 4.41970 0.451084
\(97\) −15.6959 −1.59368 −0.796838 0.604193i \(-0.793495\pi\)
−0.796838 + 0.604193i \(0.793495\pi\)
\(98\) −13.5554 11.3896i −1.36930 1.15052i
\(99\) −2.13976 + 2.53405i −0.215054 + 0.254682i
\(100\) 1.48928 21.9364i 0.148928 2.19364i
\(101\) −3.17273 −0.315699 −0.157849 0.987463i \(-0.550456\pi\)
−0.157849 + 0.987463i \(0.550456\pi\)
\(102\) 12.9492i 1.28216i
\(103\) −8.09081 −0.797211 −0.398605 0.917123i \(-0.630506\pi\)
−0.398605 + 0.917123i \(0.630506\pi\)
\(104\) 31.9839i 3.13628i
\(105\) 5.44420 2.31532i 0.531299 0.225952i
\(106\) 31.5171i 3.06121i
\(107\) −11.5492 −1.11650 −0.558250 0.829673i \(-0.688527\pi\)
−0.558250 + 0.829673i \(0.688527\pi\)
\(108\) −4.39737 −0.423137
\(109\) 12.2689i 1.17515i −0.809171 0.587573i \(-0.800083\pi\)
0.809171 0.587573i \(-0.199917\pi\)
\(110\) −0.942524 18.7341i −0.0898661 1.78623i
\(111\) 3.79008i 0.359738i
\(112\) −16.2631 5.92534i −1.53672 0.559892i
\(113\) 5.43099i 0.510904i −0.966822 0.255452i \(-0.917776\pi\)
0.966822 0.255452i \(-0.0822243\pi\)
\(114\) 10.8294 1.01427
\(115\) 1.87220 + 2.00362i 0.174584 + 0.186838i
\(116\) 38.0908i 3.53664i
\(117\) 5.27466i 0.487643i
\(118\) 4.29160i 0.395073i
\(119\) −4.63699 + 12.7270i −0.425072 + 1.16668i
\(120\) 9.90691 9.25713i 0.904373 0.845056i
\(121\) −1.84283 10.8445i −0.167530 0.985867i
\(122\) 18.5203 1.67675
\(123\) 5.95804 0.537218
\(124\) 13.9071i 1.24890i
\(125\) −7.06239 8.66733i −0.631679 0.775230i
\(126\) 6.28758 + 2.29084i 0.560142 + 0.204084i
\(127\) 14.9817 1.32941 0.664707 0.747104i \(-0.268556\pi\)
0.664707 + 0.747104i \(0.268556\pi\)
\(128\) 13.6591 1.20730
\(129\) −7.87280 −0.693162
\(130\) −20.3674 21.7970i −1.78634 1.91173i
\(131\) 0.877747 0.0766891 0.0383446 0.999265i \(-0.487792\pi\)
0.0383446 + 0.999265i \(0.487792\pi\)
\(132\) 9.40934 11.1432i 0.818978 0.969888i
\(133\) −10.6436 3.87791i −0.922915 0.336257i
\(134\) 4.15913i 0.359294i
\(135\) −1.63381 + 1.52665i −0.140616 + 0.131393i
\(136\) 31.0441i 2.66201i
\(137\) 19.7845i 1.69030i −0.534529 0.845150i \(-0.679511\pi\)
0.534529 0.845150i \(-0.320489\pi\)
\(138\) 3.10180i 0.264043i
\(139\) 11.5988 0.983800 0.491900 0.870652i \(-0.336303\pi\)
0.491900 + 0.870652i \(0.336303\pi\)
\(140\) −23.9402 + 10.1813i −2.02331 + 0.860480i
\(141\) −6.85157 −0.577006
\(142\) 12.5213 1.05076
\(143\) −13.3663 11.2865i −1.11774 0.943827i
\(144\) 6.54214 0.545179
\(145\) −13.2241 14.1524i −1.09820 1.17529i
\(146\) 34.5371i 2.85831i
\(147\) −5.35935 4.50304i −0.442032 0.371404i
\(148\) 16.6664i 1.36997i
\(149\) 6.43246i 0.526967i −0.964664 0.263484i \(-0.915128\pi\)
0.964664 0.263484i \(-0.0848715\pi\)
\(150\) 0.856613 12.6175i 0.0699421 1.03021i
\(151\) 20.2373i 1.64689i −0.567396 0.823445i \(-0.692049\pi\)
0.567396 0.823445i \(-0.307951\pi\)
\(152\) −25.9622 −2.10581
\(153\) 5.11968i 0.413902i
\(154\) −19.2590 + 11.0312i −1.55194 + 0.888920i
\(155\) 4.82819 + 5.16709i 0.387809 + 0.415031i
\(156\) 23.1947i 1.85706i
\(157\) 19.2805 1.53876 0.769378 0.638794i \(-0.220566\pi\)
0.769378 + 0.638794i \(0.220566\pi\)
\(158\) 5.10670i 0.406267i
\(159\) 12.4608i 0.988205i
\(160\) −7.22095 + 6.74734i −0.570866 + 0.533424i
\(161\) 1.11072 3.04857i 0.0875373 0.240261i
\(162\) −2.52930 −0.198721
\(163\) 17.2041i 1.34753i −0.738946 0.673765i \(-0.764676\pi\)
0.738946 0.673765i \(-0.235324\pi\)
\(164\) −26.1997 −2.04585
\(165\) −0.372642 7.40683i −0.0290101 0.576621i
\(166\) 7.96427i 0.618147i
\(167\) 5.88119i 0.455100i 0.973766 + 0.227550i \(0.0730716\pi\)
−0.973766 + 0.227550i \(0.926928\pi\)
\(168\) −15.0737 5.49199i −1.16296 0.423716i
\(169\) −14.8221 −1.14016
\(170\) 19.7689 + 21.1566i 1.51621 + 1.62264i
\(171\) 4.28158 0.327421
\(172\) 34.6197 2.63972
\(173\) 1.71236i 0.130188i 0.997879 + 0.0650941i \(0.0207348\pi\)
−0.997879 + 0.0650941i \(0.979265\pi\)
\(174\) 21.9093i 1.66094i
\(175\) −5.36010 + 12.0942i −0.405186 + 0.914234i
\(176\) −13.9986 + 16.5781i −1.05519 + 1.24962i
\(177\) 1.69675i 0.127536i
\(178\) 12.3480i 0.925523i
\(179\) −7.42437 −0.554924 −0.277462 0.960737i \(-0.589493\pi\)
−0.277462 + 0.960737i \(0.589493\pi\)
\(180\) 7.18448 6.71325i 0.535499 0.500376i
\(181\) 7.98549i 0.593556i 0.954946 + 0.296778i \(0.0959122\pi\)
−0.954946 + 0.296778i \(0.904088\pi\)
\(182\) −12.0834 + 33.1649i −0.895680 + 2.45834i
\(183\) 7.32231 0.541281
\(184\) 7.43617i 0.548202i
\(185\) 5.78613 + 6.19227i 0.425405 + 0.455265i
\(186\) 7.99918i 0.586528i
\(187\) 12.9735 + 10.9549i 0.948719 + 0.801102i
\(188\) 30.1289 2.19738
\(189\) 2.48590 + 0.905718i 0.180822 + 0.0658813i
\(190\) −17.6932 + 16.5327i −1.28360 + 1.19941i
\(191\) 1.11911 0.0809760 0.0404880 0.999180i \(-0.487109\pi\)
0.0404880 + 0.999180i \(0.487109\pi\)
\(192\) 1.90553 0.137520
\(193\) −25.2805 −1.81973 −0.909865 0.414904i \(-0.863815\pi\)
−0.909865 + 0.414904i \(0.863815\pi\)
\(194\) 39.6996 2.85027
\(195\) −8.05257 8.61780i −0.576656 0.617134i
\(196\) 23.5671 + 19.8015i 1.68336 + 1.41440i
\(197\) 17.1708 1.22337 0.611683 0.791103i \(-0.290493\pi\)
0.611683 + 0.791103i \(0.290493\pi\)
\(198\) 5.41211 6.40938i 0.384622 0.455495i
\(199\) 23.6135i 1.67392i −0.547267 0.836958i \(-0.684332\pi\)
0.547267 0.836958i \(-0.315668\pi\)
\(200\) −2.05362 + 30.2488i −0.145213 + 2.13891i
\(201\) 1.64438i 0.115986i
\(202\) 8.02481 0.564623
\(203\) −7.84549 + 21.5333i −0.550645 + 1.51134i
\(204\) 22.5131i 1.57624i
\(205\) −9.73430 + 9.09584i −0.679873 + 0.635281i
\(206\) 20.4641 1.42580
\(207\) 1.22635i 0.0852369i
\(208\) 34.5076i 2.39267i
\(209\) −9.16158 + 10.8498i −0.633720 + 0.750493i
\(210\) −13.7700 + 5.85615i −0.950222 + 0.404113i
\(211\) 6.53077i 0.449597i −0.974405 0.224798i \(-0.927828\pi\)
0.974405 0.224798i \(-0.0721724\pi\)
\(212\) 54.7948i 3.76332i
\(213\) 4.95049 0.339202
\(214\) 29.2113 1.99685
\(215\) 12.8627 12.0190i 0.877227 0.819690i
\(216\) 6.06368 0.412581
\(217\) 2.86443 7.86190i 0.194450 0.533700i
\(218\) 31.0317i 2.10173i
\(219\) 13.6548i 0.922704i
\(220\) 1.63865 + 32.5706i 0.110477 + 2.19591i
\(221\) 27.0046 1.81653
\(222\) 9.58626i 0.643388i
\(223\) −18.7020 −1.25238 −0.626189 0.779671i \(-0.715386\pi\)
−0.626189 + 0.779671i \(0.715386\pi\)
\(224\) 10.9869 + 4.00300i 0.734094 + 0.267462i
\(225\) 0.338675 4.98852i 0.0225784 0.332568i
\(226\) 13.7366i 0.913746i
\(227\) 20.9094i 1.38780i 0.720070 + 0.693902i \(0.244110\pi\)
−0.720070 + 0.693902i \(0.755890\pi\)
\(228\) −18.8277 −1.24690
\(229\) 8.20518i 0.542214i −0.962549 0.271107i \(-0.912610\pi\)
0.962549 0.271107i \(-0.0873896\pi\)
\(230\) −4.73536 5.06775i −0.312241 0.334158i
\(231\) −7.61436 + 4.36136i −0.500988 + 0.286957i
\(232\) 52.5247i 3.44842i
\(233\) −12.1849 −0.798261 −0.399131 0.916894i \(-0.630688\pi\)
−0.399131 + 0.916894i \(0.630688\pi\)
\(234\) 13.3412i 0.872143i
\(235\) 11.1942 10.4599i 0.730227 0.682332i
\(236\) 7.46125i 0.485686i
\(237\) 2.01901i 0.131149i
\(238\) 11.7283 32.1904i 0.760236 2.08659i
\(239\) 5.67839i 0.367304i −0.982991 0.183652i \(-0.941208\pi\)
0.982991 0.183652i \(-0.0587920\pi\)
\(240\) −10.6886 + 9.98757i −0.689948 + 0.644695i
\(241\) 18.7726 1.20925 0.604624 0.796511i \(-0.293323\pi\)
0.604624 + 0.796511i \(0.293323\pi\)
\(242\) 4.66106 + 27.4291i 0.299625 + 1.76321i
\(243\) −1.00000 −0.0641500
\(244\) −32.1989 −2.06132
\(245\) 15.6307 0.824739i 0.998611 0.0526907i
\(246\) −15.0697 −0.960808
\(247\) 22.5839i 1.43698i
\(248\) 19.1770i 1.21774i
\(249\) 3.14880i 0.199547i
\(250\) 17.8629 + 21.9223i 1.12975 + 1.38649i
\(251\) 2.11549i 0.133528i −0.997769 0.0667642i \(-0.978732\pi\)
0.997769 0.0667642i \(-0.0212675\pi\)
\(252\) −10.9314 3.98278i −0.688614 0.250892i
\(253\) −3.10762 2.62409i −0.195375 0.164975i
\(254\) −37.8934 −2.37764
\(255\) 7.81596 + 8.36459i 0.489455 + 0.523811i
\(256\) −30.7368 −1.92105
\(257\) −14.8176 −0.924296 −0.462148 0.886803i \(-0.652921\pi\)
−0.462148 + 0.886803i \(0.652921\pi\)
\(258\) 19.9127 1.23971
\(259\) 3.43274 9.42174i 0.213300 0.585438i
\(260\) 35.4102 + 37.8957i 2.19604 + 2.35019i
\(261\) 8.66218i 0.536175i
\(262\) −2.22009 −0.137157
\(263\) −13.1506 −0.810903 −0.405452 0.914117i \(-0.632886\pi\)
−0.405452 + 0.914117i \(0.632886\pi\)
\(264\) −12.9748 + 15.3657i −0.798547 + 0.945692i
\(265\) −19.0233 20.3586i −1.16859 1.25062i
\(266\) 26.9208 + 9.80840i 1.65062 + 0.601392i
\(267\) 4.88199i 0.298773i
\(268\) 7.23095i 0.441700i
\(269\) 19.7999i 1.20722i −0.797280 0.603610i \(-0.793729\pi\)
0.797280 0.603610i \(-0.206271\pi\)
\(270\) 4.13240 3.86136i 0.251490 0.234995i
\(271\) −11.6788 −0.709435 −0.354718 0.934973i \(-0.615423\pi\)
−0.354718 + 0.934973i \(0.615423\pi\)
\(272\) 33.4937i 2.03085i
\(273\) −4.77736 + 13.1123i −0.289139 + 0.793590i
\(274\) 50.0409i 3.02308i
\(275\) 11.9165 + 11.5325i 0.718590 + 0.695434i
\(276\) 5.39270i 0.324602i
\(277\) 3.48113 0.209161 0.104580 0.994516i \(-0.466650\pi\)
0.104580 + 0.994516i \(0.466650\pi\)
\(278\) −29.3369 −1.75951
\(279\) 3.16260i 0.189340i
\(280\) 33.0119 14.0394i 1.97284 0.839013i
\(281\) 22.0902i 1.31779i 0.752234 + 0.658896i \(0.228976\pi\)
−0.752234 + 0.658896i \(0.771024\pi\)
\(282\) 17.3297 1.03197
\(283\) 3.35901i 0.199672i 0.995004 + 0.0998361i \(0.0318318\pi\)
−0.995004 + 0.0998361i \(0.968168\pi\)
\(284\) −21.7692 −1.29176
\(285\) −6.99530 + 6.53648i −0.414366 + 0.387188i
\(286\) 33.8073 + 28.5471i 1.99907 + 1.68802i
\(287\) 14.8111 + 5.39630i 0.874269 + 0.318534i
\(288\) −4.41970 −0.260433
\(289\) −9.21113 −0.541831
\(290\) 33.4478 + 35.7956i 1.96412 + 2.10199i
\(291\) 15.6959 0.920109
\(292\) 60.0451i 3.51388i
\(293\) 13.6906i 0.799812i 0.916556 + 0.399906i \(0.130957\pi\)
−0.916556 + 0.399906i \(0.869043\pi\)
\(294\) 13.5554 + 11.3896i 0.790568 + 0.664252i
\(295\) −2.59035 2.77217i −0.150816 0.161402i
\(296\) 22.9818i 1.33579i
\(297\) 2.13976 2.53405i 0.124162 0.147041i
\(298\) 16.2696i 0.942475i
\(299\) −6.46856 −0.374087
\(300\) −1.48928 + 21.9364i −0.0859837 + 1.26650i
\(301\) −19.5710 7.13054i −1.12805 0.410997i
\(302\) 51.1863i 2.94544i
\(303\) 3.17273 0.182269
\(304\) 28.0107 1.60653
\(305\) −11.9633 + 11.1786i −0.685015 + 0.640085i
\(306\) 12.9492i 0.740258i
\(307\) 3.58318i 0.204503i −0.994759 0.102251i \(-0.967395\pi\)
0.994759 0.102251i \(-0.0326046\pi\)
\(308\) 33.4832 19.1785i 1.90788 1.09280i
\(309\) 8.09081 0.460270
\(310\) −12.2120 13.0691i −0.693592 0.742277i
\(311\) 4.38304i 0.248540i −0.992248 0.124270i \(-0.960341\pi\)
0.992248 0.124270i \(-0.0396588\pi\)
\(312\) 31.9839i 1.81073i
\(313\) 15.3099 0.865367 0.432683 0.901546i \(-0.357567\pi\)
0.432683 + 0.901546i \(0.357567\pi\)
\(314\) −48.7663 −2.75204
\(315\) −5.44420 + 2.31532i −0.306746 + 0.130454i
\(316\) 8.87836i 0.499447i
\(317\) 22.3499i 1.25529i −0.778499 0.627646i \(-0.784018\pi\)
0.778499 0.627646i \(-0.215982\pi\)
\(318\) 31.5171i 1.76739i
\(319\) 21.9504 + 18.5350i 1.22899 + 1.03776i
\(320\) −3.11328 + 2.90908i −0.174037 + 0.162623i
\(321\) 11.5492 0.644612
\(322\) −2.80936 + 7.71075i −0.156559 + 0.429703i
\(323\) 21.9203i 1.21968i
\(324\) 4.39737 0.244299
\(325\) 26.3128 + 1.78640i 1.45957 + 0.0990916i
\(326\) 43.5144i 2.41004i
\(327\) 12.2689i 0.678471i
\(328\) 36.1276 1.99482
\(329\) −17.0323 6.20559i −0.939020 0.342125i
\(330\) 0.942524 + 18.7341i 0.0518842 + 1.03128i
\(331\) −17.0600 −0.937702 −0.468851 0.883277i \(-0.655332\pi\)
−0.468851 + 0.883277i \(0.655332\pi\)
\(332\) 13.8464i 0.759922i
\(333\) 3.79008i 0.207695i
\(334\) 14.8753i 0.813941i
\(335\) 2.51039 + 2.68660i 0.137157 + 0.146785i
\(336\) 16.2631 + 5.92534i 0.887224 + 0.323254i
\(337\) −11.7119 −0.637989 −0.318994 0.947757i \(-0.603345\pi\)
−0.318994 + 0.947757i \(0.603345\pi\)
\(338\) 37.4895 2.03916
\(339\) 5.43099i 0.294971i
\(340\) −34.3697 36.7822i −1.86396 1.99480i
\(341\) −8.01419 6.76722i −0.433993 0.366465i
\(342\) −10.8294 −0.585588
\(343\) −9.24430 16.0481i −0.499145 0.866518i
\(344\) −47.7382 −2.57387
\(345\) −1.87220 2.00362i −0.100796 0.107871i
\(346\) 4.33107i 0.232840i
\(347\) −22.2943 −1.19682 −0.598411 0.801189i \(-0.704201\pi\)
−0.598411 + 0.801189i \(0.704201\pi\)
\(348\) 38.0908i 2.04188i
\(349\) 18.3957 0.984701 0.492351 0.870397i \(-0.336138\pi\)
0.492351 + 0.870397i \(0.336138\pi\)
\(350\) 13.5573 30.5899i 0.724669 1.63510i
\(351\) 5.27466i 0.281541i
\(352\) 9.45711 11.1997i 0.504066 0.596948i
\(353\) 20.2639 1.07854 0.539270 0.842133i \(-0.318700\pi\)
0.539270 + 0.842133i \(0.318700\pi\)
\(354\) 4.29160i 0.228096i
\(355\) −8.08817 + 7.55767i −0.429275 + 0.401120i
\(356\) 21.4679i 1.13780i
\(357\) 4.63699 12.7270i 0.245415 0.673584i
\(358\) 18.7785 0.992474
\(359\) 9.69378i 0.511618i −0.966727 0.255809i \(-0.917658\pi\)
0.966727 0.255809i \(-0.0823418\pi\)
\(360\) −9.90691 + 9.25713i −0.522140 + 0.487893i
\(361\) −0.668034 −0.0351597
\(362\) 20.1977i 1.06157i
\(363\) 1.84283 + 10.8445i 0.0967233 + 0.569191i
\(364\) 21.0078 57.6595i 1.10111 3.02218i
\(365\) −20.8461 22.3093i −1.09113 1.16772i
\(366\) −18.5203 −0.968073
\(367\) −35.0965 −1.83202 −0.916012 0.401152i \(-0.868610\pi\)
−0.916012 + 0.401152i \(0.868610\pi\)
\(368\) 8.02293i 0.418224i
\(369\) −5.95804 −0.310163
\(370\) −14.6349 15.6621i −0.760831 0.814236i
\(371\) −11.2860 + 30.9762i −0.585938 + 1.60821i
\(372\) 13.9071i 0.721052i
\(373\) −1.01774 −0.0526964 −0.0263482 0.999653i \(-0.508388\pi\)
−0.0263482 + 0.999653i \(0.508388\pi\)
\(374\) −32.8140 27.7083i −1.69677 1.43276i
\(375\) 7.06239 + 8.66733i 0.364700 + 0.447579i
\(376\) −41.5457 −2.14256
\(377\) 45.6901 2.35316
\(378\) −6.28758 2.29084i −0.323398 0.117828i
\(379\) 24.1247 1.23920 0.619601 0.784917i \(-0.287294\pi\)
0.619601 + 0.784917i \(0.287294\pi\)
\(380\) 30.7609 28.7434i 1.57800 1.47450i
\(381\) −14.9817 −0.767538
\(382\) −2.83057 −0.144825
\(383\) 15.1817 0.775749 0.387875 0.921712i \(-0.373209\pi\)
0.387875 + 0.921712i \(0.373209\pi\)
\(384\) −13.6591 −0.697036
\(385\) 5.78215 18.7501i 0.294686 0.955594i
\(386\) 63.9421 3.25456
\(387\) 7.87280 0.400197
\(388\) −69.0207 −3.50399
\(389\) −1.96963 −0.0998644 −0.0499322 0.998753i \(-0.515901\pi\)
−0.0499322 + 0.998753i \(0.515901\pi\)
\(390\) 20.3674 + 21.7970i 1.03134 + 1.10374i
\(391\) 6.27850 0.317517
\(392\) −32.4974 27.3050i −1.64137 1.37911i
\(393\) −0.877747 −0.0442765
\(394\) −43.4301 −2.18798
\(395\) −3.08233 3.29869i −0.155089 0.165975i
\(396\) −9.40934 + 11.1432i −0.472837 + 0.559965i
\(397\) 2.33578 0.117229 0.0586146 0.998281i \(-0.481332\pi\)
0.0586146 + 0.998281i \(0.481332\pi\)
\(398\) 59.7257i 2.99378i
\(399\) 10.6436 + 3.87791i 0.532845 + 0.194138i
\(400\) 2.21566 32.6356i 0.110783 1.63178i
\(401\) 30.6222 1.52920 0.764600 0.644505i \(-0.222936\pi\)
0.764600 + 0.644505i \(0.222936\pi\)
\(402\) 4.15913i 0.207439i
\(403\) −16.6817 −0.830973
\(404\) −13.9517 −0.694123
\(405\) 1.63381 1.52665i 0.0811847 0.0758599i
\(406\) 19.8436 54.4641i 0.984822 2.70301i
\(407\) −9.60425 8.10987i −0.476065 0.401992i
\(408\) 31.0441i 1.53691i
\(409\) −1.89620 −0.0937609 −0.0468804 0.998901i \(-0.514928\pi\)
−0.0468804 + 0.998901i \(0.514928\pi\)
\(410\) 24.6210 23.0061i 1.21594 1.13619i
\(411\) 19.7845i 0.975895i
\(412\) −35.5783 −1.75282
\(413\) −1.53678 + 4.21794i −0.0756199 + 0.207551i
\(414\) 3.10180i 0.152445i
\(415\) 4.80712 + 5.14454i 0.235972 + 0.252536i
\(416\) 23.3124i 1.14299i
\(417\) −11.5988 −0.567997
\(418\) 23.1724 27.4423i 1.13340 1.34225i
\(419\) 2.90534i 0.141935i −0.997479 0.0709677i \(-0.977391\pi\)
0.997479 0.0709677i \(-0.0226087\pi\)
\(420\) 23.9402 10.1813i 1.16816 0.496798i
\(421\) 30.0571 1.46489 0.732446 0.680825i \(-0.238379\pi\)
0.732446 + 0.680825i \(0.238379\pi\)
\(422\) 16.5183i 0.804098i
\(423\) 6.85157 0.333135
\(424\) 75.5583i 3.66944i
\(425\) −25.5396 1.73391i −1.23885 0.0841070i
\(426\) −12.5213 −0.606659
\(427\) 18.2025 + 6.63195i 0.880880 + 0.320942i
\(428\) −50.7860 −2.45483
\(429\) 13.3663 + 11.2865i 0.645329 + 0.544919i
\(430\) −32.5336 + 30.3997i −1.56891 + 1.46601i
\(431\) 20.5074i 0.987807i 0.869517 + 0.493904i \(0.164430\pi\)
−0.869517 + 0.493904i \(0.835570\pi\)
\(432\) −6.54214 −0.314759
\(433\) 30.0295 1.44313 0.721563 0.692349i \(-0.243424\pi\)
0.721563 + 0.692349i \(0.243424\pi\)
\(434\) −7.24500 + 19.8851i −0.347771 + 0.954516i
\(435\) 13.2241 + 14.1524i 0.634048 + 0.678554i
\(436\) 53.9509i 2.58378i
\(437\) 5.25070i 0.251175i
\(438\) 34.5371i 1.65024i
\(439\) 25.5270 1.21834 0.609169 0.793041i \(-0.291503\pi\)
0.609169 + 0.793041i \(0.291503\pi\)
\(440\) −2.25958 44.9127i −0.107721 2.14113i
\(441\) 5.35935 + 4.50304i 0.255207 + 0.214430i
\(442\) −68.3028 −3.24883
\(443\) 14.5242i 0.690065i 0.938591 + 0.345032i \(0.112132\pi\)
−0.938591 + 0.345032i \(0.887868\pi\)
\(444\) 16.6664i 0.790952i
\(445\) 7.45309 + 7.97624i 0.353310 + 0.378110i
\(446\) 47.3030 2.23986
\(447\) 6.43246i 0.304245i
\(448\) 4.73695 + 1.72587i 0.223800 + 0.0815399i
\(449\) 4.91667 0.232032 0.116016 0.993247i \(-0.462988\pi\)
0.116016 + 0.993247i \(0.462988\pi\)
\(450\) −0.856613 + 12.6175i −0.0403811 + 0.594793i
\(451\) 12.7488 15.0980i 0.600317 0.710936i
\(452\) 23.8821i 1.12332i
\(453\) 20.2373i 0.950833i
\(454\) 52.8861i 2.48207i
\(455\) −12.2125 28.7163i −0.572533 1.34624i
\(456\) 25.9622 1.21579
\(457\) 30.2232 1.41378 0.706891 0.707323i \(-0.250097\pi\)
0.706891 + 0.707323i \(0.250097\pi\)
\(458\) 20.7534i 0.969742i
\(459\) 5.11968i 0.238966i
\(460\) 8.23277 + 8.81065i 0.383855 + 0.410799i
\(461\) 21.0017 0.978146 0.489073 0.872243i \(-0.337335\pi\)
0.489073 + 0.872243i \(0.337335\pi\)
\(462\) 19.2590 11.0312i 0.896011 0.513218i
\(463\) 15.0004i 0.697126i 0.937285 + 0.348563i \(0.113330\pi\)
−0.937285 + 0.348563i \(0.886670\pi\)
\(464\) 56.6692i 2.63080i
\(465\) −4.82819 5.16709i −0.223902 0.239618i
\(466\) 30.8194 1.42768
\(467\) −10.5444 −0.487936 −0.243968 0.969783i \(-0.578449\pi\)
−0.243968 + 0.969783i \(0.578449\pi\)
\(468\) 23.1947i 1.07217i
\(469\) 1.48934 4.08775i 0.0687715 0.188755i
\(470\) −28.3134 + 26.4564i −1.30600 + 1.22034i
\(471\) −19.2805 −0.888401
\(472\) 10.2886i 0.473569i
\(473\) −16.8459 + 19.9501i −0.774577 + 0.917306i
\(474\) 5.10670i 0.234559i
\(475\) 1.45007 21.3588i 0.0665336 0.980007i
\(476\) −20.3906 + 55.9653i −0.934600 + 2.56517i
\(477\) 12.4608i 0.570541i
\(478\) 14.3624i 0.656919i
\(479\) −29.2808 −1.33787 −0.668936 0.743320i \(-0.733250\pi\)
−0.668936 + 0.743320i \(0.733250\pi\)
\(480\) 7.22095 6.74734i 0.329590 0.307972i
\(481\) −19.9914 −0.911529
\(482\) −47.4815 −2.16272
\(483\) −1.11072 + 3.04857i −0.0505397 + 0.138715i
\(484\) −8.10359 47.6875i −0.368345 2.16761i
\(485\) −25.6441 + 23.9621i −1.16444 + 1.08806i
\(486\) 2.52930 0.114732
\(487\) 8.75333i 0.396651i −0.980136 0.198326i \(-0.936450\pi\)
0.980136 0.198326i \(-0.0635504\pi\)
\(488\) 44.4002 2.00990
\(489\) 17.2041i 0.777997i
\(490\) −39.5349 + 2.08602i −1.78600 + 0.0942366i
\(491\) 8.44903i 0.381299i −0.981658 0.190650i \(-0.938941\pi\)
0.981658 0.190650i \(-0.0610595\pi\)
\(492\) 26.1997 1.18117
\(493\) −44.3476 −1.99731
\(494\) 57.1216i 2.57002i
\(495\) 0.372642 + 7.40683i 0.0167490 + 0.332912i
\(496\) 20.6902i 0.929017i
\(497\) 12.3064 + 4.48375i 0.552018 + 0.201124i
\(498\) 7.96427i 0.356887i
\(499\) 0.908981 0.0406916 0.0203458 0.999793i \(-0.493523\pi\)
0.0203458 + 0.999793i \(0.493523\pi\)
\(500\) −31.0560 38.1135i −1.38887 1.70449i
\(501\) 5.88119i 0.262752i
\(502\) 5.35071i 0.238814i
\(503\) 17.3007i 0.771402i −0.922624 0.385701i \(-0.873960\pi\)
0.922624 0.385701i \(-0.126040\pi\)
\(504\) 15.0737 + 5.49199i 0.671435 + 0.244633i
\(505\) −5.18365 + 4.84366i −0.230669 + 0.215540i
\(506\) 7.86012 + 6.63712i 0.349425 + 0.295056i
\(507\) 14.8221 0.658272
\(508\) 65.8803 2.92297
\(509\) 9.56749i 0.424072i 0.977262 + 0.212036i \(0.0680093\pi\)
−0.977262 + 0.212036i \(0.931991\pi\)
\(510\) −19.7689 21.1566i −0.875383 0.936829i
\(511\) −12.3674 + 33.9443i −0.547100 + 1.50161i
\(512\) 50.4247 2.22848
\(513\) −4.28158 −0.189037
\(514\) 37.4782 1.65309
\(515\) −13.2188 + 12.3518i −0.582492 + 0.544287i
\(516\) −34.6197 −1.52405
\(517\) −14.6607 + 17.3622i −0.644778 + 0.763589i
\(518\) −8.68245 + 23.8304i −0.381485 + 1.04705i
\(519\) 1.71236i 0.0751642i
\(520\) −48.8282 52.2556i −2.14126 2.29156i
\(521\) 0.937460i 0.0410709i 0.999789 + 0.0205354i \(0.00653709\pi\)
−0.999789 + 0.0205354i \(0.993463\pi\)
\(522\) 21.9093i 0.958943i
\(523\) 10.0718i 0.440409i −0.975454 0.220205i \(-0.929328\pi\)
0.975454 0.220205i \(-0.0706725\pi\)
\(524\) 3.85978 0.168615
\(525\) 5.36010 12.0942i 0.233934 0.527834i
\(526\) 33.2619 1.45029
\(527\) 16.1915 0.705313
\(528\) 13.9986 16.5781i 0.609213 0.721470i
\(529\) 21.4961 0.934612
\(530\) 48.1156 + 51.4930i 2.09001 + 2.23671i
\(531\) 1.69675i 0.0736327i
\(532\) −46.8038 17.0526i −2.02920 0.739324i
\(533\) 31.4266i 1.36124i
\(534\) 12.3480i 0.534351i
\(535\) −18.8692 + 17.6315i −0.815785 + 0.762278i
\(536\) 9.97099i 0.430681i
\(537\) 7.42437 0.320385
\(538\) 50.0799i 2.15910i
\(539\) −22.8787 + 3.94542i −0.985454 + 0.169941i
\(540\) −7.18448 + 6.71325i −0.309171 + 0.288892i
\(541\) 23.4799i 1.00948i 0.863272 + 0.504740i \(0.168411\pi\)
−0.863272 + 0.504740i \(0.831589\pi\)
\(542\) 29.5392 1.26882
\(543\) 7.98549i 0.342690i
\(544\) 22.6275i 0.970144i
\(545\) −18.7303 20.0450i −0.802318 0.858636i
\(546\) 12.0834 33.1649i 0.517121 1.41933i
\(547\) −0.147356 −0.00630050 −0.00315025 0.999995i \(-0.501003\pi\)
−0.00315025 + 0.999995i \(0.501003\pi\)
\(548\) 86.9996i 3.71644i
\(549\) −7.32231 −0.312508
\(550\) −30.1404 29.1691i −1.28519 1.24377i
\(551\) 37.0878i 1.58000i
\(552\) 7.43617i 0.316504i
\(553\) −1.82866 + 5.01906i −0.0777625 + 0.213432i
\(554\) −8.80483 −0.374081
\(555\) −5.78613 6.19227i −0.245607 0.262847i
\(556\) 51.0044 2.16307
\(557\) −15.6424 −0.662790 −0.331395 0.943492i \(-0.607519\pi\)
−0.331395 + 0.943492i \(0.607519\pi\)
\(558\) 7.99918i 0.338632i
\(559\) 41.5264i 1.75638i
\(560\) −35.6167 + 15.1472i −1.50508 + 0.640085i
\(561\) −12.9735 10.9549i −0.547743 0.462516i
\(562\) 55.8728i 2.35685i
\(563\) 41.6902i 1.75703i −0.477714 0.878515i \(-0.658534\pi\)
0.477714 0.878515i \(-0.341466\pi\)
\(564\) −30.1289 −1.26866
\(565\) −8.29122 8.87320i −0.348814 0.373299i
\(566\) 8.49594i 0.357111i
\(567\) −2.48590 0.905718i −0.104398 0.0380366i
\(568\) 30.0182 1.25954
\(569\) 8.89030i 0.372701i −0.982483 0.186350i \(-0.940334\pi\)
0.982483 0.186350i \(-0.0596660\pi\)
\(570\) 17.6932 16.5327i 0.741088 0.692481i
\(571\) 20.5378i 0.859478i −0.902953 0.429739i \(-0.858606\pi\)
0.902953 0.429739i \(-0.141394\pi\)
\(572\) −58.7765 49.6311i −2.45757 2.07518i
\(573\) −1.11911 −0.0467515
\(574\) −37.4616 13.6489i −1.56362 0.569693i
\(575\) 6.11765 + 0.415333i 0.255123 + 0.0173206i
\(576\) −1.90553 −0.0793971
\(577\) 20.0840 0.836107 0.418054 0.908422i \(-0.362712\pi\)
0.418054 + 0.908422i \(0.362712\pi\)
\(578\) 23.2977 0.969059
\(579\) 25.2805 1.05062
\(580\) −58.1514 62.2332i −2.41460 2.58409i
\(581\) 2.85192 7.82758i 0.118318 0.324743i
\(582\) −39.6996 −1.64560
\(583\) 31.5763 + 26.6632i 1.30776 + 1.10427i
\(584\) 82.7982i 3.42621i
\(585\) 8.05257 + 8.61780i 0.332933 + 0.356302i
\(586\) 34.6276i 1.43045i
\(587\) 27.5953 1.13898 0.569490 0.821998i \(-0.307141\pi\)
0.569490 + 0.821998i \(0.307141\pi\)
\(588\) −23.5671 19.8015i −0.971889 0.816602i
\(589\) 13.5409i 0.557945i
\(590\) 6.55177 + 7.01166i 0.269732 + 0.288665i
\(591\) −17.1708 −0.706311
\(592\) 24.7952i 1.01908i
\(593\) 40.9519i 1.68169i 0.541275 + 0.840846i \(0.317942\pi\)
−0.541275 + 0.840846i \(0.682058\pi\)
\(594\) −5.41211 + 6.40938i −0.222062 + 0.262980i
\(595\) 11.8537 + 27.8726i 0.485955 + 1.14266i
\(596\) 28.2859i 1.15864i
\(597\) 23.6135i 0.966436i
\(598\) 16.3610 0.669049
\(599\) −16.4285 −0.671251 −0.335625 0.941996i \(-0.608948\pi\)
−0.335625 + 0.941996i \(0.608948\pi\)
\(600\) 2.05362 30.2488i 0.0838387 1.23490i
\(601\) −2.68019 −0.109327 −0.0546636 0.998505i \(-0.517409\pi\)
−0.0546636 + 0.998505i \(0.517409\pi\)
\(602\) 49.5009 + 18.0353i 2.01751 + 0.735064i
\(603\) 1.64438i 0.0669643i
\(604\) 88.9911i 3.62100i
\(605\) −19.5666 14.9046i −0.795497 0.605957i
\(606\) −8.02481 −0.325985
\(607\) 26.9310i 1.09309i −0.837428 0.546547i \(-0.815942\pi\)
0.837428 0.546547i \(-0.184058\pi\)
\(608\) −18.9233 −0.767442
\(609\) 7.84549 21.5333i 0.317915 0.872572i
\(610\) 30.2587 28.2741i 1.22514 1.14478i
\(611\) 36.1397i 1.46206i
\(612\) 22.5131i 0.910040i
\(613\) −17.3037 −0.698891 −0.349445 0.936957i \(-0.613630\pi\)
−0.349445 + 0.936957i \(0.613630\pi\)
\(614\) 9.06295i 0.365751i
\(615\) 9.73430 9.09584i 0.392525 0.366780i
\(616\) −46.1711 + 26.4459i −1.86029 + 1.06554i
\(617\) 32.5802i 1.31163i 0.754923 + 0.655814i \(0.227674\pi\)
−0.754923 + 0.655814i \(0.772326\pi\)
\(618\) −20.4641 −0.823187
\(619\) 30.1512i 1.21188i 0.795511 + 0.605940i \(0.207203\pi\)
−0.795511 + 0.605940i \(0.792797\pi\)
\(620\) 21.2313 + 22.7216i 0.852671 + 0.912523i
\(621\) 1.22635i 0.0492116i
\(622\) 11.0860i 0.444510i
\(623\) 4.42170 12.1361i 0.177152 0.486223i
\(624\) 34.5076i 1.38141i
\(625\) −24.7706 3.37898i −0.990824 0.135159i
\(626\) −38.7234 −1.54770
\(627\) 9.16158 10.8498i 0.365878 0.433297i
\(628\) 84.7838 3.38324
\(629\) 19.4040 0.773688
\(630\) 13.7700 5.85615i 0.548611 0.233315i
\(631\) −46.9350 −1.86845 −0.934227 0.356680i \(-0.883909\pi\)
−0.934227 + 0.356680i \(0.883909\pi\)
\(632\) 12.2427i 0.486987i
\(633\) 6.53077i 0.259575i
\(634\) 56.5295i 2.24508i
\(635\) 24.4773 22.8719i 0.971353 0.907643i
\(636\) 54.7948i 2.17275i
\(637\) −23.7520 + 28.2688i −0.941089 + 1.12005i
\(638\) −55.5192 46.8807i −2.19803 1.85602i
\(639\) −4.95049 −0.195838
\(640\) 22.3163 20.8526i 0.882130 0.824272i
\(641\) 27.4786 1.08534 0.542670 0.839946i \(-0.317413\pi\)
0.542670 + 0.839946i \(0.317413\pi\)
\(642\) −29.2113 −1.15288
\(643\) 4.30470 0.169761 0.0848805 0.996391i \(-0.472949\pi\)
0.0848805 + 0.996391i \(0.472949\pi\)
\(644\) 4.88426 13.4057i 0.192467 0.528258i
\(645\) −12.8627 + 12.0190i −0.506467 + 0.473248i
\(646\) 55.4432i 2.18138i
\(647\) 11.8230 0.464808 0.232404 0.972619i \(-0.425341\pi\)
0.232404 + 0.972619i \(0.425341\pi\)
\(648\) −6.06368 −0.238204
\(649\) 4.29965 + 3.63064i 0.168776 + 0.142515i
\(650\) −66.5529 4.51834i −2.61042 0.177224i
\(651\) −2.86443 + 7.86190i −0.112266 + 0.308132i
\(652\) 75.6529i 2.96280i
\(653\) 10.1480i 0.397121i −0.980089 0.198561i \(-0.936373\pi\)
0.980089 0.198561i \(-0.0636267\pi\)
\(654\) 31.0317i 1.21344i
\(655\) 1.43407 1.34001i 0.0560338 0.0523586i
\(656\) −38.9783 −1.52185
\(657\) 13.6548i 0.532723i
\(658\) 43.0798 + 15.6958i 1.67942 + 0.611886i
\(659\) 25.3086i 0.985882i −0.870063 0.492941i \(-0.835922\pi\)
0.870063 0.492941i \(-0.164078\pi\)
\(660\) −1.63865 32.5706i −0.0637842 1.26781i
\(661\) 38.8425i 1.51080i 0.655265 + 0.755399i \(0.272557\pi\)
−0.655265 + 0.755399i \(0.727443\pi\)
\(662\) 43.1499 1.67707
\(663\) −27.0046 −1.04877
\(664\) 19.0933i 0.740965i
\(665\) −23.3098 + 9.91325i −0.903915 + 0.384419i
\(666\) 9.58626i 0.371460i
\(667\) 10.6228 0.411317
\(668\) 25.8618i 1.00062i
\(669\) 18.7020 0.723061
\(670\) −6.34954 6.79523i −0.245304 0.262523i
\(671\) 15.6680 18.5551i 0.604857 0.716312i
\(672\) −10.9869 4.00300i −0.423829 0.154419i
\(673\) −3.24113 −0.124936 −0.0624681 0.998047i \(-0.519897\pi\)
−0.0624681 + 0.998047i \(0.519897\pi\)
\(674\) 29.6230 1.14103
\(675\) −0.338675 + 4.98852i −0.0130356 + 0.192008i
\(676\) −65.1782 −2.50685
\(677\) 14.4950i 0.557089i 0.960423 + 0.278544i \(0.0898520\pi\)
−0.960423 + 0.278544i \(0.910148\pi\)
\(678\) 13.7366i 0.527551i
\(679\) 39.0183 + 14.2160i 1.49739 + 0.545562i
\(680\) 47.3935 + 50.7202i 1.81746 + 1.94503i
\(681\) 20.9094i 0.801249i
\(682\) 20.2703 + 17.1163i 0.776191 + 0.655419i
\(683\) 17.8839i 0.684309i −0.939644 0.342154i \(-0.888843\pi\)
0.939644 0.342154i \(-0.111157\pi\)
\(684\) 18.8277 0.719896
\(685\) −30.2040 32.3241i −1.15403 1.23504i
\(686\) 23.3816 + 40.5906i 0.892715 + 1.54976i
\(687\) 8.20518i 0.313047i
\(688\) 51.5050 1.96361
\(689\) 65.7265 2.50398
\(690\) 4.73536 + 5.06775i 0.180272 + 0.192926i
\(691\) 49.9283i 1.89936i −0.313219 0.949681i \(-0.601407\pi\)
0.313219 0.949681i \(-0.398593\pi\)
\(692\) 7.52988i 0.286243i
\(693\) 7.61436 4.36136i 0.289246 0.165674i
\(694\) 56.3891 2.14050
\(695\) 18.9503 17.7074i 0.718825 0.671678i
\(696\) 52.5247i 1.99094i
\(697\) 30.5032i 1.15539i
\(698\) −46.5284 −1.76113
\(699\) 12.1849 0.460876
\(700\) −23.5704 + 53.1826i −0.890876 + 2.01012i
\(701\) 6.73723i 0.254462i −0.991873 0.127231i \(-0.959391\pi\)
0.991873 0.127231i \(-0.0406089\pi\)
\(702\) 13.3412i 0.503532i
\(703\) 16.2275i 0.612034i
\(704\) 4.07739 4.82871i 0.153672 0.181989i
\(705\) −11.1942 + 10.4599i −0.421597 + 0.393944i
\(706\) −51.2536 −1.92896
\(707\) 7.88708 + 2.87360i 0.296624 + 0.108073i
\(708\) 7.46125i 0.280411i
\(709\) −10.5335 −0.395592 −0.197796 0.980243i \(-0.563378\pi\)
−0.197796 + 0.980243i \(0.563378\pi\)
\(710\) 20.4574 19.1156i 0.767754 0.717397i
\(711\) 2.01901i 0.0757190i
\(712\) 29.6028i 1.10941i
\(713\) −3.87844 −0.145249
\(714\) −11.7283 + 32.1904i −0.438922 + 1.20470i
\(715\) −39.0685 + 1.96556i −1.46108 + 0.0735078i
\(716\) −32.6477 −1.22010
\(717\) 5.67839i 0.212063i
\(718\) 24.5185i 0.915022i
\(719\) 53.0463i 1.97830i 0.146926 + 0.989148i \(0.453062\pi\)
−0.146926 + 0.989148i \(0.546938\pi\)
\(720\) 10.6886 9.98757i 0.398342 0.372215i
\(721\) 20.1129 + 7.32799i 0.749043 + 0.272909i
\(722\) 1.68966 0.0628827
\(723\) −18.7726 −0.698160
\(724\) 35.1152i 1.30504i
\(725\) −43.2114 2.93367i −1.60483 0.108954i
\(726\) −4.66106 27.4291i −0.172988 1.01799i
\(727\) 38.0980 1.41298 0.706488 0.707725i \(-0.250278\pi\)
0.706488 + 0.707725i \(0.250278\pi\)
\(728\) −28.9684 + 79.5086i −1.07364 + 2.94678i
\(729\) 1.00000 0.0370370
\(730\) 52.7260 + 56.4270i 1.95148 + 2.08846i
\(731\) 40.3062i 1.49078i
\(732\) 32.1989 1.19011
\(733\) 23.1051i 0.853408i 0.904391 + 0.426704i \(0.140325\pi\)
−0.904391 + 0.426704i \(0.859675\pi\)
\(734\) 88.7697 3.27655
\(735\) −15.6307 + 0.824739i −0.576548 + 0.0304210i
\(736\) 5.42008i 0.199787i
\(737\) −4.16694 3.51858i −0.153491 0.129609i
\(738\) 15.0697 0.554723
\(739\) 49.3616i 1.81579i 0.419193 + 0.907897i \(0.362313\pi\)
−0.419193 + 0.907897i \(0.637687\pi\)
\(740\) 25.4438 + 27.2297i 0.935331 + 1.00098i
\(741\) 22.5839i 0.829641i
\(742\) 28.5456 78.3483i 1.04794 2.87626i
\(743\) 23.1357 0.848767 0.424384 0.905483i \(-0.360491\pi\)
0.424384 + 0.905483i \(0.360491\pi\)
\(744\) 19.1770i 0.703063i
\(745\) −9.82012 10.5094i −0.359781 0.385035i
\(746\) 2.57416 0.0942468
\(747\) 3.14880i 0.115209i
\(748\) 57.0495 + 48.1728i 2.08593 + 1.76137i
\(749\) 28.7100 + 10.4603i 1.04904 + 0.382211i
\(750\) −17.8629 21.9223i −0.652262 0.800489i
\(751\) 19.0911 0.696643 0.348322 0.937375i \(-0.386752\pi\)
0.348322 + 0.937375i \(0.386752\pi\)
\(752\) 44.8239 1.63456
\(753\) 2.11549i 0.0770927i
\(754\) −115.564 −4.20859
\(755\) −30.8953 33.0640i −1.12440 1.20332i
\(756\) 10.9314 + 3.98278i 0.397571 + 0.144852i
\(757\) 50.0487i 1.81905i −0.415650 0.909525i \(-0.636446\pi\)
0.415650 0.909525i \(-0.363554\pi\)
\(758\) −61.0187 −2.21630
\(759\) 3.10762 + 2.62409i 0.112800 + 0.0952484i
\(760\) −42.4173 + 39.6352i −1.53864 + 1.43772i
\(761\) −2.79970 −0.101489 −0.0507444 0.998712i \(-0.516159\pi\)
−0.0507444 + 0.998712i \(0.516159\pi\)
\(762\) 37.8934 1.37273
\(763\) −11.1122 + 30.4992i −0.402287 + 1.10414i
\(764\) 4.92115 0.178041
\(765\) −7.81596 8.36459i −0.282587 0.302422i
\(766\) −38.3991 −1.38742
\(767\) 8.94979 0.323158
\(768\) 30.7368 1.10912
\(769\) 17.6150 0.635212 0.317606 0.948223i \(-0.397121\pi\)
0.317606 + 0.948223i \(0.397121\pi\)
\(770\) −14.6248 + 47.4247i −0.527042 + 1.70907i
\(771\) 14.8176 0.533642
\(772\) −111.168 −4.00102
\(773\) −19.1967 −0.690457 −0.345228 0.938519i \(-0.612199\pi\)
−0.345228 + 0.938519i \(0.612199\pi\)
\(774\) −19.9127 −0.715747
\(775\) 15.7767 + 1.07110i 0.566716 + 0.0384749i
\(776\) 95.1749 3.41658
\(777\) −3.43274 + 9.42174i −0.123149 + 0.338003i
\(778\) 4.98180 0.178606
\(779\) −25.5098 −0.913985
\(780\) −35.4102 37.8957i −1.26789 1.35688i
\(781\) 10.5929 12.5448i 0.379043 0.448888i
\(782\) −15.8802 −0.567876
\(783\) 8.66218i 0.309561i
\(784\) 35.0616 + 29.4595i 1.25220 + 1.05213i
\(785\) 31.5008 29.4347i 1.12431 1.05057i
\(786\) 2.22009 0.0791879
\(787\) 49.9063i 1.77897i 0.456966 + 0.889484i \(0.348936\pi\)
−0.456966 + 0.889484i \(0.651064\pi\)
\(788\) 75.5063 2.68980
\(789\) 13.1506 0.468175
\(790\) 7.79615 + 8.34338i 0.277374 + 0.296844i
\(791\) −4.91894 + 13.5009i −0.174897 + 0.480035i
\(792\) 12.9748 15.3657i 0.461041 0.545996i
\(793\) 38.6227i 1.37153i
\(794\) −5.90788 −0.209663
\(795\) 19.0233 + 20.3586i 0.674686 + 0.722044i
\(796\) 103.837i 3.68042i
\(797\) −50.0048 −1.77126 −0.885631 0.464390i \(-0.846274\pi\)
−0.885631 + 0.464390i \(0.846274\pi\)
\(798\) −26.9208 9.80840i −0.952986 0.347214i
\(799\) 35.0778i 1.24096i
\(800\) −1.49684 + 22.0477i −0.0529214 + 0.779505i
\(801\) 4.88199i 0.172496i
\(802\) −77.4529 −2.73496
\(803\) 34.6019 + 29.2180i 1.22107 + 1.03108i
\(804\) 7.23095i 0.255016i
\(805\) −2.83938 6.67647i −0.100075 0.235315i
\(806\) 42.1930 1.48618
\(807\) 19.7999i 0.696988i
\(808\) 19.2385 0.676806
\(809\) 3.95612i 0.139090i −0.997579 0.0695449i \(-0.977845\pi\)
0.997579 0.0695449i \(-0.0221547\pi\)
\(810\) −4.13240 + 3.86136i −0.145198 + 0.135674i
\(811\) −15.5581 −0.546318 −0.273159 0.961969i \(-0.588068\pi\)
−0.273159 + 0.961969i \(0.588068\pi\)
\(812\) −34.4995 + 94.6898i −1.21070 + 3.32296i
\(813\) 11.6788 0.409593
\(814\) 24.2921 + 20.5123i 0.851437 + 0.718957i
\(815\) −26.2647 28.1083i −0.920011 0.984590i
\(816\) 33.4937i 1.17251i
\(817\) 33.7081 1.17930
\(818\) 4.79606 0.167690
\(819\) 4.77736 13.1123i 0.166934 0.458180i
\(820\) −42.8054 + 39.9978i −1.49483 + 1.39678i
\(821\) 12.6375i 0.441052i −0.975381 0.220526i \(-0.929223\pi\)
0.975381 0.220526i \(-0.0707774\pi\)
\(822\) 50.0409i 1.74538i
\(823\) 51.2750i 1.78733i −0.448730 0.893667i \(-0.648124\pi\)
0.448730 0.893667i \(-0.351876\pi\)
\(824\) 49.0601 1.70909
\(825\) −11.9165 11.5325i −0.414878 0.401509i
\(826\) 3.88698 10.6685i 0.135245 0.371203i
\(827\) 40.9493 1.42395 0.711974 0.702206i \(-0.247802\pi\)
0.711974 + 0.702206i \(0.247802\pi\)
\(828\) 5.39270i 0.187409i
\(829\) 5.57913i 0.193771i 0.995296 + 0.0968856i \(0.0308881\pi\)
−0.995296 + 0.0968856i \(0.969112\pi\)
\(830\) −12.1587 13.0121i −0.422033 0.451657i
\(831\) −3.48113 −0.120759
\(832\) 10.0510i 0.348457i
\(833\) 23.0541 27.4382i 0.798778 0.950676i
\(834\) 29.3369 1.01586
\(835\) 8.97853 + 9.60875i 0.310715 + 0.332525i
\(836\) −40.2869 + 47.7104i −1.39335 + 1.65010i
\(837\) 3.16260i 0.109316i
\(838\) 7.34850i 0.253850i
\(839\) 21.3749i 0.737942i 0.929441 + 0.368971i \(0.120290\pi\)
−0.929441 + 0.368971i \(0.879710\pi\)
\(840\) −33.0119 + 14.0394i −1.13902 + 0.484405i
\(841\) −46.0333 −1.58736
\(842\) −76.0234 −2.61994
\(843\) 22.0902i 0.760827i
\(844\) 28.7182i 0.988523i
\(845\) −24.2165 + 22.6281i −0.833072 + 0.778432i
\(846\) −17.3297 −0.595807
\(847\) −5.24102 + 28.6275i −0.180084 + 0.983651i
\(848\) 81.5203i 2.79942i
\(849\) 3.35901i 0.115281i
\(850\) 64.5974 + 4.38558i 2.21567 + 0.150424i
\(851\) −4.64795 −0.159330
\(852\) 21.7692 0.745799
\(853\) 24.9537i 0.854398i −0.904158 0.427199i \(-0.859500\pi\)
0.904158 0.427199i \(-0.140500\pi\)
\(854\) −46.0396 16.7742i −1.57544 0.574001i
\(855\) 6.99530 6.53648i 0.239234 0.223543i
\(856\) 70.0305 2.39359
\(857\) 26.2752i 0.897543i 0.893647 + 0.448771i \(0.148138\pi\)
−0.893647 + 0.448771i \(0.851862\pi\)
\(858\) −33.8073 28.5471i −1.15416 0.974581i
\(859\) 4.31760i 0.147315i −0.997284 0.0736573i \(-0.976533\pi\)
0.997284 0.0736573i \(-0.0234671\pi\)
\(860\) 56.5620 52.8521i 1.92875 1.80224i
\(861\) −14.8111 5.39630i −0.504759 0.183905i
\(862\) 51.8695i 1.76668i
\(863\) 34.2800i 1.16690i 0.812147 + 0.583452i \(0.198298\pi\)
−0.812147 + 0.583452i \(0.801702\pi\)
\(864\) 4.41970 0.150361
\(865\) 2.61417 + 2.79767i 0.0888846 + 0.0951237i
\(866\) −75.9537 −2.58101
\(867\) 9.21113 0.312826
\(868\) 12.5959 34.5717i 0.427534 1.17344i
\(869\) 5.11629 + 4.32021i 0.173558 + 0.146553i
\(870\) −33.4478 35.7956i −1.13399 1.21358i
\(871\) −8.67354 −0.293892
\(872\) 74.3947i 2.51932i
\(873\) −15.6959 −0.531225
\(874\) 13.2806i 0.449224i
\(875\) 9.70621 + 27.9426i 0.328130 + 0.944633i
\(876\) 60.0451i 2.02874i
\(877\) 16.9574 0.572610 0.286305 0.958139i \(-0.407573\pi\)
0.286305 + 0.958139i \(0.407573\pi\)
\(878\) −64.5655 −2.17898
\(879\) 13.6906i 0.461772i
\(880\) 2.43788 + 48.4566i 0.0821808 + 1.63347i
\(881\) 24.9230i 0.839678i −0.907599 0.419839i \(-0.862086\pi\)
0.907599 0.419839i \(-0.137914\pi\)
\(882\) −13.5554 11.3896i −0.456435 0.383506i
\(883\) 50.6335i 1.70395i 0.523579 + 0.851977i \(0.324597\pi\)
−0.523579 + 0.851977i \(0.675403\pi\)
\(884\) 118.749 3.99397
\(885\) 2.59035 + 2.77217i 0.0870735 + 0.0931855i
\(886\) 36.7361i 1.23417i
\(887\) 49.0775i 1.64786i 0.566691 + 0.823930i \(0.308223\pi\)
−0.566691 + 0.823930i \(0.691777\pi\)
\(888\) 22.9818i 0.771220i
\(889\) −37.2430 13.5692i −1.24909 0.455097i
\(890\) −18.8511 20.1743i −0.631891 0.676245i
\(891\) −2.13976 + 2.53405i −0.0716848 + 0.0848939i
\(892\) −82.2396 −2.75359
\(893\) 29.3356 0.981677
\(894\) 16.2696i 0.544138i
\(895\) −12.1300 + 11.3344i −0.405462 + 0.378868i
\(896\) −33.9550 12.3713i −1.13436 0.413295i
\(897\) 6.46856 0.215979
\(898\) −12.4357 −0.414986
\(899\) 27.3950 0.913675
\(900\) 1.48928 21.9364i 0.0496427 0.731212i
\(901\) −63.7953 −2.12533
\(902\) −32.2455 + 38.1873i −1.07366 + 1.27150i
\(903\) 19.5710 + 7.13054i 0.651281 + 0.237290i
\(904\) 32.9318i 1.09529i
\(905\) 12.1910 + 13.0468i 0.405244 + 0.433689i
\(906\) 51.1863i 1.70055i
\(907\) 14.0049i 0.465025i −0.972593 0.232512i \(-0.925305\pi\)
0.972593 0.232512i \(-0.0746946\pi\)
\(908\) 91.9463i 3.05135i
\(909\) −3.17273 −0.105233
\(910\) 30.8892 + 72.6323i 1.02397 + 2.40774i
\(911\) −14.3142 −0.474252 −0.237126 0.971479i \(-0.576205\pi\)
−0.237126 + 0.971479i \(0.576205\pi\)
\(912\) −28.0107 −0.927528
\(913\) −7.97922 6.73769i −0.264074 0.222985i
\(914\) −76.4436 −2.52853
\(915\) 11.9633 11.1786i 0.395493 0.369553i
\(916\) 36.0812i 1.19216i
\(917\) −2.18199 0.794991i −0.0720556 0.0262529i
\(918\) 12.9492i 0.427388i
\(919\) 0.700370i 0.0231031i −0.999933 0.0115515i \(-0.996323\pi\)
0.999933 0.0115515i \(-0.00367705\pi\)
\(920\) −11.3524 12.1493i −0.374279 0.400550i
\(921\) 3.58318i 0.118070i
\(922\) −53.1196 −1.74940
\(923\) 26.1122i 0.859493i
\(924\) −33.4832 + 19.1785i −1.10152 + 0.630928i
\(925\) 18.9069 + 1.28361i 0.621654 + 0.0422047i
\(926\) 37.9405i 1.24680i
\(927\) −8.09081 −0.265737
\(928\) 38.2842i 1.25674i
\(929\) 10.7090i 0.351351i 0.984448 + 0.175675i \(0.0562109\pi\)
−0.984448 + 0.175675i \(0.943789\pi\)
\(930\) 12.2120 + 13.0691i 0.400446 + 0.428554i
\(931\) 22.9465 + 19.2801i 0.752041 + 0.631881i
\(932\) −53.5817 −1.75513
\(933\) 4.38304i 0.143494i
\(934\) 26.6699 0.872667
\(935\) 37.9206 1.90781i 1.24014 0.0623920i
\(936\) 31.9839i 1.04543i
\(937\) 52.3296i 1.70953i 0.519013 + 0.854767i \(0.326300\pi\)
−0.519013 + 0.854767i \(0.673700\pi\)
\(938\) −3.76700 + 10.3392i −0.122997 + 0.337586i
\(939\) −15.3099 −0.499620
\(940\) 49.2249 45.9963i 1.60554 1.50023i
\(941\) −18.6624 −0.608375 −0.304188 0.952612i \(-0.598385\pi\)
−0.304188 + 0.952612i \(0.598385\pi\)
\(942\) 48.7663 1.58889
\(943\) 7.30661i 0.237936i
\(944\) 11.1004i 0.361287i
\(945\) 5.44420 2.31532i 0.177100 0.0753174i
\(946\) 42.6085 50.4598i 1.38532 1.64059i
\(947\) 9.59885i 0.311921i −0.987763 0.155960i \(-0.950153\pi\)
0.987763 0.155960i \(-0.0498472\pi\)
\(948\) 8.87836i 0.288356i
\(949\) 72.0243 2.33801
\(950\) −3.66766 + 54.0228i −0.118995 + 1.75273i
\(951\) 22.3499i 0.724744i
\(952\) 28.1172 77.1724i 0.911284 2.50117i
\(953\) −14.5092 −0.469999 −0.235000 0.971995i \(-0.575509\pi\)
−0.235000 + 0.971995i \(0.575509\pi\)
\(954\) 31.5171i 1.02040i
\(955\) 1.82841 1.70849i 0.0591661 0.0552855i
\(956\) 24.9700i 0.807587i
\(957\) −21.9504 18.5350i −0.709556 0.599152i
\(958\) 74.0599 2.39277
\(959\) −17.9191 + 49.1821i −0.578639 + 1.58817i
\(960\) 3.11328 2.90908i 0.100481 0.0938902i
\(961\) 20.9979 0.677353
\(962\) 50.5643 1.63026
\(963\) −11.5492 −0.372167
\(964\) 82.5500 2.65876
\(965\) −41.3036 + 38.5945i −1.32961 + 1.24240i
\(966\) 2.80936 7.71075i 0.0903895 0.248089i
\(967\) −28.9914 −0.932302 −0.466151 0.884705i \(-0.654360\pi\)
−0.466151 + 0.884705i \(0.654360\pi\)
\(968\) 11.1743 + 65.7578i 0.359156 + 2.11354i
\(969\) 21.9203i 0.704183i
\(970\) 64.8617 60.6075i 2.08258 1.94599i
\(971\) 19.0976i 0.612870i 0.951892 + 0.306435i \(0.0991362\pi\)
−0.951892 + 0.306435i \(0.900864\pi\)
\(972\) −4.39737 −0.141046
\(973\) −28.8335 10.5053i −0.924359 0.336783i
\(974\) 22.1398i 0.709406i
\(975\) −26.3128 1.78640i −0.842682 0.0572105i
\(976\) −47.9036 −1.53336
\(977\) 26.7156i 0.854708i −0.904084 0.427354i \(-0.859446\pi\)
0.904084 0.427354i \(-0.140554\pi\)
\(978\) 43.5144i 1.39144i
\(979\) −12.3712 10.4463i −0.395385 0.333865i
\(980\) 68.7342 3.62669i 2.19563 0.115850i
\(981\) 12.2689i 0.391716i
\(982\) 21.3702i 0.681949i
\(983\) 53.8774 1.71842 0.859211 0.511621i \(-0.170955\pi\)
0.859211 + 0.511621i \(0.170955\pi\)
\(984\) −36.1276 −1.15171
\(985\) 28.0538 26.2138i 0.893868 0.835240i
\(986\) 112.168 3.57217
\(987\) 17.0323 + 6.20559i 0.542143 + 0.197526i
\(988\) 99.3099i 3.15947i
\(989\) 9.65478i 0.307004i
\(990\) −0.942524 18.7341i −0.0299554 0.595409i
\(991\) −53.8681 −1.71118 −0.855588 0.517657i \(-0.826804\pi\)
−0.855588 + 0.517657i \(0.826804\pi\)
\(992\) 13.9777i 0.443794i
\(993\) 17.0600 0.541383
\(994\) −31.1266 11.3408i −0.987277 0.359707i
\(995\) −36.0496 38.5800i −1.14285 1.22307i
\(996\) 13.8464i 0.438741i
\(997\) 52.7933i 1.67198i −0.548745 0.835990i \(-0.684894\pi\)
0.548745 0.835990i \(-0.315106\pi\)
\(998\) −2.29909 −0.0727763
\(999\) 3.79008i 0.119913i
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 1155.2.k.a.769.3 48
5.4 even 2 1155.2.k.b.769.46 yes 48
7.6 odd 2 1155.2.k.b.769.4 yes 48
11.10 odd 2 inner 1155.2.k.a.769.46 yes 48
35.34 odd 2 inner 1155.2.k.a.769.45 yes 48
55.54 odd 2 1155.2.k.b.769.3 yes 48
77.76 even 2 1155.2.k.b.769.45 yes 48
385.384 even 2 inner 1155.2.k.a.769.4 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.3 48 1.1 even 1 trivial
1155.2.k.a.769.4 yes 48 385.384 even 2 inner
1155.2.k.a.769.45 yes 48 35.34 odd 2 inner
1155.2.k.a.769.46 yes 48 11.10 odd 2 inner
1155.2.k.b.769.3 yes 48 55.54 odd 2
1155.2.k.b.769.4 yes 48 7.6 odd 2
1155.2.k.b.769.45 yes 48 77.76 even 2
1155.2.k.b.769.46 yes 48 5.4 even 2