Properties

Label 1050.2.bc.a.493.1
Level $1050$
Weight $2$
Character 1050.493
Analytic conductor $8.384$
Analytic rank $0$
Dimension $8$
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] = [1050,2,Mod(157,1050)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1050.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), 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: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 493.1
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.493
Dual form 1050.2.bc.a.607.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.63896 - 0.189469i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.63896 - 0.189469i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-4.05317 + 4.05317i) q^{13} +(-2.59808 - 0.500000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-7.20977 + 1.93185i) q^{17} +(0.965926 - 0.258819i) q^{18} +(-1.13397 - 1.96410i) q^{19} +(0.866025 + 2.50000i) q^{21} +(0.707107 - 0.707107i) q^{22} +(-1.53433 + 5.72620i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.96410 - 2.86603i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.38014 + 1.15539i) q^{28} -6.92820i q^{29} +(6.46410 + 3.73205i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.965926 - 0.258819i) q^{33} +7.46410 q^{34} -1.00000 q^{36} +(-3.79435 - 1.01669i) q^{37} +(0.586988 + 2.19067i) q^{38} +(-4.96410 - 2.86603i) q^{39} +2.26795i q^{41} +(-0.189469 - 2.63896i) q^{42} +(6.31319 + 6.31319i) q^{43} +(-0.866025 + 0.500000i) q^{44} +(2.96410 - 5.13397i) q^{46} +(-0.309587 + 1.15539i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(6.92820 - 1.00000i) q^{49} +(-3.73205 - 6.46410i) q^{51} +(-5.53674 + 1.48356i) q^{52} +(-0.965926 + 0.258819i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +(1.60368 - 1.60368i) q^{57} +(-1.79315 + 6.69213i) q^{58} +(-5.73205 + 9.92820i) q^{59} +(-9.92820 + 5.73205i) q^{61} +(-5.27792 - 5.27792i) q^{62} +(-2.19067 + 1.48356i) q^{63} +1.00000i q^{64} +(0.866025 + 0.500000i) q^{66} +(-0.517638 - 1.93185i) q^{67} +(-7.20977 - 1.93185i) q^{68} -5.92820 q^{69} -8.92820 q^{71} +(0.965926 + 0.258819i) q^{72} +(1.03528 + 3.86370i) q^{73} +(3.40192 + 1.96410i) q^{74} -2.26795i q^{76} +(-1.15539 + 2.38014i) q^{77} +(4.05317 + 4.05317i) q^{78} +(2.66025 - 1.53590i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.586988 - 2.19067i) q^{82} +(7.34847 - 7.34847i) q^{83} +(-0.500000 + 2.59808i) q^{84} +(-4.46410 - 7.73205i) q^{86} +(6.69213 - 1.79315i) q^{87} +(0.965926 - 0.258819i) q^{88} +(-3.46410 - 6.00000i) q^{89} +(-9.92820 + 11.4641i) q^{91} +(-4.19187 + 4.19187i) q^{92} +(-1.93185 + 7.20977i) q^{93} +(0.598076 - 1.03590i) q^{94} +(0.866025 - 0.500000i) q^{96} +(-2.07055 - 2.07055i) q^{97} +(-6.95095 - 0.827225i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{11} + 4 q^{16} - 16 q^{19} + 4 q^{24} + 12 q^{26} + 24 q^{31} + 32 q^{34} - 8 q^{36} - 12 q^{39} - 4 q^{46} - 16 q^{51} + 4 q^{54} - 16 q^{56} - 32 q^{59} - 24 q^{61} + 8 q^{69} - 16 q^{71} + 48 q^{74} - 48 q^{79} + 4 q^{81} - 4 q^{84} - 8 q^{86} - 24 q^{91} - 16 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.63896 0.189469i 0.997433 0.0716124i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) −0.258819 + 0.965926i −0.0747146 + 0.278839i
\(13\) −4.05317 + 4.05317i −1.12415 + 1.12415i −0.133037 + 0.991111i \(0.542473\pi\)
−0.991111 + 0.133037i \(0.957527\pi\)
\(14\) −2.59808 0.500000i −0.694365 0.133631i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −7.20977 + 1.93185i −1.74863 + 0.468543i −0.984332 0.176325i \(-0.943579\pi\)
−0.764294 + 0.644868i \(0.776912\pi\)
\(18\) 0.965926 0.258819i 0.227671 0.0610042i
\(19\) −1.13397 1.96410i −0.260152 0.450596i 0.706130 0.708082i \(-0.250439\pi\)
−0.966282 + 0.257486i \(0.917106\pi\)
\(20\) 0 0
\(21\) 0.866025 + 2.50000i 0.188982 + 0.545545i
\(22\) 0.707107 0.707107i 0.150756 0.150756i
\(23\) −1.53433 + 5.72620i −0.319930 + 1.19400i 0.599381 + 0.800464i \(0.295414\pi\)
−0.919311 + 0.393532i \(0.871253\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 4.96410 2.86603i 0.973540 0.562074i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.38014 + 1.15539i 0.449804 + 0.218349i
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) 0 0
\(31\) 6.46410 + 3.73205i 1.16099 + 0.670296i 0.951540 0.307524i \(-0.0995004\pi\)
0.209447 + 0.977820i \(0.432834\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) −0.965926 0.258819i −0.168146 0.0450546i
\(34\) 7.46410 1.28008
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −3.79435 1.01669i −0.623788 0.167143i −0.0669387 0.997757i \(-0.521323\pi\)
−0.556849 + 0.830614i \(0.687990\pi\)
\(38\) 0.586988 + 2.19067i 0.0952221 + 0.355374i
\(39\) −4.96410 2.86603i −0.794892 0.458931i
\(40\) 0 0
\(41\) 2.26795i 0.354194i 0.984193 + 0.177097i \(0.0566707\pi\)
−0.984193 + 0.177097i \(0.943329\pi\)
\(42\) −0.189469 2.63896i −0.0292357 0.407200i
\(43\) 6.31319 + 6.31319i 0.962753 + 0.962753i 0.999331 0.0365779i \(-0.0116457\pi\)
−0.0365779 + 0.999331i \(0.511646\pi\)
\(44\) −0.866025 + 0.500000i −0.130558 + 0.0753778i
\(45\) 0 0
\(46\) 2.96410 5.13397i 0.437033 0.756963i
\(47\) −0.309587 + 1.15539i −0.0451579 + 0.168532i −0.984822 0.173566i \(-0.944471\pi\)
0.939664 + 0.342098i \(0.111138\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 6.92820 1.00000i 0.989743 0.142857i
\(50\) 0 0
\(51\) −3.73205 6.46410i −0.522592 0.905155i
\(52\) −5.53674 + 1.48356i −0.767807 + 0.205733i
\(53\) −0.965926 + 0.258819i −0.132680 + 0.0355515i −0.324548 0.945869i \(-0.605212\pi\)
0.191868 + 0.981421i \(0.438546\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 1.60368 1.60368i 0.212413 0.212413i
\(58\) −1.79315 + 6.69213i −0.235452 + 0.878720i
\(59\) −5.73205 + 9.92820i −0.746249 + 1.29254i 0.203359 + 0.979104i \(0.434814\pi\)
−0.949609 + 0.313438i \(0.898519\pi\)
\(60\) 0 0
\(61\) −9.92820 + 5.73205i −1.27118 + 0.733914i −0.975209 0.221284i \(-0.928975\pi\)
−0.295967 + 0.955198i \(0.595642\pi\)
\(62\) −5.27792 5.27792i −0.670296 0.670296i
\(63\) −2.19067 + 1.48356i −0.275999 + 0.186911i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0.866025 + 0.500000i 0.106600 + 0.0615457i
\(67\) −0.517638 1.93185i −0.0632396 0.236013i 0.927071 0.374887i \(-0.122318\pi\)
−0.990310 + 0.138874i \(0.955652\pi\)
\(68\) −7.20977 1.93185i −0.874313 0.234271i
\(69\) −5.92820 −0.713672
\(70\) 0 0
\(71\) −8.92820 −1.05958 −0.529791 0.848128i \(-0.677730\pi\)
−0.529791 + 0.848128i \(0.677730\pi\)
\(72\) 0.965926 + 0.258819i 0.113835 + 0.0305021i
\(73\) 1.03528 + 3.86370i 0.121170 + 0.452212i 0.999674 0.0255221i \(-0.00812481\pi\)
−0.878504 + 0.477734i \(0.841458\pi\)
\(74\) 3.40192 + 1.96410i 0.395466 + 0.228322i
\(75\) 0 0
\(76\) 2.26795i 0.260152i
\(77\) −1.15539 + 2.38014i −0.131669 + 0.271242i
\(78\) 4.05317 + 4.05317i 0.458931 + 0.458931i
\(79\) 2.66025 1.53590i 0.299302 0.172802i −0.342827 0.939398i \(-0.611385\pi\)
0.642129 + 0.766596i \(0.278051\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 0.586988 2.19067i 0.0648220 0.241919i
\(83\) 7.34847 7.34847i 0.806599 0.806599i −0.177518 0.984118i \(-0.556807\pi\)
0.984118 + 0.177518i \(0.0568069\pi\)
\(84\) −0.500000 + 2.59808i −0.0545545 + 0.283473i
\(85\) 0 0
\(86\) −4.46410 7.73205i −0.481376 0.833768i
\(87\) 6.69213 1.79315i 0.717472 0.192246i
\(88\) 0.965926 0.258819i 0.102968 0.0275902i
\(89\) −3.46410 6.00000i −0.367194 0.635999i 0.621932 0.783072i \(-0.286348\pi\)
−0.989126 + 0.147073i \(0.953015\pi\)
\(90\) 0 0
\(91\) −9.92820 + 11.4641i −1.04076 + 1.20176i
\(92\) −4.19187 + 4.19187i −0.437033 + 0.437033i
\(93\) −1.93185 + 7.20977i −0.200324 + 0.747618i
\(94\) 0.598076 1.03590i 0.0616869 0.106845i
\(95\) 0 0
\(96\) 0.866025 0.500000i 0.0883883 0.0510310i
\(97\) −2.07055 2.07055i −0.210233 0.210233i 0.594134 0.804366i \(-0.297495\pi\)
−0.804366 + 0.594134i \(0.797495\pi\)
\(98\) −6.95095 0.827225i −0.702152 0.0835624i
\(99\) 1.00000i 0.100504i
\(100\) 0 0
\(101\) 0.928203 + 0.535898i 0.0923597 + 0.0533239i 0.545468 0.838131i \(-0.316352\pi\)
−0.453109 + 0.891455i \(0.649685\pi\)
\(102\) 1.93185 + 7.20977i 0.191282 + 0.713873i
\(103\) −17.7656 4.76028i −1.75050 0.469044i −0.765765 0.643121i \(-0.777639\pi\)
−0.984732 + 0.174077i \(0.944306\pi\)
\(104\) 5.73205 0.562074
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) −14.4195 3.86370i −1.39399 0.373518i −0.517807 0.855498i \(-0.673251\pi\)
−0.876183 + 0.481979i \(0.839918\pi\)
\(108\) −0.258819 0.965926i −0.0249049 0.0929463i
\(109\) 14.6603 + 8.46410i 1.40420 + 0.810714i 0.994820 0.101651i \(-0.0324126\pi\)
0.409378 + 0.912365i \(0.365746\pi\)
\(110\) 0 0
\(111\) 3.92820i 0.372849i
\(112\) 1.48356 + 2.19067i 0.140184 + 0.206999i
\(113\) 9.14162 + 9.14162i 0.859971 + 0.859971i 0.991334 0.131363i \(-0.0419354\pi\)
−0.131363 + 0.991334i \(0.541935\pi\)
\(114\) −1.96410 + 1.13397i −0.183955 + 0.106206i
\(115\) 0 0
\(116\) 3.46410 6.00000i 0.321634 0.557086i
\(117\) 1.48356 5.53674i 0.137156 0.511871i
\(118\) 8.10634 8.10634i 0.746249 0.746249i
\(119\) −18.6603 + 6.46410i −1.71058 + 0.592563i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 11.0735 2.96713i 1.00255 0.268631i
\(123\) −2.19067 + 0.586988i −0.197526 + 0.0529270i
\(124\) 3.73205 + 6.46410i 0.335148 + 0.580493i
\(125\) 0 0
\(126\) 2.50000 0.866025i 0.222718 0.0771517i
\(127\) 3.53553 3.53553i 0.313728 0.313728i −0.532624 0.846352i \(-0.678794\pi\)
0.846352 + 0.532624i \(0.178794\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) −4.46410 + 7.73205i −0.393042 + 0.680769i
\(130\) 0 0
\(131\) 3.57180 2.06218i 0.312069 0.180173i −0.335783 0.941939i \(-0.609001\pi\)
0.647852 + 0.761766i \(0.275667\pi\)
\(132\) −0.707107 0.707107i −0.0615457 0.0615457i
\(133\) −3.36465 4.96833i −0.291752 0.430809i
\(134\) 2.00000i 0.172774i
\(135\) 0 0
\(136\) 6.46410 + 3.73205i 0.554292 + 0.320021i
\(137\) 4.89898 + 18.2832i 0.418548 + 1.56204i 0.777621 + 0.628733i \(0.216426\pi\)
−0.359073 + 0.933309i \(0.616907\pi\)
\(138\) 5.72620 + 1.53433i 0.487447 + 0.130611i
\(139\) 10.3923 0.881464 0.440732 0.897639i \(-0.354719\pi\)
0.440732 + 0.897639i \(0.354719\pi\)
\(140\) 0 0
\(141\) −1.19615 −0.100734
\(142\) 8.62398 + 2.31079i 0.723708 + 0.193917i
\(143\) −1.48356 5.53674i −0.124062 0.463005i
\(144\) −0.866025 0.500000i −0.0721688 0.0416667i
\(145\) 0 0
\(146\) 4.00000i 0.331042i
\(147\) 2.75908 + 6.43331i 0.227565 + 0.530611i
\(148\) −2.77766 2.77766i −0.228322 0.228322i
\(149\) 0.803848 0.464102i 0.0658538 0.0380207i −0.466712 0.884410i \(-0.654561\pi\)
0.532565 + 0.846389i \(0.321228\pi\)
\(150\) 0 0
\(151\) 1.92820 3.33975i 0.156915 0.271785i −0.776840 0.629698i \(-0.783178\pi\)
0.933755 + 0.357914i \(0.116512\pi\)
\(152\) −0.586988 + 2.19067i −0.0476110 + 0.177687i
\(153\) 5.27792 5.27792i 0.426694 0.426694i
\(154\) 1.73205 2.00000i 0.139573 0.161165i
\(155\) 0 0
\(156\) −2.86603 4.96410i −0.229466 0.397446i
\(157\) −4.50146 + 1.20616i −0.359256 + 0.0962622i −0.433932 0.900946i \(-0.642874\pi\)
0.0746765 + 0.997208i \(0.476208\pi\)
\(158\) −2.96713 + 0.795040i −0.236052 + 0.0632499i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) 0 0
\(161\) −2.96410 + 15.4019i −0.233604 + 1.21384i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 3.10583 11.5911i 0.243267 0.907886i −0.730979 0.682400i \(-0.760936\pi\)
0.974246 0.225486i \(-0.0723970\pi\)
\(164\) −1.13397 + 1.96410i −0.0885485 + 0.153371i
\(165\) 0 0
\(166\) −9.00000 + 5.19615i −0.698535 + 0.403300i
\(167\) 4.81105 + 4.81105i 0.372290 + 0.372290i 0.868311 0.496021i \(-0.165206\pi\)
−0.496021 + 0.868311i \(0.665206\pi\)
\(168\) 1.15539 2.38014i 0.0891406 0.183632i
\(169\) 19.8564i 1.52742i
\(170\) 0 0
\(171\) 1.96410 + 1.13397i 0.150199 + 0.0867172i
\(172\) 2.31079 + 8.62398i 0.176196 + 0.657572i
\(173\) 7.32989 + 1.96404i 0.557281 + 0.149323i 0.526457 0.850202i \(-0.323520\pi\)
0.0308241 + 0.999525i \(0.490187\pi\)
\(174\) −6.92820 −0.525226
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −11.0735 2.96713i −0.832333 0.223023i
\(178\) 1.79315 + 6.69213i 0.134402 + 0.501596i
\(179\) −7.79423 4.50000i −0.582568 0.336346i 0.179585 0.983742i \(-0.442524\pi\)
−0.762153 + 0.647397i \(0.775858\pi\)
\(180\) 0 0
\(181\) 14.3923i 1.06977i 0.844924 + 0.534886i \(0.179645\pi\)
−0.844924 + 0.534886i \(0.820355\pi\)
\(182\) 12.5570 8.50386i 0.930789 0.630348i
\(183\) −8.10634 8.10634i −0.599238 0.599238i
\(184\) 5.13397 2.96410i 0.378482 0.218516i
\(185\) 0 0
\(186\) 3.73205 6.46410i 0.273647 0.473971i
\(187\) 1.93185 7.20977i 0.141271 0.527230i
\(188\) −0.845807 + 0.845807i −0.0616869 + 0.0616869i
\(189\) −2.00000 1.73205i −0.145479 0.125988i
\(190\) 0 0
\(191\) −1.46410 2.53590i −0.105939 0.183491i 0.808183 0.588932i \(-0.200451\pi\)
−0.914121 + 0.405441i \(0.867118\pi\)
\(192\) −0.965926 + 0.258819i −0.0697097 + 0.0186787i
\(193\) 22.0082 5.89709i 1.58419 0.424482i 0.643969 0.765052i \(-0.277287\pi\)
0.940219 + 0.340570i \(0.110620\pi\)
\(194\) 1.46410 + 2.53590i 0.105116 + 0.182067i
\(195\) 0 0
\(196\) 6.50000 + 2.59808i 0.464286 + 0.185577i
\(197\) 11.9193 11.9193i 0.849213 0.849213i −0.140822 0.990035i \(-0.544974\pi\)
0.990035 + 0.140822i \(0.0449744\pi\)
\(198\) −0.258819 + 0.965926i −0.0183935 + 0.0686454i
\(199\) −6.26795 + 10.8564i −0.444323 + 0.769590i −0.998005 0.0631382i \(-0.979889\pi\)
0.553682 + 0.832728i \(0.313222\pi\)
\(200\) 0 0
\(201\) 1.73205 1.00000i 0.122169 0.0705346i
\(202\) −0.757875 0.757875i −0.0533239 0.0533239i
\(203\) −1.31268 18.2832i −0.0921319 1.28323i
\(204\) 7.46410i 0.522592i
\(205\) 0 0
\(206\) 15.9282 + 9.19615i 1.10977 + 0.640726i
\(207\) −1.53433 5.72620i −0.106643 0.397999i
\(208\) −5.53674 1.48356i −0.383904 0.102867i
\(209\) 2.26795 0.156877
\(210\) 0 0
\(211\) −19.7846 −1.36203 −0.681014 0.732270i \(-0.738461\pi\)
−0.681014 + 0.732270i \(0.738461\pi\)
\(212\) −0.965926 0.258819i −0.0663401 0.0177758i
\(213\) −2.31079 8.62398i −0.158333 0.590906i
\(214\) 12.9282 + 7.46410i 0.883754 + 0.510235i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 17.7656 + 8.62398i 1.20601 + 0.585434i
\(218\) −11.9700 11.9700i −0.810714 0.810714i
\(219\) −3.46410 + 2.00000i −0.234082 + 0.135147i
\(220\) 0 0
\(221\) 21.3923 37.0526i 1.43900 2.49242i
\(222\) −1.01669 + 3.79435i −0.0682360 + 0.254660i
\(223\) −6.59059 + 6.59059i −0.441339 + 0.441339i −0.892462 0.451123i \(-0.851024\pi\)
0.451123 + 0.892462i \(0.351024\pi\)
\(224\) −0.866025 2.50000i −0.0578638 0.167038i
\(225\) 0 0
\(226\) −6.46410 11.1962i −0.429986 0.744757i
\(227\) 3.34607 0.896575i 0.222086 0.0595078i −0.146060 0.989276i \(-0.546659\pi\)
0.368146 + 0.929768i \(0.379993\pi\)
\(228\) 2.19067 0.586988i 0.145081 0.0388743i
\(229\) 1.46410 + 2.53590i 0.0967506 + 0.167577i 0.910338 0.413866i \(-0.135822\pi\)
−0.813587 + 0.581443i \(0.802488\pi\)
\(230\) 0 0
\(231\) −2.59808 0.500000i −0.170941 0.0328976i
\(232\) −4.89898 + 4.89898i −0.321634 + 0.321634i
\(233\) 0.480473 1.79315i 0.0314769 0.117473i −0.948400 0.317077i \(-0.897299\pi\)
0.979877 + 0.199603i \(0.0639654\pi\)
\(234\) −2.86603 + 4.96410i −0.187358 + 0.324513i
\(235\) 0 0
\(236\) −9.92820 + 5.73205i −0.646271 + 0.373125i
\(237\) 2.17209 + 2.17209i 0.141092 + 0.141092i
\(238\) 19.6975 1.41421i 1.27680 0.0916698i
\(239\) 24.0000i 1.55243i 0.630468 + 0.776215i \(0.282863\pi\)
−0.630468 + 0.776215i \(0.717137\pi\)
\(240\) 0 0
\(241\) 19.2846 + 11.1340i 1.24223 + 0.717202i 0.969548 0.244902i \(-0.0787557\pi\)
0.272683 + 0.962104i \(0.412089\pi\)
\(242\) −2.58819 9.65926i −0.166375 0.620921i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) −11.4641 −0.733914
\(245\) 0 0
\(246\) 2.26795 0.144599
\(247\) 12.5570 + 3.36465i 0.798985 + 0.214087i
\(248\) −1.93185 7.20977i −0.122673 0.457821i
\(249\) 9.00000 + 5.19615i 0.570352 + 0.329293i
\(250\) 0 0
\(251\) 7.33975i 0.463281i −0.972801 0.231640i \(-0.925591\pi\)
0.972801 0.231640i \(-0.0744092\pi\)
\(252\) −2.63896 + 0.189469i −0.166239 + 0.0119354i
\(253\) −4.19187 4.19187i −0.263541 0.263541i
\(254\) −4.33013 + 2.50000i −0.271696 + 0.156864i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.619174 + 2.31079i −0.0386230 + 0.144143i −0.982545 0.186026i \(-0.940439\pi\)
0.943922 + 0.330169i \(0.107106\pi\)
\(258\) 6.31319 6.31319i 0.393042 0.393042i
\(259\) −10.2058 1.96410i −0.634156 0.122043i
\(260\) 0 0
\(261\) 3.46410 + 6.00000i 0.214423 + 0.371391i
\(262\) −3.98382 + 1.06746i −0.246121 + 0.0659480i
\(263\) 28.8391 7.72741i 1.77829 0.476492i 0.788023 0.615646i \(-0.211105\pi\)
0.990271 + 0.139154i \(0.0444383\pi\)
\(264\) 0.500000 + 0.866025i 0.0307729 + 0.0533002i
\(265\) 0 0
\(266\) 1.96410 + 5.66987i 0.120427 + 0.347642i
\(267\) 4.89898 4.89898i 0.299813 0.299813i
\(268\) 0.517638 1.93185i 0.0316198 0.118007i
\(269\) 12.6603 21.9282i 0.771909 1.33699i −0.164606 0.986359i \(-0.552635\pi\)
0.936515 0.350627i \(-0.114031\pi\)
\(270\) 0 0
\(271\) 6.92820 4.00000i 0.420858 0.242983i −0.274586 0.961563i \(-0.588541\pi\)
0.695444 + 0.718580i \(0.255208\pi\)
\(272\) −5.27792 5.27792i −0.320021 0.320021i
\(273\) −13.6431 6.62278i −0.825717 0.400829i
\(274\) 18.9282i 1.14349i
\(275\) 0 0
\(276\) −5.13397 2.96410i −0.309029 0.178418i
\(277\) −5.69402 21.2504i −0.342120 1.27681i −0.895940 0.444174i \(-0.853497\pi\)
0.553820 0.832636i \(-0.313170\pi\)
\(278\) −10.0382 2.68973i −0.602051 0.161319i
\(279\) −7.46410 −0.446864
\(280\) 0 0
\(281\) −27.9282 −1.66606 −0.833028 0.553230i \(-0.813395\pi\)
−0.833028 + 0.553230i \(0.813395\pi\)
\(282\) 1.15539 + 0.309587i 0.0688027 + 0.0184356i
\(283\) −3.24453 12.1087i −0.192867 0.719790i −0.992809 0.119712i \(-0.961803\pi\)
0.799941 0.600078i \(-0.204864\pi\)
\(284\) −7.73205 4.46410i −0.458813 0.264896i
\(285\) 0 0
\(286\) 5.73205i 0.338943i
\(287\) 0.429705 + 5.98502i 0.0253647 + 0.353285i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 33.5263 19.3564i 1.97213 1.13861i
\(290\) 0 0
\(291\) 1.46410 2.53590i 0.0858272 0.148657i
\(292\) −1.03528 + 3.86370i −0.0605850 + 0.226106i
\(293\) 1.22474 1.22474i 0.0715504 0.0715504i −0.670426 0.741976i \(-0.733889\pi\)
0.741976 + 0.670426i \(0.233889\pi\)
\(294\) −1.00000 6.92820i −0.0583212 0.404061i
\(295\) 0 0
\(296\) 1.96410 + 3.40192i 0.114161 + 0.197733i
\(297\) 0.965926 0.258819i 0.0560487 0.0150182i
\(298\) −0.896575 + 0.240237i −0.0519372 + 0.0139165i
\(299\) −16.9904 29.4282i −0.982579 1.70188i
\(300\) 0 0
\(301\) 17.8564 + 15.4641i 1.02923 + 0.891336i
\(302\) −2.72689 + 2.72689i −0.156915 + 0.156915i
\(303\) −0.277401 + 1.03528i −0.0159363 + 0.0594751i
\(304\) 1.13397 1.96410i 0.0650379 0.112649i
\(305\) 0 0
\(306\) −6.46410 + 3.73205i −0.369528 + 0.213347i
\(307\) 15.8338 + 15.8338i 0.903680 + 0.903680i 0.995752 0.0920724i \(-0.0293491\pi\)
−0.0920724 + 0.995752i \(0.529349\pi\)
\(308\) −2.19067 + 1.48356i −0.124825 + 0.0845339i
\(309\) 18.3923i 1.04630i
\(310\) 0 0
\(311\) 17.7846 + 10.2679i 1.00847 + 0.582242i 0.910744 0.412971i \(-0.135509\pi\)
0.0977286 + 0.995213i \(0.468842\pi\)
\(312\) 1.48356 + 5.53674i 0.0839903 + 0.313456i
\(313\) −30.1146 8.06918i −1.70218 0.456097i −0.728691 0.684843i \(-0.759871\pi\)
−0.973486 + 0.228746i \(0.926538\pi\)
\(314\) 4.66025 0.262993
\(315\) 0 0
\(316\) 3.07180 0.172802
\(317\) 13.5230 + 3.62347i 0.759525 + 0.203514i 0.617739 0.786383i \(-0.288049\pi\)
0.141786 + 0.989897i \(0.454715\pi\)
\(318\) 0.258819 + 0.965926i 0.0145139 + 0.0541664i
\(319\) 6.00000 + 3.46410i 0.335936 + 0.193952i
\(320\) 0 0
\(321\) 14.9282i 0.833211i
\(322\) 6.84941 14.1100i 0.381703 0.786317i
\(323\) 11.9700 + 11.9700i 0.666031 + 0.666031i
\(324\) 0.866025 0.500000i 0.0481125 0.0277778i
\(325\) 0 0
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) −4.38134 + 16.3514i −0.242289 + 0.904234i
\(328\) 1.60368 1.60368i 0.0885485 0.0885485i
\(329\) −0.598076 + 3.10770i −0.0329730 + 0.171333i
\(330\) 0 0
\(331\) −12.8923 22.3301i −0.708625 1.22737i −0.965367 0.260895i \(-0.915982\pi\)
0.256742 0.966480i \(-0.417351\pi\)
\(332\) 10.0382 2.68973i 0.550918 0.147618i
\(333\) 3.79435 1.01669i 0.207929 0.0557145i
\(334\) −3.40192 5.89230i −0.186145 0.322413i
\(335\) 0 0
\(336\) −1.73205 + 2.00000i −0.0944911 + 0.109109i
\(337\) −7.82894 + 7.82894i −0.426470 + 0.426470i −0.887424 0.460954i \(-0.847507\pi\)
0.460954 + 0.887424i \(0.347507\pi\)
\(338\) −5.13922 + 19.1798i −0.279537 + 1.04324i
\(339\) −6.46410 + 11.1962i −0.351082 + 0.608092i
\(340\) 0 0
\(341\) −6.46410 + 3.73205i −0.350051 + 0.202102i
\(342\) −1.60368 1.60368i −0.0867172 0.0867172i
\(343\) 18.0938 3.95164i 0.976972 0.213368i
\(344\) 8.92820i 0.481376i
\(345\) 0 0
\(346\) −6.57180 3.79423i −0.353302 0.203979i
\(347\) −0.757875 2.82843i −0.0406848 0.151838i 0.942595 0.333937i \(-0.108377\pi\)
−0.983280 + 0.182099i \(0.941711\pi\)
\(348\) 6.69213 + 1.79315i 0.358736 + 0.0961230i
\(349\) −1.85641 −0.0993712 −0.0496856 0.998765i \(-0.515822\pi\)
−0.0496856 + 0.998765i \(0.515822\pi\)
\(350\) 0 0
\(351\) 5.73205 0.305954
\(352\) 0.965926 + 0.258819i 0.0514840 + 0.0137951i
\(353\) 1.79315 + 6.69213i 0.0954398 + 0.356186i 0.997086 0.0762887i \(-0.0243071\pi\)
−0.901646 + 0.432475i \(0.857640\pi\)
\(354\) 9.92820 + 5.73205i 0.527678 + 0.304655i
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) −11.0735 16.3514i −0.586070 0.865407i
\(358\) 6.36396 + 6.36396i 0.336346 + 0.336346i
\(359\) 4.39230 2.53590i 0.231817 0.133840i −0.379593 0.925154i \(-0.623936\pi\)
0.611410 + 0.791314i \(0.290603\pi\)
\(360\) 0 0
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) 3.72500 13.9019i 0.195782 0.730668i
\(363\) −7.07107 + 7.07107i −0.371135 + 0.371135i
\(364\) −14.3301 + 4.96410i −0.751103 + 0.260190i
\(365\) 0 0
\(366\) 5.73205 + 9.92820i 0.299619 + 0.518955i
\(367\) −29.4768 + 7.89829i −1.53868 + 0.412288i −0.925838 0.377920i \(-0.876640\pi\)
−0.612840 + 0.790207i \(0.709973\pi\)
\(368\) −5.72620 + 1.53433i −0.298499 + 0.0799826i
\(369\) −1.13397 1.96410i −0.0590324 0.102247i
\(370\) 0 0
\(371\) −2.50000 + 0.866025i −0.129794 + 0.0449618i
\(372\) −5.27792 + 5.27792i −0.273647 + 0.273647i
\(373\) 6.72930 25.1141i 0.348430 1.30036i −0.540124 0.841585i \(-0.681623\pi\)
0.888554 0.458772i \(-0.151711\pi\)
\(374\) −3.73205 + 6.46410i −0.192980 + 0.334251i
\(375\) 0 0
\(376\) 1.03590 0.598076i 0.0534224 0.0308434i
\(377\) 28.0812 + 28.0812i 1.44626 + 1.44626i
\(378\) 1.48356 + 2.19067i 0.0763063 + 0.112676i
\(379\) 3.92820i 0.201778i 0.994898 + 0.100889i \(0.0321687\pi\)
−0.994898 + 0.100889i \(0.967831\pi\)
\(380\) 0 0
\(381\) 4.33013 + 2.50000i 0.221839 + 0.128079i
\(382\) 0.757875 + 2.82843i 0.0387762 + 0.144715i
\(383\) 21.2318 + 5.68904i 1.08489 + 0.290696i 0.756599 0.653879i \(-0.226859\pi\)
0.328294 + 0.944575i \(0.393526\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −22.7846 −1.15971
\(387\) −8.62398 2.31079i −0.438382 0.117464i
\(388\) −0.757875 2.82843i −0.0384753 0.143592i
\(389\) 31.7321 + 18.3205i 1.60888 + 0.928887i 0.989622 + 0.143699i \(0.0458996\pi\)
0.619257 + 0.785188i \(0.287434\pi\)
\(390\) 0 0
\(391\) 44.2487i 2.23775i
\(392\) −5.60609 4.19187i −0.283150 0.211722i
\(393\) 2.91636 + 2.91636i 0.147111 + 0.147111i
\(394\) −14.5981 + 8.42820i −0.735440 + 0.424607i
\(395\) 0 0
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 7.45001 27.8038i 0.373905 1.39543i −0.481033 0.876702i \(-0.659738\pi\)
0.854938 0.518730i \(-0.173595\pi\)
\(398\) 8.86422 8.86422i 0.444323 0.444323i
\(399\) 3.92820 4.53590i 0.196656 0.227079i
\(400\) 0 0
\(401\) −0.964102 1.66987i −0.0481449 0.0833895i 0.840949 0.541115i \(-0.181998\pi\)
−0.889094 + 0.457725i \(0.848664\pi\)
\(402\) −1.93185 + 0.517638i −0.0963520 + 0.0258174i
\(403\) −41.3268 + 11.0735i −2.05863 + 0.551609i
\(404\) 0.535898 + 0.928203i 0.0266619 + 0.0461798i
\(405\) 0 0
\(406\) −3.46410 + 18.0000i −0.171920 + 0.893325i
\(407\) 2.77766 2.77766i 0.137683 0.137683i
\(408\) −1.93185 + 7.20977i −0.0956409 + 0.356937i
\(409\) −14.3923 + 24.9282i −0.711654 + 1.23262i 0.252582 + 0.967575i \(0.418720\pi\)
−0.964236 + 0.265045i \(0.914613\pi\)
\(410\) 0 0
\(411\) −16.3923 + 9.46410i −0.808573 + 0.466830i
\(412\) −13.0053 13.0053i −0.640726 0.640726i
\(413\) −13.2456 + 27.2862i −0.651771 + 1.34266i
\(414\) 5.92820i 0.291355i
\(415\) 0 0
\(416\) 4.96410 + 2.86603i 0.243385 + 0.140518i
\(417\) 2.68973 + 10.0382i 0.131716 + 0.491573i
\(418\) −2.19067 0.586988i −0.107149 0.0287105i
\(419\) 11.0526 0.539953 0.269976 0.962867i \(-0.412984\pi\)
0.269976 + 0.962867i \(0.412984\pi\)
\(420\) 0 0
\(421\) −13.8564 −0.675320 −0.337660 0.941268i \(-0.609635\pi\)
−0.337660 + 0.941268i \(0.609635\pi\)
\(422\) 19.1105 + 5.12063i 0.930283 + 0.249269i
\(423\) −0.309587 1.15539i −0.0150526 0.0561772i
\(424\) 0.866025 + 0.500000i 0.0420579 + 0.0242821i
\(425\) 0 0
\(426\) 8.92820i 0.432573i
\(427\) −25.1141 + 17.0077i −1.21536 + 0.823062i
\(428\) −10.5558 10.5558i −0.510235 0.510235i
\(429\) 4.96410 2.86603i 0.239669 0.138373i
\(430\) 0 0
\(431\) 16.8564 29.1962i 0.811945 1.40633i −0.0995567 0.995032i \(-0.531742\pi\)
0.911501 0.411297i \(-0.134924\pi\)
\(432\) 0.258819 0.965926i 0.0124524 0.0464731i
\(433\) −11.3137 + 11.3137i −0.543702 + 0.543702i −0.924612 0.380910i \(-0.875611\pi\)
0.380910 + 0.924612i \(0.375611\pi\)
\(434\) −14.9282 12.9282i −0.716577 0.620574i
\(435\) 0 0
\(436\) 8.46410 + 14.6603i 0.405357 + 0.702099i
\(437\) 12.9867 3.47979i 0.621240 0.166461i
\(438\) 3.86370 1.03528i 0.184615 0.0494674i
\(439\) 10.0000 + 17.3205i 0.477274 + 0.826663i 0.999661 0.0260459i \(-0.00829161\pi\)
−0.522387 + 0.852709i \(0.674958\pi\)
\(440\) 0 0
\(441\) −5.50000 + 4.33013i −0.261905 + 0.206197i
\(442\) −30.2533 + 30.2533i −1.43900 + 1.43900i
\(443\) −7.20977 + 26.9072i −0.342546 + 1.27840i 0.552906 + 0.833244i \(0.313519\pi\)
−0.895452 + 0.445157i \(0.853148\pi\)
\(444\) 1.96410 3.40192i 0.0932121 0.161448i
\(445\) 0 0
\(446\) 8.07180 4.66025i 0.382211 0.220669i
\(447\) 0.656339 + 0.656339i 0.0310438 + 0.0310438i
\(448\) 0.189469 + 2.63896i 0.00895155 + 0.124679i
\(449\) 13.9282i 0.657313i 0.944450 + 0.328656i \(0.106596\pi\)
−0.944450 + 0.328656i \(0.893404\pi\)
\(450\) 0 0
\(451\) −1.96410 1.13397i −0.0924859 0.0533968i
\(452\) 3.34607 + 12.4877i 0.157386 + 0.587371i
\(453\) 3.72500 + 0.998111i 0.175016 + 0.0468954i
\(454\) −3.46410 −0.162578
\(455\) 0 0
\(456\) −2.26795 −0.106206
\(457\) −15.3161 4.10394i −0.716458 0.191974i −0.117867 0.993029i \(-0.537606\pi\)
−0.598591 + 0.801055i \(0.704272\pi\)
\(458\) −0.757875 2.82843i −0.0354132 0.132164i
\(459\) 6.46410 + 3.73205i 0.301718 + 0.174197i
\(460\) 0 0
\(461\) 38.6410i 1.79969i 0.436208 + 0.899846i \(0.356321\pi\)
−0.436208 + 0.899846i \(0.643679\pi\)
\(462\) 2.38014 + 1.15539i 0.110734 + 0.0537538i
\(463\) 16.0604 + 16.0604i 0.746389 + 0.746389i 0.973799 0.227410i \(-0.0730257\pi\)
−0.227410 + 0.973799i \(0.573026\pi\)
\(464\) 6.00000 3.46410i 0.278543 0.160817i
\(465\) 0 0
\(466\) −0.928203 + 1.60770i −0.0429982 + 0.0744750i
\(467\) 1.65445 6.17449i 0.0765588 0.285721i −0.917023 0.398833i \(-0.869415\pi\)
0.993582 + 0.113112i \(0.0360819\pi\)
\(468\) 4.05317 4.05317i 0.187358 0.187358i
\(469\) −1.73205 5.00000i −0.0799787 0.230879i
\(470\) 0 0
\(471\) −2.33013 4.03590i −0.107367 0.185964i
\(472\) 11.0735 2.96713i 0.509698 0.136573i
\(473\) −8.62398 + 2.31079i −0.396531 + 0.106250i
\(474\) −1.53590 2.66025i −0.0705461 0.122190i
\(475\) 0 0
\(476\) −19.3923 3.73205i −0.888845 0.171058i
\(477\) 0.707107 0.707107i 0.0323762 0.0323762i
\(478\) 6.21166 23.1822i 0.284115 1.06033i
\(479\) −14.5359 + 25.1769i −0.664162 + 1.15036i 0.315350 + 0.948976i \(0.397878\pi\)
−0.979512 + 0.201387i \(0.935455\pi\)
\(480\) 0 0
\(481\) 19.5000 11.2583i 0.889123 0.513336i
\(482\) −15.7458 15.7458i −0.717202 0.717202i
\(483\) −15.6443 + 1.12321i −0.711839 + 0.0511078i
\(484\) 10.0000i 0.454545i
\(485\) 0 0
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) −1.51575 5.65685i −0.0686852 0.256337i 0.923042 0.384699i \(-0.125695\pi\)
−0.991727 + 0.128362i \(0.959028\pi\)
\(488\) 11.0735 + 2.96713i 0.501273 + 0.134316i
\(489\) 12.0000 0.542659
\(490\) 0 0
\(491\) −11.7128 −0.528592 −0.264296 0.964442i \(-0.585140\pi\)
−0.264296 + 0.964442i \(0.585140\pi\)
\(492\) −2.19067 0.586988i −0.0987631 0.0264635i
\(493\) 13.3843 + 49.9507i 0.602797 + 2.24967i
\(494\) −11.2583 6.50000i −0.506536 0.292449i
\(495\) 0 0
\(496\) 7.46410i 0.335148i
\(497\) −23.5612 + 1.69161i −1.05686 + 0.0758793i
\(498\) −7.34847 7.34847i −0.329293 0.329293i
\(499\) −24.2487 + 14.0000i −1.08552 + 0.626726i −0.932381 0.361478i \(-0.882272\pi\)
−0.153141 + 0.988204i \(0.548939\pi\)
\(500\) 0 0
\(501\) −3.40192 + 5.89230i −0.151987 + 0.263249i
\(502\) −1.89967 + 7.08965i −0.0847862 + 0.316427i
\(503\) −9.62209 + 9.62209i −0.429028 + 0.429028i −0.888297 0.459269i \(-0.848111\pi\)
0.459269 + 0.888297i \(0.348111\pi\)
\(504\) 2.59808 + 0.500000i 0.115728 + 0.0222718i
\(505\) 0 0
\(506\) 2.96410 + 5.13397i 0.131770 + 0.228233i
\(507\) 19.1798 5.13922i 0.851806 0.228241i
\(508\) 4.82963 1.29410i 0.214280 0.0574162i
\(509\) 5.19615 + 9.00000i 0.230315 + 0.398918i 0.957901 0.287099i \(-0.0926909\pi\)
−0.727586 + 0.686017i \(0.759358\pi\)
\(510\) 0 0
\(511\) 3.46410 + 10.0000i 0.153243 + 0.442374i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −0.586988 + 2.19067i −0.0259162 + 0.0967205i
\(514\) 1.19615 2.07180i 0.0527600 0.0913830i
\(515\) 0 0
\(516\) −7.73205 + 4.46410i −0.340385 + 0.196521i
\(517\) −0.845807 0.845807i −0.0371986 0.0371986i
\(518\) 9.34967 + 4.53862i 0.410801 + 0.199416i
\(519\) 7.58846i 0.333096i
\(520\) 0 0
\(521\) 27.8205 + 16.0622i 1.21884 + 0.703697i 0.964669 0.263463i \(-0.0848647\pi\)
0.254169 + 0.967160i \(0.418198\pi\)
\(522\) −1.79315 6.69213i −0.0784841 0.292907i
\(523\) 5.93426 + 1.59008i 0.259487 + 0.0695293i 0.386217 0.922408i \(-0.373782\pi\)
−0.126730 + 0.991937i \(0.540448\pi\)
\(524\) 4.12436 0.180173
\(525\) 0 0
\(526\) −29.8564 −1.30180
\(527\) −53.8144 14.4195i −2.34419 0.628125i
\(528\) −0.258819 0.965926i −0.0112637 0.0420365i
\(529\) −10.5167 6.07180i −0.457246 0.263991i
\(530\) 0 0
\(531\) 11.4641i 0.497500i
\(532\) −0.429705 5.98502i −0.0186301 0.259484i
\(533\) −9.19239 9.19239i −0.398167 0.398167i
\(534\) −6.00000 + 3.46410i −0.259645 + 0.149906i
\(535\) 0 0
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 2.32937 8.69333i 0.100520 0.375145i
\(538\) −17.9043 + 17.9043i −0.771909 + 0.771909i
\(539\) −2.59808 + 6.50000i −0.111907 + 0.279975i
\(540\) 0 0
\(541\) −15.4641 26.7846i −0.664854 1.15156i −0.979325 0.202293i \(-0.935161\pi\)
0.314471 0.949267i \(-0.398173\pi\)
\(542\) −7.72741 + 2.07055i −0.331921 + 0.0889378i
\(543\) −13.9019 + 3.72500i −0.596588 + 0.159855i
\(544\) 3.73205 + 6.46410i 0.160010 + 0.277146i
\(545\) 0 0
\(546\) 11.4641 + 9.92820i 0.490618 + 0.424888i
\(547\) 18.1817 18.1817i 0.777394 0.777394i −0.201993 0.979387i \(-0.564742\pi\)
0.979387 + 0.201993i \(0.0647419\pi\)
\(548\) −4.89898 + 18.2832i −0.209274 + 0.781021i
\(549\) 5.73205 9.92820i 0.244638 0.423725i
\(550\) 0 0
\(551\) −13.6077 + 7.85641i −0.579707 + 0.334694i
\(552\) 4.19187 + 4.19187i 0.178418 + 0.178418i
\(553\) 6.72930 4.55721i 0.286159 0.193792i
\(554\) 22.0000i 0.934690i
\(555\) 0 0
\(556\) 9.00000 + 5.19615i 0.381685 + 0.220366i
\(557\) −1.25693 4.69093i −0.0532579 0.198761i 0.934171 0.356826i \(-0.116141\pi\)
−0.987429 + 0.158065i \(0.949474\pi\)
\(558\) 7.20977 + 1.93185i 0.305214 + 0.0817818i
\(559\) −51.1769 −2.16455
\(560\) 0 0
\(561\) 7.46410 0.315135
\(562\) 26.9766 + 7.22835i 1.13794 + 0.304910i
\(563\) −0.619174 2.31079i −0.0260951 0.0973881i 0.951650 0.307184i \(-0.0993867\pi\)
−0.977745 + 0.209796i \(0.932720\pi\)
\(564\) −1.03590 0.598076i −0.0436192 0.0251836i
\(565\) 0 0
\(566\) 12.5359i 0.526923i
\(567\) 1.15539 2.38014i 0.0485220 0.0999565i
\(568\) 6.31319 + 6.31319i 0.264896 + 0.264896i
\(569\) 27.5263 15.8923i 1.15396 0.666240i 0.204112 0.978948i \(-0.434569\pi\)
0.949849 + 0.312707i \(0.101236\pi\)
\(570\) 0 0
\(571\) 6.92820 12.0000i 0.289936 0.502184i −0.683858 0.729615i \(-0.739699\pi\)
0.973794 + 0.227431i \(0.0730325\pi\)
\(572\) 1.48356 5.53674i 0.0620309 0.231503i
\(573\) 2.07055 2.07055i 0.0864986 0.0864986i
\(574\) 1.13397 5.89230i 0.0473312 0.245940i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −20.3538 + 5.45378i −0.847339 + 0.227044i −0.656264 0.754531i \(-0.727864\pi\)
−0.191076 + 0.981575i \(0.561198\pi\)
\(578\) −37.3937 + 10.0196i −1.55537 + 0.416761i
\(579\) 11.3923 + 19.7321i 0.473448 + 0.820036i
\(580\) 0 0
\(581\) 18.0000 20.7846i 0.746766 0.862291i
\(582\) −2.07055 + 2.07055i −0.0858272 + 0.0858272i
\(583\) 0.258819 0.965926i 0.0107192 0.0400046i
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0 0
\(586\) −1.50000 + 0.866025i −0.0619644 + 0.0357752i
\(587\) −15.0759 15.0759i −0.622248 0.622248i 0.323858 0.946106i \(-0.395020\pi\)
−0.946106 + 0.323858i \(0.895020\pi\)
\(588\) −0.827225 + 6.95095i −0.0341142 + 0.286652i
\(589\) 16.9282i 0.697514i
\(590\) 0 0
\(591\) 14.5981 + 8.42820i 0.600485 + 0.346690i
\(592\) −1.01669 3.79435i −0.0417859 0.155947i
\(593\) 40.9478 + 10.9719i 1.68153 + 0.450563i 0.968181 0.250250i \(-0.0805129\pi\)
0.713344 + 0.700814i \(0.247180\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 0.928203 0.0380207
\(597\) −12.1087 3.24453i −0.495578 0.132790i
\(598\) 8.79487 + 32.8229i 0.359649 + 1.34223i
\(599\) 36.2487 + 20.9282i 1.48108 + 0.855103i 0.999770 0.0214460i \(-0.00682701\pi\)
0.481312 + 0.876549i \(0.340160\pi\)
\(600\) 0 0
\(601\) 28.7846i 1.17415i −0.809533 0.587074i \(-0.800280\pi\)
0.809533 0.587074i \(-0.199720\pi\)
\(602\) −13.2456 19.5588i −0.539849 0.797155i
\(603\) 1.41421 + 1.41421i 0.0575912 + 0.0575912i
\(604\) 3.33975 1.92820i 0.135892 0.0784575i
\(605\) 0 0
\(606\) 0.535898 0.928203i 0.0217694 0.0377057i
\(607\) 4.93117 18.4034i 0.200150 0.746969i −0.790724 0.612173i \(-0.790295\pi\)
0.990873 0.134796i \(-0.0430379\pi\)
\(608\) −1.60368 + 1.60368i −0.0650379 + 0.0650379i
\(609\) 17.3205 6.00000i 0.701862 0.243132i
\(610\) 0 0
\(611\) −3.42820 5.93782i −0.138690 0.240219i
\(612\) 7.20977 1.93185i 0.291438 0.0780905i
\(613\) 17.3173 4.64016i 0.699440 0.187414i 0.108460 0.994101i \(-0.465408\pi\)
0.590980 + 0.806686i \(0.298741\pi\)
\(614\) −11.1962 19.3923i −0.451840 0.782610i
\(615\) 0 0
\(616\) 2.50000 0.866025i 0.100728 0.0348932i
\(617\) −2.17209 + 2.17209i −0.0874450 + 0.0874450i −0.749476 0.662031i \(-0.769695\pi\)
0.662031 + 0.749476i \(0.269695\pi\)
\(618\) −4.76028 + 17.7656i −0.191486 + 0.714637i
\(619\) −5.79423 + 10.0359i −0.232890 + 0.403377i −0.958657 0.284563i \(-0.908151\pi\)
0.725768 + 0.687940i \(0.241485\pi\)
\(620\) 0 0
\(621\) 5.13397 2.96410i 0.206019 0.118945i
\(622\) −14.5211 14.5211i −0.582242 0.582242i
\(623\) −10.2784 15.1774i −0.411797 0.608070i
\(624\) 5.73205i 0.229466i
\(625\) 0 0
\(626\) 27.0000 + 15.5885i 1.07914 + 0.623040i
\(627\) 0.586988 + 2.19067i 0.0234421 + 0.0874870i
\(628\) −4.50146 1.20616i −0.179628 0.0481311i
\(629\) 29.3205 1.16909
\(630\) 0 0
\(631\) 42.7846 1.70323 0.851614 0.524169i \(-0.175624\pi\)
0.851614 + 0.524169i \(0.175624\pi\)
\(632\) −2.96713 0.795040i −0.118026 0.0316250i
\(633\) −5.12063 19.1105i −0.203527 0.759573i
\(634\) −12.1244 7.00000i −0.481520 0.278006i
\(635\) 0 0
\(636\) 1.00000i 0.0396526i
\(637\) −24.0280 + 32.1344i −0.952025 + 1.27321i
\(638\) −4.89898 4.89898i −0.193952 0.193952i
\(639\) 7.73205 4.46410i 0.305875 0.176597i
\(640\) 0 0
\(641\) −15.9641 + 27.6506i −0.630544 + 1.09213i 0.356897 + 0.934144i \(0.383835\pi\)
−0.987441 + 0.157991i \(0.949498\pi\)
\(642\) −3.86370 + 14.4195i −0.152488 + 0.569094i
\(643\) −29.2180 + 29.2180i −1.15225 + 1.15225i −0.166144 + 0.986101i \(0.553132\pi\)
−0.986101 + 0.166144i \(0.946868\pi\)
\(644\) −10.2679 + 11.8564i −0.404614 + 0.467208i
\(645\) 0 0
\(646\) −8.46410 14.6603i −0.333016 0.576800i
\(647\) 4.26122 1.14179i 0.167526 0.0448884i −0.174081 0.984731i \(-0.555695\pi\)
0.341607 + 0.939843i \(0.389029\pi\)
\(648\) −0.965926 + 0.258819i −0.0379452 + 0.0101674i
\(649\) −5.73205 9.92820i −0.225003 0.389716i
\(650\) 0 0
\(651\) −3.73205 + 19.3923i −0.146271 + 0.760044i
\(652\) 8.48528 8.48528i 0.332309 0.332309i
\(653\) 6.39615 23.8707i 0.250301 0.934134i −0.720344 0.693617i \(-0.756016\pi\)
0.970645 0.240518i \(-0.0773172\pi\)
\(654\) 8.46410 14.6603i 0.330973 0.573261i
\(655\) 0 0
\(656\) −1.96410 + 1.13397i −0.0766853 + 0.0442743i
\(657\) −2.82843 2.82843i −0.110347 0.110347i
\(658\) 1.38203 2.84701i 0.0538771 0.110988i
\(659\) 39.7128i 1.54699i −0.633801 0.773496i \(-0.718506\pi\)
0.633801 0.773496i \(-0.281494\pi\)
\(660\) 0 0
\(661\) 7.85641 + 4.53590i 0.305579 + 0.176426i 0.644946 0.764228i \(-0.276880\pi\)
−0.339368 + 0.940654i \(0.610213\pi\)
\(662\) 6.67355 + 24.9060i 0.259375 + 0.968000i
\(663\) 41.3268 + 11.0735i 1.60500 + 0.430058i
\(664\) −10.3923 −0.403300
\(665\) 0 0
\(666\) −3.92820 −0.152215
\(667\) 39.6723 + 10.6302i 1.53612 + 0.411602i
\(668\) 1.76097 + 6.57201i 0.0681338 + 0.254279i
\(669\) −8.07180 4.66025i −0.312074 0.180176i
\(670\) 0 0
\(671\) 11.4641i 0.442567i
\(672\) 2.19067 1.48356i 0.0845070 0.0572297i
\(673\) −17.5254 17.5254i −0.675553 0.675553i 0.283438 0.958991i \(-0.408525\pi\)
−0.958991 + 0.283438i \(0.908525\pi\)
\(674\) 9.58846 5.53590i 0.369334 0.213235i
\(675\) 0 0
\(676\) 9.92820 17.1962i 0.381854 0.661390i
\(677\) −12.9360 + 48.2777i −0.497170 + 1.85546i 0.0203517 + 0.999793i \(0.493521\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(678\) 9.14162 9.14162i 0.351082 0.351082i
\(679\) −5.85641 5.07180i −0.224748 0.194638i
\(680\) 0 0
\(681\) 1.73205 + 3.00000i 0.0663723 + 0.114960i
\(682\) 7.20977 1.93185i 0.276076 0.0739744i
\(683\) 13.6617 3.66063i 0.522749 0.140070i 0.0122111 0.999925i \(-0.496113\pi\)
0.510538 + 0.859855i \(0.329446\pi\)
\(684\) 1.13397 + 1.96410i 0.0433586 + 0.0750993i
\(685\) 0 0
\(686\) −18.5000 0.866025i −0.706333 0.0330650i
\(687\) −2.07055 + 2.07055i −0.0789965 + 0.0789965i
\(688\) −2.31079 + 8.62398i −0.0880980 + 0.328786i
\(689\) 2.86603 4.96410i 0.109187 0.189117i
\(690\) 0 0
\(691\) −34.8564 + 20.1244i −1.32600 + 0.765567i −0.984678 0.174380i \(-0.944208\pi\)
−0.341322 + 0.939947i \(0.610875\pi\)
\(692\) 5.36585 + 5.36585i 0.203979 + 0.203979i
\(693\) −0.189469 2.63896i −0.00719732 0.100246i
\(694\) 2.92820i 0.111153i
\(695\) 0 0
\(696\) −6.00000 3.46410i −0.227429 0.131306i
\(697\) −4.38134 16.3514i −0.165955 0.619353i
\(698\) 1.79315 + 0.480473i 0.0678718 + 0.0181862i
\(699\) 1.85641 0.0702157
\(700\) 0 0
\(701\) −4.14359 −0.156501 −0.0782507 0.996934i \(-0.524933\pi\)
−0.0782507 + 0.996934i \(0.524933\pi\)
\(702\) −5.53674 1.48356i −0.208971 0.0559935i
\(703\) 2.30581 + 8.60540i 0.0869653 + 0.324559i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 0 0
\(706\) 6.92820i 0.260746i
\(707\) 2.55103 + 1.23835i 0.0959412 + 0.0465729i
\(708\) −8.10634 8.10634i −0.304655 0.304655i
\(709\) −23.3205 + 13.4641i −0.875820 + 0.505655i −0.869278 0.494324i \(-0.835416\pi\)
−0.00654213 + 0.999979i \(0.502082\pi\)
\(710\) 0 0
\(711\) −1.53590 + 2.66025i −0.0576007 + 0.0997673i
\(712\) −1.79315 + 6.69213i −0.0672012 + 0.250798i
\(713\) −31.2886 + 31.2886i −1.17177 + 1.17177i
\(714\) 6.46410 + 18.6603i 0.241913 + 0.698342i
\(715\) 0 0
\(716\) −4.50000 7.79423i −0.168173 0.291284i
\(717\) −23.1822 + 6.21166i −0.865756 + 0.231979i
\(718\) −4.89898 + 1.31268i −0.182828 + 0.0489887i
\(719\) −3.19615 5.53590i −0.119196 0.206454i 0.800253 0.599662i \(-0.204698\pi\)
−0.919449 + 0.393208i \(0.871365\pi\)
\(720\) 0 0
\(721\) −47.7846 9.19615i −1.77959 0.342483i
\(722\) −9.79796 + 9.79796i −0.364642 + 0.364642i
\(723\) −5.76337 + 21.5092i −0.214342 + 0.799935i
\(724\) −7.19615 + 12.4641i −0.267443 + 0.463225i
\(725\) 0 0
\(726\) 8.66025 5.00000i 0.321412 0.185567i
\(727\) 10.8468 + 10.8468i 0.402287 + 0.402287i 0.879038 0.476751i \(-0.158186\pi\)
−0.476751 + 0.879038i \(0.658186\pi\)
\(728\) 15.1266 1.08604i 0.560631 0.0402515i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) −57.7128 33.3205i −2.13459 1.23240i
\(732\) −2.96713 11.0735i −0.109668 0.409287i
\(733\) −14.5397 3.89589i −0.537034 0.143898i −0.0198997 0.999802i \(-0.506335\pi\)
−0.517135 + 0.855904i \(0.673001\pi\)
\(734\) 30.5167 1.12639
\(735\) 0 0
\(736\) 5.92820 0.218516
\(737\) 1.93185 + 0.517638i 0.0711607 + 0.0190674i
\(738\) 0.586988 + 2.19067i 0.0216073 + 0.0806397i
\(739\) −17.2583 9.96410i −0.634858 0.366535i 0.147773 0.989021i \(-0.452789\pi\)
−0.782631 + 0.622486i \(0.786123\pi\)
\(740\) 0 0
\(741\) 13.0000i 0.477567i
\(742\) 2.63896 0.189469i 0.0968792 0.00695561i
\(743\) 5.50455 + 5.50455i 0.201942 + 0.201942i 0.800832 0.598889i \(-0.204391\pi\)
−0.598889 + 0.800832i \(0.704391\pi\)
\(744\) 6.46410 3.73205i 0.236985 0.136824i
\(745\) 0 0
\(746\) −13.0000 + 22.5167i −0.475964 + 0.824394i
\(747\) −2.68973 + 10.0382i −0.0984119 + 0.367278i
\(748\) 5.27792 5.27792i 0.192980 0.192980i
\(749\) −38.7846 7.46410i −1.41716 0.272732i
\(750\) 0 0
\(751\) 6.92820 + 12.0000i 0.252814 + 0.437886i 0.964299 0.264814i \(-0.0853107\pi\)
−0.711486 + 0.702701i \(0.751977\pi\)
\(752\) −1.15539 + 0.309587i −0.0421329 + 0.0112895i
\(753\) 7.08965 1.89967i 0.258361 0.0692277i
\(754\) −19.8564 34.3923i −0.723128 1.25249i
\(755\) 0 0
\(756\) −0.866025 2.50000i −0.0314970 0.0909241i
\(757\) 26.6670 26.6670i 0.969228 0.969228i −0.0303124 0.999540i \(-0.509650\pi\)
0.999540 + 0.0303124i \(0.00965021\pi\)
\(758\) 1.01669 3.79435i 0.0369280 0.137817i
\(759\) 2.96410 5.13397i 0.107590 0.186351i
\(760\) 0 0
\(761\) 41.8923 24.1865i 1.51859 0.876761i 0.518834 0.854875i \(-0.326366\pi\)
0.999760 0.0218864i \(-0.00696721\pi\)
\(762\) −3.53553 3.53553i −0.128079 0.128079i
\(763\) 40.2915 + 19.5588i 1.45865 + 0.708074i
\(764\) 2.92820i 0.105939i
\(765\) 0 0
\(766\) −19.0359 10.9904i −0.687795 0.397099i
\(767\) −17.0077 63.4737i −0.614113 2.29190i
\(768\) −0.965926 0.258819i −0.0348548 0.00933933i
\(769\) 10.8038 0.389597 0.194798 0.980843i \(-0.437595\pi\)
0.194798 + 0.980843i \(0.437595\pi\)
\(770\) 0 0
\(771\) −2.39230 −0.0861568
\(772\) 22.0082 + 5.89709i 0.792094 + 0.212241i
\(773\) −9.41404 35.1337i −0.338600 1.26367i −0.899914 0.436068i \(-0.856371\pi\)
0.561314 0.827603i \(-0.310296\pi\)
\(774\) 7.73205 + 4.46410i 0.277923 + 0.160459i
\(775\) 0 0
\(776\) 2.92820i 0.105116i
\(777\) −0.744272 10.3664i −0.0267006 0.371891i
\(778\) −25.9091 25.9091i −0.928887 0.928887i
\(779\) 4.45448 2.57180i 0.159598 0.0921442i
\(780\) 0 0
\(781\) 4.46410 7.73205i 0.159738 0.276675i
\(782\) −11.4524 + 42.7410i −0.409537 + 1.52841i
\(783\) −4.89898 + 4.89898i −0.175075 + 0.175075i
\(784\) 4.33013 + 5.50000i 0.154647 + 0.196429i
\(785\) 0 0
\(786\) −2.06218 3.57180i −0.0735554 0.127402i
\(787\) −2.31079 + 0.619174i −0.0823707 + 0.0220712i −0.299769 0.954012i \(-0.596910\pi\)
0.217398 + 0.976083i \(0.430243\pi\)
\(788\) 16.2820 4.36276i 0.580024 0.155417i
\(789\) 14.9282 + 25.8564i 0.531458 + 0.920512i
\(790\) 0 0
\(791\) 25.8564 + 22.3923i 0.919348 + 0.796179i
\(792\) −0.707107 + 0.707107i −0.0251259 + 0.0251259i
\(793\) 17.0077 63.4737i 0.603962 2.25402i
\(794\) −14.3923 + 24.9282i −0.510764 + 0.884669i
\(795\) 0 0
\(796\) −10.8564 + 6.26795i −0.384795 + 0.222162i
\(797\) 21.1117 + 21.1117i 0.747814 + 0.747814i 0.974068 0.226255i \(-0.0726481\pi\)
−0.226255 + 0.974068i \(0.572648\pi\)
\(798\) −4.96833 + 3.36465i −0.175877 + 0.119107i
\(799\) 8.92820i 0.315857i
\(800\) 0 0
\(801\) 6.00000 + 3.46410i 0.212000 + 0.122398i
\(802\) 0.499056 + 1.86250i 0.0176223 + 0.0657672i
\(803\) −3.86370 1.03528i −0.136347 0.0365341i
\(804\) 2.00000 0.0705346
\(805\) 0 0
\(806\) 42.7846 1.50702
\(807\) 24.4577 + 6.55343i 0.860953 + 0.230692i
\(808\) −0.277401 1.03528i −0.00975895 0.0364209i
\(809\) −22.2058 12.8205i −0.780713 0.450745i 0.0559697 0.998432i \(-0.482175\pi\)
−0.836683 + 0.547687i \(0.815508\pi\)
\(810\) 0 0
\(811\) 2.51666i 0.0883719i −0.999023 0.0441860i \(-0.985931\pi\)
0.999023 0.0441860i \(-0.0140694\pi\)
\(812\) 8.00481 16.4901i 0.280914 0.578689i
\(813\) 5.65685 + 5.65685i 0.198395 + 0.198395i
\(814\) −3.40192 + 1.96410i −0.119237 + 0.0688417i
\(815\) 0 0
\(816\) 3.73205 6.46410i 0.130648 0.226289i
\(817\) 5.24075 19.5588i 0.183351 0.684274i
\(818\) 20.3538 20.3538i 0.711654 0.711654i
\(819\) 2.86603 14.8923i 0.100147 0.520379i
\(820\) 0 0
\(821\) 11.9282 + 20.6603i 0.416297 + 0.721048i 0.995564 0.0940904i \(-0.0299943\pi\)
−0.579266 + 0.815138i \(0.696661\pi\)
\(822\) 18.2832 4.89898i 0.637701 0.170872i
\(823\) −34.4959 + 9.24316i −1.20245 + 0.322196i −0.803796 0.594904i \(-0.797190\pi\)
−0.398656 + 0.917101i \(0.630523\pi\)
\(824\) 9.19615 + 15.9282i 0.320363 + 0.554885i
\(825\) 0 0
\(826\) 19.8564 22.9282i 0.690893 0.797774i
\(827\) −31.0112 + 31.0112i −1.07836 + 1.07836i −0.0817074 + 0.996656i \(0.526037\pi\)
−0.996656 + 0.0817074i \(0.973963\pi\)
\(828\) 1.53433 5.72620i 0.0533217 0.198999i
\(829\) 8.26795 14.3205i 0.287158 0.497372i −0.685972 0.727628i \(-0.740623\pi\)
0.973130 + 0.230256i \(0.0739563\pi\)
\(830\) 0 0
\(831\) 19.0526 11.0000i 0.660926 0.381586i
\(832\) −4.05317 4.05317i −0.140518 0.140518i
\(833\) −48.0189 + 20.5940i −1.66376 + 0.713541i
\(834\) 10.3923i 0.359856i
\(835\) 0 0
\(836\) 1.96410 + 1.13397i 0.0679299 + 0.0392193i
\(837\) −1.93185 7.20977i −0.0667746 0.249206i
\(838\) −10.6760 2.86061i −0.368795 0.0988182i
\(839\) 8.53590 0.294692 0.147346 0.989085i \(-0.452927\pi\)
0.147346 + 0.989085i \(0.452927\pi\)
\(840\) 0 0
\(841\) −19.0000 −0.655172
\(842\) 13.3843 + 3.58630i 0.461252 + 0.123592i
\(843\) −7.22835 26.9766i −0.248958 0.929123i
\(844\) −17.1340 9.89230i −0.589776 0.340507i
\(845\) 0 0
\(846\) 1.19615i 0.0411246i
\(847\) 14.8356 + 21.9067i 0.509759 + 0.752723i
\(848\) −0.707107 0.707107i −0.0242821 0.0242821i
\(849\) 10.8564 6.26795i 0.372591 0.215115i
\(850\) 0 0
\(851\) 11.6436 20.1673i 0.399137 0.691326i
\(852\) 2.31079 8.62398i 0.0791663 0.295453i
\(853\) 5.56892 5.56892i 0.190676 0.190676i −0.605312 0.795988i \(-0.706952\pi\)
0.795988 + 0.605312i \(0.206952\pi\)
\(854\) 28.6603 9.92820i 0.980734 0.339736i
\(855\) 0 0
\(856\) 7.46410 + 12.9282i 0.255118 + 0.441877i
\(857\) 15.4548 4.14110i 0.527926 0.141457i 0.0149958 0.999888i \(-0.495227\pi\)
0.512931 + 0.858430i \(0.328560\pi\)
\(858\) −5.53674 + 1.48356i −0.189021 + 0.0506480i
\(859\) −6.80385 11.7846i −0.232144 0.402086i 0.726295 0.687384i \(-0.241241\pi\)
−0.958439 + 0.285298i \(0.907907\pi\)
\(860\) 0 0
\(861\) −5.66987 + 1.96410i −0.193229 + 0.0669364i
\(862\) −23.8386 + 23.8386i −0.811945 + 0.811945i
\(863\) 10.2598 38.2903i 0.349249 1.30342i −0.538319 0.842741i \(-0.680941\pi\)
0.887569 0.460675i \(-0.152393\pi\)
\(864\) −0.500000 + 0.866025i −0.0170103 + 0.0294628i
\(865\) 0 0
\(866\) 13.8564 8.00000i 0.470860 0.271851i
\(867\) 27.3741 + 27.3741i 0.929673 + 0.929673i
\(868\) 11.0735 + 16.3514i 0.375858 + 0.555002i
\(869\) 3.07180i 0.104204i
\(870\) 0 0
\(871\) 9.92820 + 5.73205i 0.336404 + 0.194223i
\(872\) −4.38134 16.3514i −0.148371 0.553728i
\(873\) 2.82843 + 0.757875i 0.0957278 + 0.0256502i
\(874\) −13.4449 −0.454779
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) 3.79435 + 1.01669i 0.128126 + 0.0343313i 0.322312 0.946633i \(-0.395540\pi\)
−0.194186 + 0.980965i \(0.562207\pi\)
\(878\) −5.17638 19.3185i −0.174694 0.651968i
\(879\) 1.50000 + 0.866025i 0.0505937 + 0.0292103i
\(880\) 0 0
\(881\) 36.9090i 1.24349i 0.783218 + 0.621747i \(0.213577\pi\)
−0.783218 + 0.621747i \(0.786423\pi\)
\(882\) 6.43331 2.75908i 0.216621 0.0929029i
\(883\) 24.6980 + 24.6980i 0.831153 + 0.831153i 0.987675 0.156522i \(-0.0500281\pi\)
−0.156522 + 0.987675i \(0.550028\pi\)
\(884\) 37.0526 21.3923i 1.24621 0.719501i
\(885\) 0 0
\(886\) 13.9282 24.1244i 0.467927 0.810474i
\(887\) 0.896575 3.34607i 0.0301041 0.112350i −0.949239 0.314556i \(-0.898144\pi\)
0.979343 + 0.202206i \(0.0648111\pi\)
\(888\) −2.77766 + 2.77766i −0.0932121 + 0.0932121i
\(889\) 8.66025 10.0000i 0.290456 0.335389i
\(890\) 0 0
\(891\) 0.500000 + 0.866025i 0.0167506 + 0.0290129i
\(892\) −9.00292 + 2.41233i −0.301440 + 0.0807706i
\(893\) 2.62038 0.702128i 0.0876875 0.0234958i
\(894\) −0.464102 0.803848i −0.0155219 0.0268847i
\(895\) 0 0
\(896\) 0.500000 2.59808i 0.0167038 0.0867956i
\(897\) 24.0280 24.0280i 0.802272 0.802272i
\(898\) 3.60488 13.4536i 0.120297 0.448953i
\(899\) 25.8564 44.7846i 0.862359 1.49365i
\(900\) 0 0
\(901\) 6.46410 3.73205i 0.215350 0.124333i
\(902\) 1.60368 + 1.60368i 0.0533968 + 0.0533968i
\(903\) −10.3156 + 21.2504i −0.343282 + 0.707168i
\(904\) 12.9282i 0.429986i
\(905\) 0 0
\(906\) −3.33975 1.92820i −0.110956 0.0640603i
\(907\) 0.554803 + 2.07055i 0.0184219 + 0.0687516i 0.974525 0.224279i \(-0.0720028\pi\)
−0.956103 + 0.293031i \(0.905336\pi\)
\(908\) 3.34607 + 0.896575i 0.111043 + 0.0297539i
\(909\) −1.07180 −0.0355493
\(910\) 0 0
\(911\) −2.28719 −0.0757779 −0.0378889 0.999282i \(-0.512063\pi\)
−0.0378889 + 0.999282i \(0.512063\pi\)
\(912\) 2.19067 + 0.586988i 0.0725404 + 0.0194371i
\(913\) 2.68973 + 10.0382i 0.0890170 + 0.332216i
\(914\) 13.7321 + 7.92820i 0.454216 + 0.262242i
\(915\) 0 0
\(916\) 2.92820i 0.0967506i
\(917\) 9.03511 6.11875i 0.298365 0.202059i
\(918\) −5.27792 5.27792i −0.174197 0.174197i
\(919\) −38.7846 + 22.3923i −1.27939 + 0.738654i −0.976736 0.214448i \(-0.931205\pi\)
−0.302651 + 0.953102i \(0.597872\pi\)
\(920\) 0 0
\(921\) −11.1962 + 19.3923i −0.368926 + 0.638998i
\(922\) 10.0010 37.3244i 0.329366 1.22921i
\(923\) 36.1875 36.1875i 1.19113 1.19113i
\(924\) −2.00000 1.73205i −0.0657952 0.0569803i
\(925\) 0 0
\(926\) −11.3564 19.6699i −0.373195 0.646392i
\(927\) 17.7656 4.76028i 0.583499 0.156348i
\(928\) −6.69213 + 1.79315i −0.219680 + 0.0588631i
\(929\) −8.06218 13.9641i −0.264511 0.458147i 0.702924 0.711265i \(-0.251877\pi\)
−0.967436 + 0.253118i \(0.918544\pi\)
\(930\) 0 0
\(931\) −9.82051 12.4737i −0.321854 0.408810i
\(932\) 1.31268 1.31268i 0.0429982 0.0429982i
\(933\) −5.31508 + 19.8362i −0.174008 + 0.649407i
\(934\) −3.19615 + 5.53590i −0.104581 + 0.181140i
\(935\) 0 0
\(936\) −4.96410 + 2.86603i −0.162257 + 0.0936790i
\(937\) 6.79367 + 6.79367i 0.221939 + 0.221939i 0.809315 0.587375i \(-0.199839\pi\)
−0.587375 + 0.809315i \(0.699839\pi\)
\(938\) 0.378937 + 5.27792i 0.0123727 + 0.172330i
\(939\) 31.1769i 1.01742i
\(940\) 0 0
\(941\) 6.67949 + 3.85641i 0.217745 + 0.125715i 0.604906 0.796297i \(-0.293211\pi\)
−0.387161 + 0.922012i \(0.626544\pi\)
\(942\) 1.20616 + 4.50146i 0.0392989 + 0.146665i
\(943\) −12.9867 3.47979i −0.422906 0.113317i
\(944\) −11.4641 −0.373125
\(945\) 0 0
\(946\) 8.92820 0.290281
\(947\) −17.5254 4.69591i −0.569498 0.152596i −0.0374316 0.999299i \(-0.511918\pi\)
−0.532066 + 0.846703i \(0.678584\pi\)
\(948\) 0.795040 + 2.96713i 0.0258217 + 0.0963678i
\(949\) −19.8564 11.4641i −0.644566 0.372140i
\(950\) 0 0
\(951\) 14.0000i 0.453981i
\(952\) 17.7656 + 8.62398i 0.575786 + 0.279505i
\(953\) −32.2223 32.2223i −1.04378 1.04378i −0.998997 0.0447862i \(-0.985739\pi\)
−0.0447862 0.998997i \(-0.514261\pi\)
\(954\) −0.866025 + 0.500000i −0.0280386 + 0.0161881i
\(955\) 0 0
\(956\) −12.0000 + 20.7846i −0.388108 + 0.672222i
\(957\) −1.79315 + 6.69213i −0.0579643 + 0.216326i
\(958\) 20.5569 20.5569i 0.664162 0.664162i
\(959\) 16.3923 + 47.3205i 0.529335 + 1.52806i
\(960\) 0 0
\(961\) 12.3564 + 21.4019i 0.398594 + 0.690385i
\(962\) −21.7494 + 5.82774i −0.701230 + 0.187894i
\(963\) 14.4195 3.86370i 0.464663 0.124506i
\(964\) 11.1340 + 19.2846i 0.358601 + 0.621115i
\(965\) 0 0
\(966\) 15.4019 + 2.96410i 0.495549 + 0.0953684i
\(967\) −21.1117 + 21.1117i −0.678905 + 0.678905i −0.959753 0.280847i \(-0.909385\pi\)
0.280847 + 0.959753i \(0.409385\pi\)
\(968\) 2.58819 9.65926i 0.0831876 0.310460i
\(969\) −8.46410 + 14.6603i −0.271906 + 0.470955i
\(970\) 0 0
\(971\) −38.2128 + 22.0622i −1.22631 + 0.708009i −0.966255 0.257586i \(-0.917073\pi\)
−0.260052 + 0.965595i \(0.583740\pi\)
\(972\) 0.707107 + 0.707107i 0.0226805 + 0.0226805i
\(973\) 27.4249 1.96902i 0.879201 0.0631238i
\(974\) 5.85641i 0.187651i
\(975\) 0 0
\(976\) −9.92820 5.73205i −0.317794 0.183478i
\(977\) 7.76457 + 28.9778i 0.248411 + 0.927081i 0.971638 + 0.236472i \(0.0759910\pi\)
−0.723228 + 0.690610i \(0.757342\pi\)
\(978\) −11.5911 3.10583i −0.370643 0.0993134i
\(979\) 6.92820 0.221426
\(980\) 0 0
\(981\) −16.9282 −0.540476
\(982\) 11.3137 + 3.03150i 0.361035 + 0.0967390i
\(983\) −14.5261 54.2120i −0.463309 1.72909i −0.662435 0.749119i \(-0.730477\pi\)
0.199126 0.979974i \(-0.436190\pi\)
\(984\) 1.96410 + 1.13397i 0.0626133 + 0.0361498i
\(985\) 0 0
\(986\) 51.7128i 1.64687i
\(987\) −3.15660 + 0.226633i −0.100476 + 0.00721382i
\(988\) 9.19239 + 9.19239i 0.292449 + 0.292449i
\(989\) −45.8372 + 26.4641i −1.45754 + 0.841509i
\(990\) 0 0
\(991\) −12.3923 + 21.4641i −0.393655 + 0.681830i −0.992928 0.118714i \(-0.962123\pi\)
0.599274 + 0.800544i \(0.295456\pi\)
\(992\) 1.93185 7.20977i 0.0613364 0.228910i
\(993\) 18.2325 18.2325i 0.578590 0.578590i
\(994\) 23.1962 + 4.46410i 0.735737 + 0.141593i
\(995\) 0 0
\(996\) 5.19615 + 9.00000i 0.164646 + 0.285176i
\(997\) −3.58630 + 0.960947i −0.113579 + 0.0304335i −0.315161 0.949038i \(-0.602059\pi\)
0.201582 + 0.979472i \(0.435392\pi\)
\(998\) 27.0459 7.24693i 0.856124 0.229398i
\(999\) 1.96410 + 3.40192i 0.0621414 + 0.107632i
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 1050.2.bc.a.493.1 8
5.2 odd 4 1050.2.bc.d.157.2 yes 8
5.3 odd 4 1050.2.bc.d.157.1 yes 8
5.4 even 2 inner 1050.2.bc.a.493.2 yes 8
7.5 odd 6 1050.2.bc.d.943.2 yes 8
35.12 even 12 inner 1050.2.bc.a.607.1 yes 8
35.19 odd 6 1050.2.bc.d.943.1 yes 8
35.33 even 12 inner 1050.2.bc.a.607.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1050.2.bc.a.493.1 8 1.1 even 1 trivial
1050.2.bc.a.493.2 yes 8 5.4 even 2 inner
1050.2.bc.a.607.1 yes 8 35.12 even 12 inner
1050.2.bc.a.607.2 yes 8 35.33 even 12 inner
1050.2.bc.d.157.1 yes 8 5.3 odd 4
1050.2.bc.d.157.2 yes 8 5.2 odd 4
1050.2.bc.d.943.1 yes 8 35.19 odd 6
1050.2.bc.d.943.2 yes 8 7.5 odd 6