Properties

Label 570.2.f.a.341.1
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [570,2,Mod(341,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("570.341");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (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: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 341.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.a.341.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +0.585786 q^{7} -1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.00000 + 1.41421i) q^{6} +0.585786 q^{7} -1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +1.00000i q^{10} +5.41421i q^{11} +(-1.00000 - 1.41421i) q^{12} +2.24264i q^{13} -0.585786 q^{14} +(-1.41421 + 1.00000i) q^{15} +1.00000 q^{16} +2.82843i q^{17} +(1.00000 - 2.82843i) q^{18} +(4.24264 + 1.00000i) q^{19} -1.00000i q^{20} +(-0.585786 - 0.828427i) q^{21} -5.41421i q^{22} -6.00000i q^{23} +(1.00000 + 1.41421i) q^{24} -1.00000 q^{25} -2.24264i q^{26} +(5.00000 - 1.41421i) q^{27} +0.585786 q^{28} -5.07107 q^{29} +(1.41421 - 1.00000i) q^{30} +6.82843i q^{31} -1.00000 q^{32} +(7.65685 - 5.41421i) q^{33} -2.82843i q^{34} -0.585786i q^{35} +(-1.00000 + 2.82843i) q^{36} +2.24264i q^{37} +(-4.24264 - 1.00000i) q^{38} +(3.17157 - 2.24264i) q^{39} +1.00000i q^{40} +11.0711 q^{41} +(0.585786 + 0.828427i) q^{42} +6.58579 q^{43} +5.41421i q^{44} +(2.82843 + 1.00000i) q^{45} +6.00000i q^{46} +3.17157i q^{47} +(-1.00000 - 1.41421i) q^{48} -6.65685 q^{49} +1.00000 q^{50} +(4.00000 - 2.82843i) q^{51} +2.24264i q^{52} +3.17157 q^{53} +(-5.00000 + 1.41421i) q^{54} +5.41421 q^{55} -0.585786 q^{56} +(-2.82843 - 7.00000i) q^{57} +5.07107 q^{58} +12.8284 q^{59} +(-1.41421 + 1.00000i) q^{60} -4.48528 q^{61} -6.82843i q^{62} +(-0.585786 + 1.65685i) q^{63} +1.00000 q^{64} +2.24264 q^{65} +(-7.65685 + 5.41421i) q^{66} +2.82843i q^{68} +(-8.48528 + 6.00000i) q^{69} +0.585786i q^{70} +2.82843 q^{71} +(1.00000 - 2.82843i) q^{72} +2.48528 q^{73} -2.24264i q^{74} +(1.00000 + 1.41421i) q^{75} +(4.24264 + 1.00000i) q^{76} +3.17157i q^{77} +(-3.17157 + 2.24264i) q^{78} +13.3137i q^{79} -1.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} -11.0711 q^{82} -12.8284i q^{83} +(-0.585786 - 0.828427i) q^{84} +2.82843 q^{85} -6.58579 q^{86} +(5.07107 + 7.17157i) q^{87} -5.41421i q^{88} -10.5858 q^{89} +(-2.82843 - 1.00000i) q^{90} +1.31371i q^{91} -6.00000i q^{92} +(9.65685 - 6.82843i) q^{93} -3.17157i q^{94} +(1.00000 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +6.58579i q^{97} +6.65685 q^{98} +(-15.3137 - 5.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{12} - 8 q^{14} + 4 q^{16} + 4 q^{18} - 8 q^{21} + 4 q^{24} - 4 q^{25} + 20 q^{27} + 8 q^{28} + 8 q^{29} - 4 q^{32} + 8 q^{33} - 4 q^{36} + 24 q^{39} + 16 q^{41} + 8 q^{42} + 32 q^{43} - 4 q^{48} - 4 q^{49} + 4 q^{50} + 16 q^{51} + 24 q^{53} - 20 q^{54} + 16 q^{55} - 8 q^{56} - 8 q^{58} + 40 q^{59} + 16 q^{61} - 8 q^{63} + 4 q^{64} - 8 q^{65} - 8 q^{66} + 4 q^{72} - 24 q^{73} + 4 q^{75} - 24 q^{78} - 28 q^{81} - 16 q^{82} - 8 q^{84} - 32 q^{86} - 8 q^{87} - 48 q^{89} + 16 q^{93} + 4 q^{95} + 4 q^{96} + 4 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 1.41421i −0.577350 0.816497i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.00000 + 1.41421i 0.408248 + 0.577350i
\(7\) 0.585786 0.221406 0.110703 0.993854i \(-0.464690\pi\)
0.110703 + 0.993854i \(0.464690\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 1.00000i 0.316228i
\(11\) 5.41421i 1.63245i 0.577736 + 0.816223i \(0.303936\pi\)
−0.577736 + 0.816223i \(0.696064\pi\)
\(12\) −1.00000 1.41421i −0.288675 0.408248i
\(13\) 2.24264i 0.621997i 0.950410 + 0.310998i \(0.100663\pi\)
−0.950410 + 0.310998i \(0.899337\pi\)
\(14\) −0.585786 −0.156558
\(15\) −1.41421 + 1.00000i −0.365148 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 2.82843i 0.685994i 0.939336 + 0.342997i \(0.111442\pi\)
−0.939336 + 0.342997i \(0.888558\pi\)
\(18\) 1.00000 2.82843i 0.235702 0.666667i
\(19\) 4.24264 + 1.00000i 0.973329 + 0.229416i
\(20\) 1.00000i 0.223607i
\(21\) −0.585786 0.828427i −0.127829 0.180778i
\(22\) 5.41421i 1.15431i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 1.00000 + 1.41421i 0.204124 + 0.288675i
\(25\) −1.00000 −0.200000
\(26\) 2.24264i 0.439818i
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) 0.585786 0.110703
\(29\) −5.07107 −0.941674 −0.470837 0.882220i \(-0.656048\pi\)
−0.470837 + 0.882220i \(0.656048\pi\)
\(30\) 1.41421 1.00000i 0.258199 0.182574i
\(31\) 6.82843i 1.22642i 0.789919 + 0.613211i \(0.210122\pi\)
−0.789919 + 0.613211i \(0.789878\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.65685 5.41421i 1.33289 0.942494i
\(34\) 2.82843i 0.485071i
\(35\) 0.585786i 0.0990160i
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 2.24264i 0.368688i 0.982862 + 0.184344i \(0.0590160\pi\)
−0.982862 + 0.184344i \(0.940984\pi\)
\(38\) −4.24264 1.00000i −0.688247 0.162221i
\(39\) 3.17157 2.24264i 0.507858 0.359110i
\(40\) 1.00000i 0.158114i
\(41\) 11.0711 1.72901 0.864505 0.502624i \(-0.167632\pi\)
0.864505 + 0.502624i \(0.167632\pi\)
\(42\) 0.585786 + 0.828427i 0.0903888 + 0.127829i
\(43\) 6.58579 1.00432 0.502162 0.864774i \(-0.332538\pi\)
0.502162 + 0.864774i \(0.332538\pi\)
\(44\) 5.41421i 0.816223i
\(45\) 2.82843 + 1.00000i 0.421637 + 0.149071i
\(46\) 6.00000i 0.884652i
\(47\) 3.17157i 0.462621i 0.972880 + 0.231311i \(0.0743014\pi\)
−0.972880 + 0.231311i \(0.925699\pi\)
\(48\) −1.00000 1.41421i −0.144338 0.204124i
\(49\) −6.65685 −0.950979
\(50\) 1.00000 0.141421
\(51\) 4.00000 2.82843i 0.560112 0.396059i
\(52\) 2.24264i 0.310998i
\(53\) 3.17157 0.435649 0.217825 0.975988i \(-0.430104\pi\)
0.217825 + 0.975988i \(0.430104\pi\)
\(54\) −5.00000 + 1.41421i −0.680414 + 0.192450i
\(55\) 5.41421 0.730052
\(56\) −0.585786 −0.0782790
\(57\) −2.82843 7.00000i −0.374634 0.927173i
\(58\) 5.07107 0.665864
\(59\) 12.8284 1.67012 0.835059 0.550160i \(-0.185433\pi\)
0.835059 + 0.550160i \(0.185433\pi\)
\(60\) −1.41421 + 1.00000i −0.182574 + 0.129099i
\(61\) −4.48528 −0.574281 −0.287141 0.957888i \(-0.592705\pi\)
−0.287141 + 0.957888i \(0.592705\pi\)
\(62\) 6.82843i 0.867211i
\(63\) −0.585786 + 1.65685i −0.0738022 + 0.208744i
\(64\) 1.00000 0.125000
\(65\) 2.24264 0.278165
\(66\) −7.65685 + 5.41421i −0.942494 + 0.666444i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 2.82843i 0.342997i
\(69\) −8.48528 + 6.00000i −1.02151 + 0.722315i
\(70\) 0.585786i 0.0700149i
\(71\) 2.82843 0.335673 0.167836 0.985815i \(-0.446322\pi\)
0.167836 + 0.985815i \(0.446322\pi\)
\(72\) 1.00000 2.82843i 0.117851 0.333333i
\(73\) 2.48528 0.290880 0.145440 0.989367i \(-0.453540\pi\)
0.145440 + 0.989367i \(0.453540\pi\)
\(74\) 2.24264i 0.260702i
\(75\) 1.00000 + 1.41421i 0.115470 + 0.163299i
\(76\) 4.24264 + 1.00000i 0.486664 + 0.114708i
\(77\) 3.17157i 0.361434i
\(78\) −3.17157 + 2.24264i −0.359110 + 0.253929i
\(79\) 13.3137i 1.49791i 0.662621 + 0.748955i \(0.269444\pi\)
−0.662621 + 0.748955i \(0.730556\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) −11.0711 −1.22259
\(83\) 12.8284i 1.40810i −0.710149 0.704051i \(-0.751372\pi\)
0.710149 0.704051i \(-0.248628\pi\)
\(84\) −0.585786 0.828427i −0.0639145 0.0903888i
\(85\) 2.82843 0.306786
\(86\) −6.58579 −0.710164
\(87\) 5.07107 + 7.17157i 0.543676 + 0.768873i
\(88\) 5.41421i 0.577157i
\(89\) −10.5858 −1.12209 −0.561046 0.827785i \(-0.689601\pi\)
−0.561046 + 0.827785i \(0.689601\pi\)
\(90\) −2.82843 1.00000i −0.298142 0.105409i
\(91\) 1.31371i 0.137714i
\(92\) 6.00000i 0.625543i
\(93\) 9.65685 6.82843i 1.00137 0.708075i
\(94\) 3.17157i 0.327123i
\(95\) 1.00000 4.24264i 0.102598 0.435286i
\(96\) 1.00000 + 1.41421i 0.102062 + 0.144338i
\(97\) 6.58579i 0.668685i 0.942452 + 0.334343i \(0.108514\pi\)
−0.942452 + 0.334343i \(0.891486\pi\)
\(98\) 6.65685 0.672444
\(99\) −15.3137 5.41421i −1.53909 0.544149i
\(100\) −1.00000 −0.100000
\(101\) 7.65685i 0.761885i 0.924599 + 0.380943i \(0.124401\pi\)
−0.924599 + 0.380943i \(0.875599\pi\)
\(102\) −4.00000 + 2.82843i −0.396059 + 0.280056i
\(103\) 4.34315i 0.427943i −0.976840 0.213971i \(-0.931360\pi\)
0.976840 0.213971i \(-0.0686399\pi\)
\(104\) 2.24264i 0.219909i
\(105\) −0.828427 + 0.585786i −0.0808462 + 0.0571669i
\(106\) −3.17157 −0.308050
\(107\) −3.65685 −0.353521 −0.176761 0.984254i \(-0.556562\pi\)
−0.176761 + 0.984254i \(0.556562\pi\)
\(108\) 5.00000 1.41421i 0.481125 0.136083i
\(109\) 2.34315i 0.224433i 0.993684 + 0.112216i \(0.0357950\pi\)
−0.993684 + 0.112216i \(0.964205\pi\)
\(110\) −5.41421 −0.516225
\(111\) 3.17157 2.24264i 0.301032 0.212862i
\(112\) 0.585786 0.0553516
\(113\) −12.8284 −1.20680 −0.603398 0.797440i \(-0.706187\pi\)
−0.603398 + 0.797440i \(0.706187\pi\)
\(114\) 2.82843 + 7.00000i 0.264906 + 0.655610i
\(115\) −6.00000 −0.559503
\(116\) −5.07107 −0.470837
\(117\) −6.34315 2.24264i −0.586424 0.207332i
\(118\) −12.8284 −1.18095
\(119\) 1.65685i 0.151884i
\(120\) 1.41421 1.00000i 0.129099 0.0912871i
\(121\) −18.3137 −1.66488
\(122\) 4.48528 0.406078
\(123\) −11.0711 15.6569i −0.998245 1.41173i
\(124\) 6.82843i 0.613211i
\(125\) 1.00000i 0.0894427i
\(126\) 0.585786 1.65685i 0.0521860 0.147604i
\(127\) 12.8284i 1.13834i 0.822220 + 0.569169i \(0.192735\pi\)
−0.822220 + 0.569169i \(0.807265\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −6.58579 9.31371i −0.579846 0.820026i
\(130\) −2.24264 −0.196693
\(131\) 4.92893i 0.430643i 0.976543 + 0.215321i \(0.0690799\pi\)
−0.976543 + 0.215321i \(0.930920\pi\)
\(132\) 7.65685 5.41421i 0.666444 0.471247i
\(133\) 2.48528 + 0.585786i 0.215501 + 0.0507941i
\(134\) 0 0
\(135\) −1.41421 5.00000i −0.121716 0.430331i
\(136\) 2.82843i 0.242536i
\(137\) 14.4853i 1.23756i 0.785564 + 0.618781i \(0.212373\pi\)
−0.785564 + 0.618781i \(0.787627\pi\)
\(138\) 8.48528 6.00000i 0.722315 0.510754i
\(139\) 18.1421 1.53880 0.769398 0.638770i \(-0.220556\pi\)
0.769398 + 0.638770i \(0.220556\pi\)
\(140\) 0.585786i 0.0495080i
\(141\) 4.48528 3.17157i 0.377729 0.267095i
\(142\) −2.82843 −0.237356
\(143\) −12.1421 −1.01538
\(144\) −1.00000 + 2.82843i −0.0833333 + 0.235702i
\(145\) 5.07107i 0.421129i
\(146\) −2.48528 −0.205683
\(147\) 6.65685 + 9.41421i 0.549048 + 0.776471i
\(148\) 2.24264i 0.184344i
\(149\) 14.4853i 1.18668i −0.804952 0.593340i \(-0.797809\pi\)
0.804952 0.593340i \(-0.202191\pi\)
\(150\) −1.00000 1.41421i −0.0816497 0.115470i
\(151\) 20.4853i 1.66707i −0.552468 0.833534i \(-0.686314\pi\)
0.552468 0.833534i \(-0.313686\pi\)
\(152\) −4.24264 1.00000i −0.344124 0.0811107i
\(153\) −8.00000 2.82843i −0.646762 0.228665i
\(154\) 3.17157i 0.255573i
\(155\) 6.82843 0.548472
\(156\) 3.17157 2.24264i 0.253929 0.179555i
\(157\) −23.7990 −1.89937 −0.949683 0.313212i \(-0.898595\pi\)
−0.949683 + 0.313212i \(0.898595\pi\)
\(158\) 13.3137i 1.05918i
\(159\) −3.17157 4.48528i −0.251522 0.355706i
\(160\) 1.00000i 0.0790569i
\(161\) 3.51472i 0.276999i
\(162\) 7.00000 + 5.65685i 0.549972 + 0.444444i
\(163\) 12.7279 0.996928 0.498464 0.866910i \(-0.333898\pi\)
0.498464 + 0.866910i \(0.333898\pi\)
\(164\) 11.0711 0.864505
\(165\) −5.41421 7.65685i −0.421496 0.596085i
\(166\) 12.8284i 0.995679i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0.585786 + 0.828427i 0.0451944 + 0.0639145i
\(169\) 7.97056 0.613120
\(170\) −2.82843 −0.216930
\(171\) −7.07107 + 11.0000i −0.540738 + 0.841191i
\(172\) 6.58579 0.502162
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −5.07107 7.17157i −0.384437 0.543676i
\(175\) −0.585786 −0.0442813
\(176\) 5.41421i 0.408112i
\(177\) −12.8284 18.1421i −0.964244 1.36365i
\(178\) 10.5858 0.793438
\(179\) 21.7990 1.62933 0.814667 0.579930i \(-0.196920\pi\)
0.814667 + 0.579930i \(0.196920\pi\)
\(180\) 2.82843 + 1.00000i 0.210819 + 0.0745356i
\(181\) 10.8284i 0.804871i −0.915448 0.402435i \(-0.868164\pi\)
0.915448 0.402435i \(-0.131836\pi\)
\(182\) 1.31371i 0.0973786i
\(183\) 4.48528 + 6.34315i 0.331562 + 0.468899i
\(184\) 6.00000i 0.442326i
\(185\) 2.24264 0.164882
\(186\) −9.65685 + 6.82843i −0.708075 + 0.500685i
\(187\) −15.3137 −1.11985
\(188\) 3.17157i 0.231311i
\(189\) 2.92893 0.828427i 0.213048 0.0602592i
\(190\) −1.00000 + 4.24264i −0.0725476 + 0.307794i
\(191\) 10.2426i 0.741131i 0.928806 + 0.370566i \(0.120836\pi\)
−0.928806 + 0.370566i \(0.879164\pi\)
\(192\) −1.00000 1.41421i −0.0721688 0.102062i
\(193\) 19.5563i 1.40770i −0.710350 0.703848i \(-0.751463\pi\)
0.710350 0.703848i \(-0.248537\pi\)
\(194\) 6.58579i 0.472832i
\(195\) −2.24264 3.17157i −0.160599 0.227121i
\(196\) −6.65685 −0.475490
\(197\) 18.1421i 1.29257i 0.763095 + 0.646287i \(0.223679\pi\)
−0.763095 + 0.646287i \(0.776321\pi\)
\(198\) 15.3137 + 5.41421i 1.08830 + 0.384771i
\(199\) −16.9706 −1.20301 −0.601506 0.798869i \(-0.705432\pi\)
−0.601506 + 0.798869i \(0.705432\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0 0
\(202\) 7.65685i 0.538734i
\(203\) −2.97056 −0.208493
\(204\) 4.00000 2.82843i 0.280056 0.198030i
\(205\) 11.0711i 0.773237i
\(206\) 4.34315i 0.302601i
\(207\) 16.9706 + 6.00000i 1.17954 + 0.417029i
\(208\) 2.24264i 0.155499i
\(209\) −5.41421 + 22.9706i −0.374509 + 1.58891i
\(210\) 0.828427 0.585786i 0.0571669 0.0404231i
\(211\) 2.00000i 0.137686i 0.997628 + 0.0688428i \(0.0219307\pi\)
−0.997628 + 0.0688428i \(0.978069\pi\)
\(212\) 3.17157 0.217825
\(213\) −2.82843 4.00000i −0.193801 0.274075i
\(214\) 3.65685 0.249977
\(215\) 6.58579i 0.449147i
\(216\) −5.00000 + 1.41421i −0.340207 + 0.0962250i
\(217\) 4.00000i 0.271538i
\(218\) 2.34315i 0.158698i
\(219\) −2.48528 3.51472i −0.167940 0.237503i
\(220\) 5.41421 0.365026
\(221\) −6.34315 −0.426686
\(222\) −3.17157 + 2.24264i −0.212862 + 0.150516i
\(223\) 18.0000i 1.20537i 0.797980 + 0.602685i \(0.205902\pi\)
−0.797980 + 0.602685i \(0.794098\pi\)
\(224\) −0.585786 −0.0391395
\(225\) 1.00000 2.82843i 0.0666667 0.188562i
\(226\) 12.8284 0.853334
\(227\) 2.34315 0.155520 0.0777600 0.996972i \(-0.475223\pi\)
0.0777600 + 0.996972i \(0.475223\pi\)
\(228\) −2.82843 7.00000i −0.187317 0.463586i
\(229\) 8.48528 0.560723 0.280362 0.959894i \(-0.409546\pi\)
0.280362 + 0.959894i \(0.409546\pi\)
\(230\) 6.00000 0.395628
\(231\) 4.48528 3.17157i 0.295110 0.208674i
\(232\) 5.07107 0.332932
\(233\) 17.7990i 1.16605i 0.812454 + 0.583025i \(0.198131\pi\)
−0.812454 + 0.583025i \(0.801869\pi\)
\(234\) 6.34315 + 2.24264i 0.414664 + 0.146606i
\(235\) 3.17157 0.206891
\(236\) 12.8284 0.835059
\(237\) 18.8284 13.3137i 1.22304 0.864818i
\(238\) 1.65685i 0.107398i
\(239\) 0.100505i 0.00650113i −0.999995 0.00325057i \(-0.998965\pi\)
0.999995 0.00325057i \(-0.00103469\pi\)
\(240\) −1.41421 + 1.00000i −0.0912871 + 0.0645497i
\(241\) 8.48528i 0.546585i −0.961931 0.273293i \(-0.911887\pi\)
0.961931 0.273293i \(-0.0881127\pi\)
\(242\) 18.3137 1.17725
\(243\) −1.00000 + 15.5563i −0.0641500 + 0.997940i
\(244\) −4.48528 −0.287141
\(245\) 6.65685i 0.425291i
\(246\) 11.0711 + 15.6569i 0.705866 + 0.998245i
\(247\) −2.24264 + 9.51472i −0.142696 + 0.605407i
\(248\) 6.82843i 0.433606i
\(249\) −18.1421 + 12.8284i −1.14971 + 0.812969i
\(250\) 1.00000i 0.0632456i
\(251\) 4.92893i 0.311111i 0.987827 + 0.155556i \(0.0497168\pi\)
−0.987827 + 0.155556i \(0.950283\pi\)
\(252\) −0.585786 + 1.65685i −0.0369011 + 0.104372i
\(253\) 32.4853 2.04233
\(254\) 12.8284i 0.804927i
\(255\) −2.82843 4.00000i −0.177123 0.250490i
\(256\) 1.00000 0.0625000
\(257\) −28.1421 −1.75546 −0.877729 0.479157i \(-0.840942\pi\)
−0.877729 + 0.479157i \(0.840942\pi\)
\(258\) 6.58579 + 9.31371i 0.410013 + 0.579846i
\(259\) 1.31371i 0.0816299i
\(260\) 2.24264 0.139083
\(261\) 5.07107 14.3431i 0.313891 0.887818i
\(262\) 4.92893i 0.304510i
\(263\) 11.1716i 0.688869i −0.938810 0.344434i \(-0.888071\pi\)
0.938810 0.344434i \(-0.111929\pi\)
\(264\) −7.65685 + 5.41421i −0.471247 + 0.333222i
\(265\) 3.17157i 0.194828i
\(266\) −2.48528 0.585786i −0.152382 0.0359169i
\(267\) 10.5858 + 14.9706i 0.647840 + 0.916184i
\(268\) 0 0
\(269\) 24.3848 1.48677 0.743383 0.668866i \(-0.233220\pi\)
0.743383 + 0.668866i \(0.233220\pi\)
\(270\) 1.41421 + 5.00000i 0.0860663 + 0.304290i
\(271\) −28.9706 −1.75984 −0.879918 0.475125i \(-0.842403\pi\)
−0.879918 + 0.475125i \(0.842403\pi\)
\(272\) 2.82843i 0.171499i
\(273\) 1.85786 1.31371i 0.112443 0.0795093i
\(274\) 14.4853i 0.875088i
\(275\) 5.41421i 0.326489i
\(276\) −8.48528 + 6.00000i −0.510754 + 0.361158i
\(277\) 24.9706 1.50034 0.750168 0.661247i \(-0.229973\pi\)
0.750168 + 0.661247i \(0.229973\pi\)
\(278\) −18.1421 −1.08809
\(279\) −19.3137 6.82843i −1.15628 0.408807i
\(280\) 0.585786i 0.0350074i
\(281\) 0.928932 0.0554154 0.0277077 0.999616i \(-0.491179\pi\)
0.0277077 + 0.999616i \(0.491179\pi\)
\(282\) −4.48528 + 3.17157i −0.267095 + 0.188864i
\(283\) 12.7279 0.756596 0.378298 0.925684i \(-0.376509\pi\)
0.378298 + 0.925684i \(0.376509\pi\)
\(284\) 2.82843 0.167836
\(285\) −7.00000 + 2.82843i −0.414644 + 0.167542i
\(286\) 12.1421 0.717980
\(287\) 6.48528 0.382814
\(288\) 1.00000 2.82843i 0.0589256 0.166667i
\(289\) 9.00000 0.529412
\(290\) 5.07107i 0.297783i
\(291\) 9.31371 6.58579i 0.545979 0.386066i
\(292\) 2.48528 0.145440
\(293\) −3.17157 −0.185285 −0.0926426 0.995699i \(-0.529531\pi\)
−0.0926426 + 0.995699i \(0.529531\pi\)
\(294\) −6.65685 9.41421i −0.388236 0.549048i
\(295\) 12.8284i 0.746900i
\(296\) 2.24264i 0.130351i
\(297\) 7.65685 + 27.0711i 0.444296 + 1.57082i
\(298\) 14.4853i 0.839110i
\(299\) 13.4558 0.778172
\(300\) 1.00000 + 1.41421i 0.0577350 + 0.0816497i
\(301\) 3.85786 0.222364
\(302\) 20.4853i 1.17880i
\(303\) 10.8284 7.65685i 0.622077 0.439875i
\(304\) 4.24264 + 1.00000i 0.243332 + 0.0573539i
\(305\) 4.48528i 0.256826i
\(306\) 8.00000 + 2.82843i 0.457330 + 0.161690i
\(307\) 18.1421i 1.03543i 0.855554 + 0.517713i \(0.173217\pi\)
−0.855554 + 0.517713i \(0.826783\pi\)
\(308\) 3.17157i 0.180717i
\(309\) −6.14214 + 4.34315i −0.349414 + 0.247073i
\(310\) −6.82843 −0.387829
\(311\) 5.07107i 0.287554i 0.989610 + 0.143777i \(0.0459248\pi\)
−0.989610 + 0.143777i \(0.954075\pi\)
\(312\) −3.17157 + 2.24264i −0.179555 + 0.126965i
\(313\) −16.8284 −0.951199 −0.475599 0.879662i \(-0.657769\pi\)
−0.475599 + 0.879662i \(0.657769\pi\)
\(314\) 23.7990 1.34305
\(315\) 1.65685 + 0.585786i 0.0933532 + 0.0330053i
\(316\) 13.3137i 0.748955i
\(317\) 0.343146 0.0192730 0.00963649 0.999954i \(-0.496933\pi\)
0.00963649 + 0.999954i \(0.496933\pi\)
\(318\) 3.17157 + 4.48528i 0.177853 + 0.251522i
\(319\) 27.4558i 1.53723i
\(320\) 1.00000i 0.0559017i
\(321\) 3.65685 + 5.17157i 0.204106 + 0.288649i
\(322\) 3.51472i 0.195868i
\(323\) −2.82843 + 12.0000i −0.157378 + 0.667698i
\(324\) −7.00000 5.65685i −0.388889 0.314270i
\(325\) 2.24264i 0.124399i
\(326\) −12.7279 −0.704934
\(327\) 3.31371 2.34315i 0.183248 0.129576i
\(328\) −11.0711 −0.611297
\(329\) 1.85786i 0.102427i
\(330\) 5.41421 + 7.65685i 0.298043 + 0.421496i
\(331\) 16.9706i 0.932786i −0.884577 0.466393i \(-0.845553\pi\)
0.884577 0.466393i \(-0.154447\pi\)
\(332\) 12.8284i 0.704051i
\(333\) −6.34315 2.24264i −0.347602 0.122896i
\(334\) 0 0
\(335\) 0 0
\(336\) −0.585786 0.828427i −0.0319573 0.0451944i
\(337\) 29.2132i 1.59134i −0.605727 0.795672i \(-0.707118\pi\)
0.605727 0.795672i \(-0.292882\pi\)
\(338\) −7.97056 −0.433541
\(339\) 12.8284 + 18.1421i 0.696745 + 0.985346i
\(340\) 2.82843 0.153393
\(341\) −36.9706 −2.00207
\(342\) 7.07107 11.0000i 0.382360 0.594812i
\(343\) −8.00000 −0.431959
\(344\) −6.58579 −0.355082
\(345\) 6.00000 + 8.48528i 0.323029 + 0.456832i
\(346\) 6.00000 0.322562
\(347\) 30.2843i 1.62574i −0.582442 0.812872i \(-0.697903\pi\)
0.582442 0.812872i \(-0.302097\pi\)
\(348\) 5.07107 + 7.17157i 0.271838 + 0.384437i
\(349\) −10.9706 −0.587241 −0.293620 0.955922i \(-0.594860\pi\)
−0.293620 + 0.955922i \(0.594860\pi\)
\(350\) 0.585786 0.0313116
\(351\) 3.17157 + 11.2132i 0.169286 + 0.598517i
\(352\) 5.41421i 0.288579i
\(353\) 8.82843i 0.469890i 0.972009 + 0.234945i \(0.0754910\pi\)
−0.972009 + 0.234945i \(0.924509\pi\)
\(354\) 12.8284 + 18.1421i 0.681823 + 0.964244i
\(355\) 2.82843i 0.150117i
\(356\) −10.5858 −0.561046
\(357\) 2.34315 1.65685i 0.124012 0.0876900i
\(358\) −21.7990 −1.15211
\(359\) 19.4142i 1.02464i 0.858794 + 0.512322i \(0.171214\pi\)
−0.858794 + 0.512322i \(0.828786\pi\)
\(360\) −2.82843 1.00000i −0.149071 0.0527046i
\(361\) 17.0000 + 8.48528i 0.894737 + 0.446594i
\(362\) 10.8284i 0.569129i
\(363\) 18.3137 + 25.8995i 0.961220 + 1.35937i
\(364\) 1.31371i 0.0688570i
\(365\) 2.48528i 0.130086i
\(366\) −4.48528 6.34315i −0.234449 0.331562i
\(367\) −14.2426 −0.743460 −0.371730 0.928341i \(-0.621235\pi\)
−0.371730 + 0.928341i \(0.621235\pi\)
\(368\) 6.00000i 0.312772i
\(369\) −11.0711 + 31.3137i −0.576337 + 1.63013i
\(370\) −2.24264 −0.116589
\(371\) 1.85786 0.0964555
\(372\) 9.65685 6.82843i 0.500685 0.354037i
\(373\) 14.0416i 0.727048i −0.931585 0.363524i \(-0.881573\pi\)
0.931585 0.363524i \(-0.118427\pi\)
\(374\) 15.3137 0.791853
\(375\) 1.41421 1.00000i 0.0730297 0.0516398i
\(376\) 3.17157i 0.163561i
\(377\) 11.3726i 0.585718i
\(378\) −2.92893 + 0.828427i −0.150648 + 0.0426097i
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 1.00000 4.24264i 0.0512989 0.217643i
\(381\) 18.1421 12.8284i 0.929450 0.657220i
\(382\) 10.2426i 0.524059i
\(383\) −32.1421 −1.64239 −0.821193 0.570650i \(-0.806691\pi\)
−0.821193 + 0.570650i \(0.806691\pi\)
\(384\) 1.00000 + 1.41421i 0.0510310 + 0.0721688i
\(385\) 3.17157 0.161638
\(386\) 19.5563i 0.995392i
\(387\) −6.58579 + 18.6274i −0.334774 + 0.946885i
\(388\) 6.58579i 0.334343i
\(389\) 20.3431i 1.03144i −0.856758 0.515719i \(-0.827525\pi\)
0.856758 0.515719i \(-0.172475\pi\)
\(390\) 2.24264 + 3.17157i 0.113561 + 0.160599i
\(391\) 16.9706 0.858238
\(392\) 6.65685 0.336222
\(393\) 6.97056 4.92893i 0.351618 0.248632i
\(394\) 18.1421i 0.913988i
\(395\) 13.3137 0.669885
\(396\) −15.3137 5.41421i −0.769543 0.272074i
\(397\) 16.9706 0.851728 0.425864 0.904787i \(-0.359970\pi\)
0.425864 + 0.904787i \(0.359970\pi\)
\(398\) 16.9706 0.850657
\(399\) −1.65685 4.10051i −0.0829465 0.205282i
\(400\) −1.00000 −0.0500000
\(401\) 18.3848 0.918092 0.459046 0.888413i \(-0.348191\pi\)
0.459046 + 0.888413i \(0.348191\pi\)
\(402\) 0 0
\(403\) −15.3137 −0.762830
\(404\) 7.65685i 0.380943i
\(405\) −5.65685 + 7.00000i −0.281091 + 0.347833i
\(406\) 2.97056 0.147427
\(407\) −12.1421 −0.601863
\(408\) −4.00000 + 2.82843i −0.198030 + 0.140028i
\(409\) 4.48528i 0.221783i −0.993833 0.110891i \(-0.964629\pi\)
0.993833 0.110891i \(-0.0353706\pi\)
\(410\) 11.0711i 0.546761i
\(411\) 20.4853 14.4853i 1.01046 0.714506i
\(412\) 4.34315i 0.213971i
\(413\) 7.51472 0.369775
\(414\) −16.9706 6.00000i −0.834058 0.294884i
\(415\) −12.8284 −0.629723
\(416\) 2.24264i 0.109955i
\(417\) −18.1421 25.6569i −0.888424 1.25642i
\(418\) 5.41421 22.9706i 0.264818 1.12353i
\(419\) 6.38478i 0.311917i −0.987764 0.155958i \(-0.950153\pi\)
0.987764 0.155958i \(-0.0498466\pi\)
\(420\) −0.828427 + 0.585786i −0.0404231 + 0.0285835i
\(421\) 24.2843i 1.18354i −0.806106 0.591771i \(-0.798429\pi\)
0.806106 0.591771i \(-0.201571\pi\)
\(422\) 2.00000i 0.0973585i
\(423\) −8.97056 3.17157i −0.436164 0.154207i
\(424\) −3.17157 −0.154025
\(425\) 2.82843i 0.137199i
\(426\) 2.82843 + 4.00000i 0.137038 + 0.193801i
\(427\) −2.62742 −0.127150
\(428\) −3.65685 −0.176761
\(429\) 12.1421 + 17.1716i 0.586228 + 0.829051i
\(430\) 6.58579i 0.317595i
\(431\) 19.3137 0.930309 0.465154 0.885230i \(-0.345999\pi\)
0.465154 + 0.885230i \(0.345999\pi\)
\(432\) 5.00000 1.41421i 0.240563 0.0680414i
\(433\) 14.3848i 0.691288i 0.938366 + 0.345644i \(0.112340\pi\)
−0.938366 + 0.345644i \(0.887660\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 7.17157 5.07107i 0.343851 0.243139i
\(436\) 2.34315i 0.112216i
\(437\) 6.00000 25.4558i 0.287019 1.21772i
\(438\) 2.48528 + 3.51472i 0.118751 + 0.167940i
\(439\) 39.9411i 1.90629i −0.302520 0.953143i \(-0.597828\pi\)
0.302520 0.953143i \(-0.402172\pi\)
\(440\) −5.41421 −0.258113
\(441\) 6.65685 18.8284i 0.316993 0.896592i
\(442\) 6.34315 0.301713
\(443\) 18.0000i 0.855206i 0.903967 + 0.427603i \(0.140642\pi\)
−0.903967 + 0.427603i \(0.859358\pi\)
\(444\) 3.17157 2.24264i 0.150516 0.106431i
\(445\) 10.5858i 0.501814i
\(446\) 18.0000i 0.852325i
\(447\) −20.4853 + 14.4853i −0.968921 + 0.685130i
\(448\) 0.585786 0.0276758
\(449\) 16.2426 0.766538 0.383269 0.923637i \(-0.374798\pi\)
0.383269 + 0.923637i \(0.374798\pi\)
\(450\) −1.00000 + 2.82843i −0.0471405 + 0.133333i
\(451\) 59.9411i 2.82252i
\(452\) −12.8284 −0.603398
\(453\) −28.9706 + 20.4853i −1.36116 + 0.962482i
\(454\) −2.34315 −0.109969
\(455\) 1.31371 0.0615876
\(456\) 2.82843 + 7.00000i 0.132453 + 0.327805i
\(457\) −0.828427 −0.0387522 −0.0193761 0.999812i \(-0.506168\pi\)
−0.0193761 + 0.999812i \(0.506168\pi\)
\(458\) −8.48528 −0.396491
\(459\) 4.00000 + 14.1421i 0.186704 + 0.660098i
\(460\) −6.00000 −0.279751
\(461\) 28.1421i 1.31071i −0.755321 0.655355i \(-0.772519\pi\)
0.755321 0.655355i \(-0.227481\pi\)
\(462\) −4.48528 + 3.17157i −0.208674 + 0.147555i
\(463\) 19.2132 0.892913 0.446457 0.894805i \(-0.352686\pi\)
0.446457 + 0.894805i \(0.352686\pi\)
\(464\) −5.07107 −0.235418
\(465\) −6.82843 9.65685i −0.316661 0.447826i
\(466\) 17.7990i 0.824522i
\(467\) 25.7990i 1.19383i −0.802303 0.596917i \(-0.796392\pi\)
0.802303 0.596917i \(-0.203608\pi\)
\(468\) −6.34315 2.24264i −0.293212 0.103666i
\(469\) 0 0
\(470\) −3.17157 −0.146294
\(471\) 23.7990 + 33.6569i 1.09660 + 1.55083i
\(472\) −12.8284 −0.590476
\(473\) 35.6569i 1.63950i
\(474\) −18.8284 + 13.3137i −0.864818 + 0.611519i
\(475\) −4.24264 1.00000i −0.194666 0.0458831i
\(476\) 1.65685i 0.0759418i
\(477\) −3.17157 + 8.97056i −0.145216 + 0.410734i
\(478\) 0.100505i 0.00459699i
\(479\) 3.41421i 0.155999i −0.996953 0.0779997i \(-0.975147\pi\)
0.996953 0.0779997i \(-0.0248533\pi\)
\(480\) 1.41421 1.00000i 0.0645497 0.0456435i
\(481\) −5.02944 −0.229323
\(482\) 8.48528i 0.386494i
\(483\) −4.97056 + 3.51472i −0.226168 + 0.159925i
\(484\) −18.3137 −0.832441
\(485\) 6.58579 0.299045
\(486\) 1.00000 15.5563i 0.0453609 0.705650i
\(487\) 36.1421i 1.63776i −0.573967 0.818878i \(-0.694596\pi\)
0.573967 0.818878i \(-0.305404\pi\)
\(488\) 4.48528 0.203039
\(489\) −12.7279 18.0000i −0.575577 0.813988i
\(490\) 6.65685i 0.300726i
\(491\) 43.5563i 1.96567i −0.184485 0.982835i \(-0.559062\pi\)
0.184485 0.982835i \(-0.440938\pi\)
\(492\) −11.0711 15.6569i −0.499122 0.705866i
\(493\) 14.3431i 0.645983i
\(494\) 2.24264 9.51472i 0.100901 0.428087i
\(495\) −5.41421 + 15.3137i −0.243351 + 0.688300i
\(496\) 6.82843i 0.306605i
\(497\) 1.65685 0.0743201
\(498\) 18.1421 12.8284i 0.812969 0.574856i
\(499\) −25.6569 −1.14856 −0.574279 0.818659i \(-0.694718\pi\)
−0.574279 + 0.818659i \(0.694718\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 0 0
\(502\) 4.92893i 0.219989i
\(503\) 14.2843i 0.636904i −0.947939 0.318452i \(-0.896837\pi\)
0.947939 0.318452i \(-0.103163\pi\)
\(504\) 0.585786 1.65685i 0.0260930 0.0738022i
\(505\) 7.65685 0.340726
\(506\) −32.4853 −1.44415
\(507\) −7.97056 11.2721i −0.353985 0.500611i
\(508\) 12.8284i 0.569169i
\(509\) −4.10051 −0.181752 −0.0908758 0.995862i \(-0.528967\pi\)
−0.0908758 + 0.995862i \(0.528967\pi\)
\(510\) 2.82843 + 4.00000i 0.125245 + 0.177123i
\(511\) 1.45584 0.0644028
\(512\) −1.00000 −0.0441942
\(513\) 22.6274 1.00000i 0.999025 0.0441511i
\(514\) 28.1421 1.24130
\(515\) −4.34315 −0.191382
\(516\) −6.58579 9.31371i −0.289923 0.410013i
\(517\) −17.1716 −0.755205
\(518\) 1.31371i 0.0577210i
\(519\) 6.00000 + 8.48528i 0.263371 + 0.372463i
\(520\) −2.24264 −0.0983463
\(521\) −14.3848 −0.630208 −0.315104 0.949057i \(-0.602039\pi\)
−0.315104 + 0.949057i \(0.602039\pi\)
\(522\) −5.07107 + 14.3431i −0.221955 + 0.627782i
\(523\) 8.97056i 0.392255i 0.980578 + 0.196128i \(0.0628367\pi\)
−0.980578 + 0.196128i \(0.937163\pi\)
\(524\) 4.92893i 0.215321i
\(525\) 0.585786 + 0.828427i 0.0255658 + 0.0361555i
\(526\) 11.1716i 0.487104i
\(527\) −19.3137 −0.841318
\(528\) 7.65685 5.41421i 0.333222 0.235623i
\(529\) −13.0000 −0.565217
\(530\) 3.17157i 0.137764i
\(531\) −12.8284 + 36.2843i −0.556706 + 1.57460i
\(532\) 2.48528 + 0.585786i 0.107751 + 0.0253971i
\(533\) 24.8284i 1.07544i
\(534\) −10.5858 14.9706i −0.458092 0.647840i
\(535\) 3.65685i 0.158100i
\(536\) 0 0
\(537\) −21.7990 30.8284i −0.940696 1.33034i
\(538\) −24.3848 −1.05130
\(539\) 36.0416i 1.55242i
\(540\) −1.41421 5.00000i −0.0608581 0.215166i
\(541\) −42.9706 −1.84745 −0.923724 0.383058i \(-0.874871\pi\)
−0.923724 + 0.383058i \(0.874871\pi\)
\(542\) 28.9706 1.24439
\(543\) −15.3137 + 10.8284i −0.657174 + 0.464692i
\(544\) 2.82843i 0.121268i
\(545\) 2.34315 0.100369
\(546\) −1.85786 + 1.31371i −0.0795093 + 0.0562215i
\(547\) 13.1716i 0.563176i 0.959535 + 0.281588i \(0.0908611\pi\)
−0.959535 + 0.281588i \(0.909139\pi\)
\(548\) 14.4853i 0.618781i
\(549\) 4.48528 12.6863i 0.191427 0.541438i
\(550\) 5.41421i 0.230863i
\(551\) −21.5147 5.07107i −0.916558 0.216035i
\(552\) 8.48528 6.00000i 0.361158 0.255377i
\(553\) 7.79899i 0.331647i
\(554\) −24.9706 −1.06090
\(555\) −2.24264 3.17157i −0.0951948 0.134626i
\(556\) 18.1421 0.769398
\(557\) 28.6274i 1.21298i 0.795090 + 0.606491i \(0.207424\pi\)
−0.795090 + 0.606491i \(0.792576\pi\)
\(558\) 19.3137 + 6.82843i 0.817614 + 0.289070i
\(559\) 14.7696i 0.624686i
\(560\) 0.585786i 0.0247540i
\(561\) 15.3137 + 21.6569i 0.646545 + 0.914353i
\(562\) −0.928932 −0.0391846
\(563\) 13.6569 0.575568 0.287784 0.957695i \(-0.407082\pi\)
0.287784 + 0.957695i \(0.407082\pi\)
\(564\) 4.48528 3.17157i 0.188864 0.133547i
\(565\) 12.8284i 0.539696i
\(566\) −12.7279 −0.534994
\(567\) −4.10051 3.31371i −0.172205 0.139163i
\(568\) −2.82843 −0.118678
\(569\) 28.9289 1.21276 0.606382 0.795174i \(-0.292620\pi\)
0.606382 + 0.795174i \(0.292620\pi\)
\(570\) 7.00000 2.82843i 0.293198 0.118470i
\(571\) −1.65685 −0.0693372 −0.0346686 0.999399i \(-0.511038\pi\)
−0.0346686 + 0.999399i \(0.511038\pi\)
\(572\) −12.1421 −0.507688
\(573\) 14.4853 10.2426i 0.605131 0.427892i
\(574\) −6.48528 −0.270690
\(575\) 6.00000i 0.250217i
\(576\) −1.00000 + 2.82843i −0.0416667 + 0.117851i
\(577\) −19.1716 −0.798123 −0.399062 0.916924i \(-0.630664\pi\)
−0.399062 + 0.916924i \(0.630664\pi\)
\(578\) −9.00000 −0.374351
\(579\) −27.6569 + 19.5563i −1.14938 + 0.812734i
\(580\) 5.07107i 0.210565i
\(581\) 7.51472i 0.311763i
\(582\) −9.31371 + 6.58579i −0.386066 + 0.272990i
\(583\) 17.1716i 0.711174i
\(584\) −2.48528 −0.102842
\(585\) −2.24264 + 6.34315i −0.0927218 + 0.262257i
\(586\) 3.17157 0.131016
\(587\) 3.17157i 0.130905i −0.997856 0.0654524i \(-0.979151\pi\)
0.997856 0.0654524i \(-0.0208491\pi\)
\(588\) 6.65685 + 9.41421i 0.274524 + 0.388236i
\(589\) −6.82843 + 28.9706i −0.281360 + 1.19371i
\(590\) 12.8284i 0.528138i
\(591\) 25.6569 18.1421i 1.05538 0.746268i
\(592\) 2.24264i 0.0921720i
\(593\) 12.1421i 0.498618i −0.968424 0.249309i \(-0.919797\pi\)
0.968424 0.249309i \(-0.0802034\pi\)
\(594\) −7.65685 27.0711i −0.314165 1.11074i
\(595\) 1.65685 0.0679244
\(596\) 14.4853i 0.593340i
\(597\) 16.9706 + 24.0000i 0.694559 + 0.982255i
\(598\) −13.4558 −0.550250
\(599\) −21.1716 −0.865047 −0.432524 0.901623i \(-0.642377\pi\)
−0.432524 + 0.901623i \(0.642377\pi\)
\(600\) −1.00000 1.41421i −0.0408248 0.0577350i
\(601\) 4.00000i 0.163163i −0.996667 0.0815817i \(-0.974003\pi\)
0.996667 0.0815817i \(-0.0259972\pi\)
\(602\) −3.85786 −0.157235
\(603\) 0 0
\(604\) 20.4853i 0.833534i
\(605\) 18.3137i 0.744558i
\(606\) −10.8284 + 7.65685i −0.439875 + 0.311038i
\(607\) 1.51472i 0.0614805i 0.999527 + 0.0307403i \(0.00978647\pi\)
−0.999527 + 0.0307403i \(0.990214\pi\)
\(608\) −4.24264 1.00000i −0.172062 0.0405554i
\(609\) 2.97056 + 4.20101i 0.120373 + 0.170234i
\(610\) 4.48528i 0.181604i
\(611\) −7.11270 −0.287749
\(612\) −8.00000 2.82843i −0.323381 0.114332i
\(613\) −23.1127 −0.933513 −0.466757 0.884386i \(-0.654578\pi\)
−0.466757 + 0.884386i \(0.654578\pi\)
\(614\) 18.1421i 0.732157i
\(615\) −15.6569 + 11.0711i −0.631345 + 0.446429i
\(616\) 3.17157i 0.127786i
\(617\) 18.8284i 0.758004i −0.925396 0.379002i \(-0.876267\pi\)
0.925396 0.379002i \(-0.123733\pi\)
\(618\) 6.14214 4.34315i 0.247073 0.174707i
\(619\) 41.4558 1.66625 0.833126 0.553084i \(-0.186549\pi\)
0.833126 + 0.553084i \(0.186549\pi\)
\(620\) 6.82843 0.274236
\(621\) −8.48528 30.0000i −0.340503 1.20386i
\(622\) 5.07107i 0.203331i
\(623\) −6.20101 −0.248438
\(624\) 3.17157 2.24264i 0.126965 0.0897775i
\(625\) 1.00000 0.0400000
\(626\) 16.8284 0.672599
\(627\) 37.8995 15.3137i 1.51356 0.611571i
\(628\) −23.7990 −0.949683
\(629\) −6.34315 −0.252918
\(630\) −1.65685 0.585786i −0.0660107 0.0233383i
\(631\) 23.5147 0.936106 0.468053 0.883700i \(-0.344956\pi\)
0.468053 + 0.883700i \(0.344956\pi\)
\(632\) 13.3137i 0.529591i
\(633\) 2.82843 2.00000i 0.112420 0.0794929i
\(634\) −0.343146 −0.0136281
\(635\) 12.8284 0.509081
\(636\) −3.17157 4.48528i −0.125761 0.177853i
\(637\) 14.9289i 0.591506i
\(638\) 27.4558i 1.08699i
\(639\) −2.82843 + 8.00000i −0.111891 + 0.316475i
\(640\) 1.00000i 0.0395285i
\(641\) 11.2721 0.445220 0.222610 0.974908i \(-0.428542\pi\)
0.222610 + 0.974908i \(0.428542\pi\)
\(642\) −3.65685 5.17157i −0.144325 0.204106i
\(643\) −20.7279 −0.817429 −0.408715 0.912662i \(-0.634023\pi\)
−0.408715 + 0.912662i \(0.634023\pi\)
\(644\) 3.51472i 0.138499i
\(645\) −9.31371 + 6.58579i −0.366727 + 0.259315i
\(646\) 2.82843 12.0000i 0.111283 0.472134i
\(647\) 2.68629i 0.105609i 0.998605 + 0.0528045i \(0.0168160\pi\)
−0.998605 + 0.0528045i \(0.983184\pi\)
\(648\) 7.00000 + 5.65685i 0.274986 + 0.222222i
\(649\) 69.4558i 2.72638i
\(650\) 2.24264i 0.0879636i
\(651\) 5.65685 4.00000i 0.221710 0.156772i
\(652\) 12.7279 0.498464
\(653\) 15.1127i 0.591406i −0.955280 0.295703i \(-0.904446\pi\)
0.955280 0.295703i \(-0.0955538\pi\)
\(654\) −3.31371 + 2.34315i −0.129576 + 0.0916242i
\(655\) 4.92893 0.192589
\(656\) 11.0711 0.432253
\(657\) −2.48528 + 7.02944i −0.0969601 + 0.274244i
\(658\) 1.85786i 0.0724271i
\(659\) 8.82843 0.343907 0.171953 0.985105i \(-0.444992\pi\)
0.171953 + 0.985105i \(0.444992\pi\)
\(660\) −5.41421 7.65685i −0.210748 0.298043i
\(661\) 3.51472i 0.136707i −0.997661 0.0683534i \(-0.978225\pi\)
0.997661 0.0683534i \(-0.0217745\pi\)
\(662\) 16.9706i 0.659580i
\(663\) 6.34315 + 8.97056i 0.246347 + 0.348388i
\(664\) 12.8284i 0.497840i
\(665\) 0.585786 2.48528i 0.0227158 0.0963751i
\(666\) 6.34315 + 2.24264i 0.245792 + 0.0869006i
\(667\) 30.4264i 1.17812i
\(668\) 0 0
\(669\) 25.4558 18.0000i 0.984180 0.695920i
\(670\) 0 0
\(671\) 24.2843i 0.937484i
\(672\) 0.585786 + 0.828427i 0.0225972 + 0.0319573i
\(673\) 37.6985i 1.45317i −0.687077 0.726585i \(-0.741106\pi\)
0.687077 0.726585i \(-0.258894\pi\)
\(674\) 29.2132i 1.12525i
\(675\) −5.00000 + 1.41421i −0.192450 + 0.0544331i
\(676\) 7.97056 0.306560
\(677\) 37.5980 1.44501 0.722504 0.691367i \(-0.242991\pi\)
0.722504 + 0.691367i \(0.242991\pi\)
\(678\) −12.8284 18.1421i −0.492673 0.696745i
\(679\) 3.85786i 0.148051i
\(680\) −2.82843 −0.108465
\(681\) −2.34315 3.31371i −0.0897895 0.126982i
\(682\) 36.9706 1.41568
\(683\) −39.2548 −1.50204 −0.751022 0.660277i \(-0.770439\pi\)
−0.751022 + 0.660277i \(0.770439\pi\)
\(684\) −7.07107 + 11.0000i −0.270369 + 0.420596i
\(685\) 14.4853 0.553454
\(686\) 8.00000 0.305441
\(687\) −8.48528 12.0000i −0.323734 0.457829i
\(688\) 6.58579 0.251081
\(689\) 7.11270i 0.270972i
\(690\) −6.00000 8.48528i −0.228416 0.323029i
\(691\) 36.9706 1.40643 0.703213 0.710979i \(-0.251748\pi\)
0.703213 + 0.710979i \(0.251748\pi\)
\(692\) −6.00000 −0.228086
\(693\) −8.97056 3.17157i −0.340764 0.120478i
\(694\) 30.2843i 1.14958i
\(695\) 18.1421i 0.688170i
\(696\) −5.07107 7.17157i −0.192218 0.271838i
\(697\) 31.3137i 1.18609i
\(698\) 10.9706 0.415242
\(699\) 25.1716 17.7990i 0.952076 0.673220i
\(700\) −0.585786 −0.0221406
\(701\) 2.48528i 0.0938678i 0.998898 + 0.0469339i \(0.0149450\pi\)
−0.998898 + 0.0469339i \(0.985055\pi\)
\(702\) −3.17157 11.2132i −0.119703 0.423215i
\(703\) −2.24264 + 9.51472i −0.0845828 + 0.358854i
\(704\) 5.41421i 0.204056i
\(705\) −3.17157 4.48528i −0.119448 0.168925i
\(706\) 8.82843i 0.332262i
\(707\) 4.48528i 0.168686i
\(708\) −12.8284 18.1421i −0.482122 0.681823i
\(709\) 19.5147 0.732891 0.366445 0.930440i \(-0.380575\pi\)
0.366445 + 0.930440i \(0.380575\pi\)
\(710\) 2.82843i 0.106149i
\(711\) −37.6569 13.3137i −1.41224 0.499303i
\(712\) 10.5858 0.396719
\(713\) 40.9706 1.53436
\(714\) −2.34315 + 1.65685i −0.0876900 + 0.0620062i
\(715\) 12.1421i 0.454090i
\(716\) 21.7990 0.814667
\(717\) −0.142136 + 0.100505i −0.00530815 + 0.00375343i
\(718\) 19.4142i 0.724532i
\(719\) 30.7279i 1.14596i −0.819570 0.572979i \(-0.805788\pi\)
0.819570 0.572979i \(-0.194212\pi\)
\(720\) 2.82843 + 1.00000i 0.105409 + 0.0372678i
\(721\) 2.54416i 0.0947493i
\(722\) −17.0000 8.48528i −0.632674 0.315789i
\(723\) −12.0000 + 8.48528i −0.446285 + 0.315571i
\(724\) 10.8284i 0.402435i
\(725\) 5.07107 0.188335
\(726\) −18.3137 25.8995i −0.679685 0.961220i
\(727\) 25.5563 0.947833 0.473916 0.880570i \(-0.342840\pi\)
0.473916 + 0.880570i \(0.342840\pi\)
\(728\) 1.31371i 0.0486893i
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 2.48528i 0.0919844i
\(731\) 18.6274i 0.688960i
\(732\) 4.48528 + 6.34315i 0.165781 + 0.234449i
\(733\) −15.5147 −0.573049 −0.286525 0.958073i \(-0.592500\pi\)
−0.286525 + 0.958073i \(0.592500\pi\)
\(734\) 14.2426 0.525705
\(735\) 9.41421 6.65685i 0.347248 0.245542i
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) 11.0711 31.3137i 0.407532 1.15267i
\(739\) −20.4853 −0.753563 −0.376782 0.926302i \(-0.622969\pi\)
−0.376782 + 0.926302i \(0.622969\pi\)
\(740\) 2.24264 0.0824411
\(741\) 15.6985 6.34315i 0.576698 0.233021i
\(742\) −1.85786 −0.0682043
\(743\) 43.1716 1.58381 0.791906 0.610643i \(-0.209089\pi\)
0.791906 + 0.610643i \(0.209089\pi\)
\(744\) −9.65685 + 6.82843i −0.354037 + 0.250342i
\(745\) −14.4853 −0.530700
\(746\) 14.0416i 0.514101i
\(747\) 36.2843 + 12.8284i 1.32757 + 0.469368i
\(748\) −15.3137 −0.559925
\(749\) −2.14214 −0.0782719
\(750\) −1.41421 + 1.00000i −0.0516398 + 0.0365148i
\(751\) 48.4853i 1.76925i −0.466300 0.884627i \(-0.654413\pi\)
0.466300 0.884627i \(-0.345587\pi\)
\(752\) 3.17157i 0.115655i
\(753\) 6.97056 4.92893i 0.254021 0.179620i
\(754\) 11.3726i 0.414165i
\(755\) −20.4853 −0.745536
\(756\) 2.92893 0.828427i 0.106524 0.0301296i
\(757\) 49.6569 1.80481 0.902405 0.430890i \(-0.141800\pi\)
0.902405 + 0.430890i \(0.141800\pi\)
\(758\) 8.00000i 0.290573i
\(759\) −32.4853 45.9411i −1.17914 1.66756i
\(760\) −1.00000 + 4.24264i −0.0362738 + 0.153897i
\(761\) 1.17157i 0.0424695i −0.999775 0.0212347i \(-0.993240\pi\)
0.999775 0.0212347i \(-0.00675974\pi\)
\(762\) −18.1421 + 12.8284i −0.657220 + 0.464725i
\(763\) 1.37258i 0.0496908i
\(764\) 10.2426i 0.370566i
\(765\) −2.82843 + 8.00000i −0.102262 + 0.289241i
\(766\) 32.1421 1.16134
\(767\) 28.7696i 1.03881i
\(768\) −1.00000 1.41421i −0.0360844 0.0510310i
\(769\) −13.3137 −0.480105 −0.240052 0.970760i \(-0.577165\pi\)
−0.240052 + 0.970760i \(0.577165\pi\)
\(770\) −3.17157 −0.114296
\(771\) 28.1421 + 39.7990i 1.01351 + 1.43333i
\(772\) 19.5563i 0.703848i
\(773\) −0.343146 −0.0123421 −0.00617105 0.999981i \(-0.501964\pi\)
−0.00617105 + 0.999981i \(0.501964\pi\)
\(774\) 6.58579 18.6274i 0.236721 0.669549i
\(775\) 6.82843i 0.245284i
\(776\) 6.58579i 0.236416i
\(777\) 1.85786 1.31371i 0.0666505 0.0471290i
\(778\) 20.3431i 0.729337i
\(779\) 46.9706 + 11.0711i 1.68290 + 0.396662i
\(780\) −2.24264 3.17157i −0.0802994 0.113561i
\(781\) 15.3137i 0.547968i
\(782\) −16.9706 −0.606866
\(783\) −25.3553 + 7.17157i −0.906126 + 0.256291i
\(784\) −6.65685 −0.237745
\(785\) 23.7990i 0.849422i
\(786\) −6.97056 + 4.92893i −0.248632 + 0.175809i
\(787\) 44.9706i 1.60303i −0.597976 0.801514i \(-0.704028\pi\)
0.597976 0.801514i \(-0.295972\pi\)
\(788\) 18.1421i 0.646287i
\(789\) −15.7990 + 11.1716i −0.562459 + 0.397719i
\(790\) −13.3137 −0.473680
\(791\) −7.51472 −0.267193
\(792\) 15.3137 + 5.41421i 0.544149 + 0.192386i
\(793\) 10.0589i 0.357201i
\(794\) −16.9706 −0.602263
\(795\) −4.48528 + 3.17157i −0.159077 + 0.112484i
\(796\) −16.9706 −0.601506
\(797\) 24.3431 0.862278 0.431139 0.902285i \(-0.358112\pi\)
0.431139 + 0.902285i \(0.358112\pi\)
\(798\) 1.65685 + 4.10051i 0.0586520 + 0.145156i
\(799\) −8.97056 −0.317356
\(800\) 1.00000 0.0353553
\(801\) 10.5858 29.9411i 0.374030 1.05792i
\(802\) −18.3848 −0.649189
\(803\) 13.4558i 0.474846i
\(804\) 0 0
\(805\) −3.51472 −0.123878
\(806\) 15.3137 0.539402
\(807\) −24.3848 34.4853i −0.858385 1.21394i
\(808\) 7.65685i 0.269367i
\(809\) 35.3137i 1.24156i 0.783983 + 0.620782i \(0.213185\pi\)
−0.783983 + 0.620782i \(0.786815\pi\)
\(810\) 5.65685 7.00000i 0.198762 0.245955i
\(811\) 13.0294i 0.457525i 0.973482 + 0.228763i \(0.0734680\pi\)
−0.973482 + 0.228763i \(0.926532\pi\)
\(812\) −2.97056 −0.104246
\(813\) 28.9706 + 40.9706i 1.01604 + 1.43690i
\(814\) 12.1421 0.425582
\(815\) 12.7279i 0.445840i
\(816\) 4.00000 2.82843i 0.140028 0.0990148i
\(817\) 27.9411 + 6.58579i 0.977536 + 0.230408i
\(818\) 4.48528i 0.156824i
\(819\) −3.71573 1.31371i −0.129838 0.0459047i
\(820\) 11.0711i 0.386618i
\(821\) 11.6569i 0.406827i 0.979093 + 0.203414i \(0.0652036\pi\)
−0.979093 + 0.203414i \(0.934796\pi\)
\(822\) −20.4853 + 14.4853i −0.714506 + 0.505232i
\(823\) 18.2426 0.635898 0.317949 0.948108i \(-0.397006\pi\)
0.317949 + 0.948108i \(0.397006\pi\)
\(824\) 4.34315i 0.151301i
\(825\) −7.65685 + 5.41421i −0.266577 + 0.188499i
\(826\) −7.51472 −0.261471
\(827\) 36.2843 1.26173 0.630864 0.775894i \(-0.282701\pi\)
0.630864 + 0.775894i \(0.282701\pi\)
\(828\) 16.9706 + 6.00000i 0.589768 + 0.208514i
\(829\) 35.5980i 1.23637i 0.786033 + 0.618184i \(0.212132\pi\)
−0.786033 + 0.618184i \(0.787868\pi\)
\(830\) 12.8284 0.445281
\(831\) −24.9706 35.3137i −0.866219 1.22502i
\(832\) 2.24264i 0.0777496i
\(833\) 18.8284i 0.652366i
\(834\) 18.1421 + 25.6569i 0.628211 + 0.888424i
\(835\) 0 0
\(836\) −5.41421 + 22.9706i −0.187254 + 0.794454i
\(837\) 9.65685 + 34.1421i 0.333790 + 1.18012i
\(838\) 6.38478i 0.220558i
\(839\) −2.82843 −0.0976481 −0.0488241 0.998807i \(-0.515547\pi\)
−0.0488241 + 0.998807i \(0.515547\pi\)
\(840\) 0.828427 0.585786i 0.0285835 0.0202116i
\(841\) −3.28427 −0.113251
\(842\) 24.2843i 0.836891i
\(843\) −0.928932 1.31371i −0.0319941 0.0452465i
\(844\) 2.00000i 0.0688428i
\(845\) 7.97056i 0.274196i
\(846\) 8.97056 + 3.17157i 0.308414 + 0.109041i
\(847\) −10.7279 −0.368616
\(848\) 3.17157 0.108912
\(849\) −12.7279 18.0000i −0.436821 0.617758i
\(850\) 2.82843i 0.0970143i
\(851\) 13.4558 0.461260
\(852\) −2.82843 4.00000i −0.0969003 0.137038i
\(853\) −12.0000 −0.410872 −0.205436 0.978671i \(-0.565861\pi\)
−0.205436 + 0.978671i \(0.565861\pi\)
\(854\) 2.62742 0.0899084
\(855\) 11.0000 + 7.07107i 0.376192 + 0.241825i
\(856\) 3.65685 0.124989
\(857\) −4.82843 −0.164936 −0.0824680 0.996594i \(-0.526280\pi\)
−0.0824680 + 0.996594i \(0.526280\pi\)
\(858\) −12.1421 17.1716i −0.414526 0.586228i
\(859\) 11.0294 0.376320 0.188160 0.982138i \(-0.439748\pi\)
0.188160 + 0.982138i \(0.439748\pi\)
\(860\) 6.58579i 0.224573i
\(861\) −6.48528 9.17157i −0.221018 0.312566i
\(862\) −19.3137 −0.657828
\(863\) −56.8284 −1.93446 −0.967231 0.253898i \(-0.918287\pi\)
−0.967231 + 0.253898i \(0.918287\pi\)
\(864\) −5.00000 + 1.41421i −0.170103 + 0.0481125i
\(865\) 6.00000i 0.204006i
\(866\) 14.3848i 0.488815i
\(867\) −9.00000 12.7279i −0.305656 0.432263i
\(868\) 4.00000i 0.135769i
\(869\) −72.0833 −2.44526
\(870\) −7.17157 + 5.07107i −0.243139 + 0.171925i
\(871\) 0 0
\(872\) 2.34315i 0.0793489i
\(873\) −18.6274 6.58579i −0.630443 0.222895i
\(874\) −6.00000 + 25.4558i −0.202953 + 0.861057i
\(875\) 0.585786i 0.0198032i
\(876\) −2.48528 3.51472i −0.0839699 0.118751i
\(877\) 40.8701i 1.38008i 0.723769 + 0.690042i \(0.242408\pi\)
−0.723769 + 0.690042i \(0.757592\pi\)
\(878\) 39.9411i 1.34795i
\(879\) 3.17157 + 4.48528i 0.106974 + 0.151285i
\(880\) 5.41421 0.182513
\(881\) 28.2843i 0.952921i 0.879196 + 0.476461i \(0.158081\pi\)
−0.879196 + 0.476461i \(0.841919\pi\)
\(882\) −6.65685 + 18.8284i −0.224148 + 0.633986i
\(883\) 21.4142 0.720646 0.360323 0.932828i \(-0.382667\pi\)
0.360323 + 0.932828i \(0.382667\pi\)
\(884\) −6.34315 −0.213343
\(885\) −18.1421 + 12.8284i −0.609841 + 0.431223i
\(886\) 18.0000i 0.604722i
\(887\) −48.8284 −1.63950 −0.819749 0.572723i \(-0.805887\pi\)
−0.819749 + 0.572723i \(0.805887\pi\)
\(888\) −3.17157 + 2.24264i −0.106431 + 0.0752581i
\(889\) 7.51472i 0.252036i
\(890\) 10.5858i 0.354836i
\(891\) 30.6274 37.8995i 1.02606 1.26968i
\(892\) 18.0000i 0.602685i
\(893\) −3.17157 + 13.4558i −0.106133 + 0.450283i
\(894\) 20.4853 14.4853i 0.685130 0.484460i
\(895\) 21.7990i 0.728660i
\(896\) −0.585786 −0.0195698
\(897\) −13.4558 19.0294i −0.449278 0.635374i
\(898\) −16.2426 −0.542024
\(899\) 34.6274i 1.15489i
\(900\) 1.00000 2.82843i 0.0333333 0.0942809i
\(901\) 8.97056i 0.298853i
\(902\) 59.9411i 1.99582i
\(903\) −3.85786 5.45584i −0.128382 0.181559i
\(904\) 12.8284 0.426667
\(905\) −10.8284 −0.359949
\(906\) 28.9706 20.4853i 0.962482 0.680578i
\(907\) 12.9706i 0.430680i −0.976539 0.215340i \(-0.930914\pi\)
0.976539 0.215340i \(-0.0690860\pi\)
\(908\) 2.34315 0.0777600
\(909\) −21.6569 7.65685i −0.718313 0.253962i
\(910\) −1.31371 −0.0435490
\(911\) −23.3137 −0.772418 −0.386209 0.922411i \(-0.626216\pi\)
−0.386209 + 0.922411i \(0.626216\pi\)
\(912\) −2.82843 7.00000i −0.0936586 0.231793i
\(913\) 69.4558 2.29865
\(914\) 0.828427 0.0274019
\(915\) 6.34315 4.48528i 0.209698 0.148279i
\(916\) 8.48528 0.280362
\(917\) 2.88730i 0.0953471i
\(918\) −4.00000 14.1421i −0.132020 0.466760i
\(919\) 37.4558 1.23555 0.617777 0.786353i \(-0.288033\pi\)
0.617777 + 0.786353i \(0.288033\pi\)
\(920\) 6.00000 0.197814
\(921\) 25.6569 18.1421i 0.845422 0.597804i
\(922\) 28.1421i 0.926812i
\(923\) 6.34315i 0.208787i
\(924\) 4.48528 3.17157i 0.147555 0.104337i
\(925\) 2.24264i 0.0737376i
\(926\) −19.2132 −0.631385
\(927\) 12.2843 + 4.34315i 0.403468 + 0.142648i
\(928\) 5.07107 0.166466
\(929\) 33.1716i 1.08832i 0.838980 + 0.544162i \(0.183152\pi\)
−0.838980 + 0.544162i \(0.816848\pi\)
\(930\) 6.82843 + 9.65685i 0.223913 + 0.316661i
\(931\) −28.2426 6.65685i −0.925615 0.218170i
\(932\) 17.7990i 0.583025i
\(933\) 7.17157 5.07107i 0.234787 0.166019i
\(934\) 25.7990i 0.844169i
\(935\) 15.3137i 0.500812i
\(936\) 6.34315 + 2.24264i 0.207332 + 0.0733030i
\(937\) −5.02944 −0.164305 −0.0821523 0.996620i \(-0.526179\pi\)
−0.0821523 + 0.996620i \(0.526179\pi\)
\(938\) 0 0
\(939\) 16.8284 + 23.7990i 0.549175 + 0.776651i
\(940\) 3.17157 0.103445
\(941\) 20.8701 0.680344 0.340172 0.940363i \(-0.389515\pi\)
0.340172 + 0.940363i \(0.389515\pi\)
\(942\) −23.7990 33.6569i −0.775413 1.09660i
\(943\) 66.4264i 2.16314i
\(944\) 12.8284 0.417530
\(945\) −0.828427 2.92893i −0.0269487 0.0952782i
\(946\) 35.6569i 1.15930i
\(947\) 2.68629i 0.0872927i 0.999047 + 0.0436464i \(0.0138975\pi\)
−0.999047 + 0.0436464i \(0.986103\pi\)
\(948\) 18.8284 13.3137i 0.611519 0.432409i
\(949\) 5.57359i 0.180926i
\(950\) 4.24264 + 1.00000i 0.137649 + 0.0324443i
\(951\) −0.343146 0.485281i −0.0111273 0.0157363i
\(952\) 1.65685i 0.0536990i
\(953\) 15.9411 0.516384 0.258192 0.966094i \(-0.416873\pi\)
0.258192 + 0.966094i \(0.416873\pi\)
\(954\) 3.17157 8.97056i 0.102683 0.290433i
\(955\) 10.2426 0.331444
\(956\) 0.100505i 0.00325057i
\(957\) −38.8284 + 27.4558i −1.25514 + 0.887521i
\(958\) 3.41421i 0.110308i
\(959\) 8.48528i 0.274004i
\(960\) −1.41421 + 1.00000i −0.0456435 + 0.0322749i
\(961\) −15.6274 −0.504110
\(962\) 5.02944 0.162156
\(963\) 3.65685 10.3431i 0.117840 0.333303i
\(964\) 8.48528i 0.273293i
\(965\) −19.5563 −0.629541
\(966\) 4.97056 3.51472i 0.159925 0.113084i
\(967\) 50.2426 1.61569 0.807847 0.589392i \(-0.200633\pi\)
0.807847 + 0.589392i \(0.200633\pi\)
\(968\) 18.3137 0.588625
\(969\) 19.7990 8.00000i 0.636035 0.256997i
\(970\) −6.58579 −0.211457
\(971\) −61.1127 −1.96120 −0.980600 0.196020i \(-0.937198\pi\)
−0.980600 + 0.196020i \(0.937198\pi\)
\(972\) −1.00000 + 15.5563i −0.0320750 + 0.498970i
\(973\) 10.6274 0.340699
\(974\) 36.1421i 1.15807i
\(975\) −3.17157 + 2.24264i −0.101572 + 0.0718220i
\(976\) −4.48528 −0.143570
\(977\) −10.2843 −0.329023 −0.164511 0.986375i \(-0.552605\pi\)
−0.164511 + 0.986375i \(0.552605\pi\)
\(978\) 12.7279 + 18.0000i 0.406994 + 0.575577i
\(979\) 57.3137i 1.83175i
\(980\) 6.65685i 0.212645i
\(981\) −6.62742 2.34315i −0.211597 0.0748109i
\(982\) 43.5563i 1.38994i
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 11.0711 + 15.6569i 0.352933 + 0.499122i
\(985\) 18.1421 0.578057
\(986\) 14.3431i 0.456779i
\(987\) 2.62742 1.85786i 0.0836316 0.0591365i
\(988\) −2.24264 + 9.51472i −0.0713479 + 0.302704i
\(989\) 39.5147i 1.25649i
\(990\) 5.41421 15.3137i 0.172075 0.486702i
\(991\) 2.97056i 0.0943630i −0.998886 0.0471815i \(-0.984976\pi\)
0.998886 0.0471815i \(-0.0150239\pi\)
\(992\) 6.82843i 0.216803i
\(993\) −24.0000 + 16.9706i −0.761617 + 0.538545i
\(994\) −1.65685 −0.0525522
\(995\) 16.9706i 0.538003i
\(996\) −18.1421 + 12.8284i −0.574856 + 0.406484i
\(997\) 0.485281 0.0153690 0.00768451 0.999970i \(-0.497554\pi\)
0.00768451 + 0.999970i \(0.497554\pi\)
\(998\) 25.6569 0.812154
\(999\) 3.17157 + 11.2132i 0.100344 + 0.354770i
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 570.2.f.a.341.1 4
3.2 odd 2 570.2.f.b.341.2 yes 4
19.18 odd 2 570.2.f.b.341.3 yes 4
57.56 even 2 inner 570.2.f.a.341.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.f.a.341.1 4 1.1 even 1 trivial
570.2.f.a.341.4 yes 4 57.56 even 2 inner
570.2.f.b.341.2 yes 4 3.2 odd 2
570.2.f.b.341.3 yes 4 19.18 odd 2