Properties

Label 390.2.x.b.49.1
Level $390$
Weight $2$
Character 390.49
Analytic conductor $3.114$
Analytic rank $0$
Dimension $12$
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] = [390,2,Mod(49,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.x (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(1.40719 - 0.536449i\) of defining polynomial
Character \(\chi\) \(=\) 390.49
Dual form 390.2.x.b.199.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.03420 - 0.928463i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.40247 + 2.42916i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.03420 - 0.928463i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.40247 + 2.42916i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.213026 - 2.22590i) q^{10} +(-0.515171 + 0.297434i) q^{11} -1.00000i q^{12} +(1.10975 - 3.43052i) q^{13} -2.80495 q^{14} +(2.22590 - 0.213026i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.98222 - 2.87649i) q^{17} +1.00000 q^{18} +(-6.59574 - 3.80805i) q^{19} +(1.82117 - 1.29743i) q^{20} -2.80495i q^{21} +(-0.515171 - 0.297434i) q^{22} +(-4.02317 + 2.32278i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.27591 + 3.77735i) q^{25} +(3.52579 - 0.754186i) q^{26} +1.00000i q^{27} +(-1.40247 - 2.42916i) q^{28} +(-1.26235 - 2.18645i) q^{29} +(1.29743 + 1.82117i) q^{30} +6.59309i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.297434 - 0.515171i) q^{33} -5.75297i q^{34} +(5.10829 - 3.63924i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.18679 + 8.98379i) q^{37} -7.61611i q^{38} +(0.754186 + 3.52579i) q^{39} +(2.03420 + 0.928463i) q^{40} +(-4.98222 + 2.87649i) q^{41} +(2.42916 - 1.40247i) q^{42} +(3.67593 + 2.12230i) q^{43} -0.594869i q^{44} +(-1.82117 + 1.29743i) q^{45} +(-4.02317 - 2.32278i) q^{46} -2.89798 q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.433868 - 0.751482i) q^{49} +(-1.63333 + 4.72570i) q^{50} +5.75297 q^{51} +(2.41604 + 2.67633i) q^{52} -13.8960i q^{53} +(-0.866025 + 0.500000i) q^{54} +(1.32412 - 0.126722i) q^{55} +(1.40247 - 2.42916i) q^{56} +7.61611 q^{57} +(1.26235 - 2.18645i) q^{58} +(8.40299 + 4.85147i) q^{59} +(-0.928463 + 2.03420i) q^{60} +(-3.41309 + 5.91165i) q^{61} +(-5.70978 + 3.29654i) q^{62} +(1.40247 + 2.42916i) q^{63} +1.00000 q^{64} +(-5.44256 + 5.94798i) q^{65} +0.594869 q^{66} +(3.93121 + 6.80906i) q^{67} +(4.98222 - 2.87649i) q^{68} +(2.32278 - 4.02317i) q^{69} +(5.70582 + 2.60429i) q^{70} +(-1.11257 - 0.642342i) q^{71} +(-0.500000 + 0.866025i) q^{72} -14.5400 q^{73} +(-5.18679 + 8.98379i) q^{74} +(-4.72570 - 1.63333i) q^{75} +(6.59574 - 3.80805i) q^{76} -1.66858i q^{77} +(-2.67633 + 2.41604i) q^{78} -1.83150 q^{79} +(0.213026 + 2.22590i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.98222 - 2.87649i) q^{82} -4.19184 q^{83} +(2.42916 + 1.40247i) q^{84} +(7.46410 + 10.4771i) q^{85} +4.24460i q^{86} +(2.18645 + 1.26235i) q^{87} +(0.515171 - 0.297434i) q^{88} +(-5.24333 + 3.02724i) q^{89} +(-2.03420 - 0.928463i) q^{90} +(6.77687 + 7.50697i) q^{91} -4.64555i q^{92} +(-3.29654 - 5.70978i) q^{93} +(-1.44899 - 2.50973i) q^{94} +(9.88140 + 13.8702i) q^{95} +1.00000i q^{96} +(8.45318 - 14.6413i) q^{97} +(0.433868 - 0.751482i) q^{98} +0.594869i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.03420 0.928463i −0.909720 0.415221i
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −1.40247 + 2.42916i −0.530085 + 0.918135i 0.469299 + 0.883040i \(0.344507\pi\)
−0.999384 + 0.0350954i \(0.988827\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.213026 2.22590i −0.0673646 0.703891i
\(11\) −0.515171 + 0.297434i −0.155330 + 0.0896798i −0.575650 0.817696i \(-0.695251\pi\)
0.420320 + 0.907376i \(0.361918\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.10975 3.43052i 0.307790 0.951454i
\(14\) −2.80495 −0.749654
\(15\) 2.22590 0.213026i 0.574724 0.0550030i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −4.98222 2.87649i −1.20837 0.697650i −0.245963 0.969279i \(-0.579104\pi\)
−0.962402 + 0.271629i \(0.912438\pi\)
\(18\) 1.00000 0.235702
\(19\) −6.59574 3.80805i −1.51317 0.873628i −0.999881 0.0154099i \(-0.995095\pi\)
−0.513286 0.858218i \(-0.671572\pi\)
\(20\) 1.82117 1.29743i 0.407226 0.290115i
\(21\) 2.80495i 0.612090i
\(22\) −0.515171 0.297434i −0.109835 0.0634132i
\(23\) −4.02317 + 2.32278i −0.838888 + 0.484332i −0.856886 0.515506i \(-0.827604\pi\)
0.0179978 + 0.999838i \(0.494271\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 3.27591 + 3.77735i 0.655182 + 0.755471i
\(26\) 3.52579 0.754186i 0.691465 0.147908i
\(27\) 1.00000i 0.192450i
\(28\) −1.40247 2.42916i −0.265043 0.459067i
\(29\) −1.26235 2.18645i −0.234412 0.406013i 0.724690 0.689075i \(-0.241983\pi\)
−0.959102 + 0.283062i \(0.908650\pi\)
\(30\) 1.29743 + 1.82117i 0.236878 + 0.332499i
\(31\) 6.59309i 1.18415i 0.805882 + 0.592077i \(0.201692\pi\)
−0.805882 + 0.592077i \(0.798308\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.297434 0.515171i 0.0517767 0.0896798i
\(34\) 5.75297i 0.986626i
\(35\) 5.10829 3.63924i 0.863459 0.615143i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 5.18679 + 8.98379i 0.852703 + 1.47693i 0.878759 + 0.477265i \(0.158372\pi\)
−0.0260561 + 0.999660i \(0.508295\pi\)
\(38\) 7.61611i 1.23550i
\(39\) 0.754186 + 3.52579i 0.120766 + 0.564578i
\(40\) 2.03420 + 0.928463i 0.321635 + 0.146803i
\(41\) −4.98222 + 2.87649i −0.778092 + 0.449232i −0.835754 0.549105i \(-0.814969\pi\)
0.0576618 + 0.998336i \(0.481636\pi\)
\(42\) 2.42916 1.40247i 0.374827 0.216406i
\(43\) 3.67593 + 2.12230i 0.560574 + 0.323648i 0.753376 0.657590i \(-0.228424\pi\)
−0.192802 + 0.981238i \(0.561757\pi\)
\(44\) 0.594869i 0.0896798i
\(45\) −1.82117 + 1.29743i −0.271484 + 0.193410i
\(46\) −4.02317 2.32278i −0.593184 0.342475i
\(47\) −2.89798 −0.422715 −0.211357 0.977409i \(-0.567788\pi\)
−0.211357 + 0.977409i \(0.567788\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −0.433868 0.751482i −0.0619812 0.107355i
\(50\) −1.63333 + 4.72570i −0.230987 + 0.668315i
\(51\) 5.75297 0.805577
\(52\) 2.41604 + 2.67633i 0.335044 + 0.371140i
\(53\) 13.8960i 1.90876i −0.298598 0.954379i \(-0.596519\pi\)
0.298598 0.954379i \(-0.403481\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 1.32412 0.126722i 0.178544 0.0170872i
\(56\) 1.40247 2.42916i 0.187414 0.324610i
\(57\) 7.61611 1.00878
\(58\) 1.26235 2.18645i 0.165754 0.287095i
\(59\) 8.40299 + 4.85147i 1.09398 + 0.631607i 0.934632 0.355616i \(-0.115729\pi\)
0.159344 + 0.987223i \(0.449062\pi\)
\(60\) −0.928463 + 2.03420i −0.119864 + 0.262614i
\(61\) −3.41309 + 5.91165i −0.437002 + 0.756910i −0.997457 0.0712755i \(-0.977293\pi\)
0.560455 + 0.828185i \(0.310626\pi\)
\(62\) −5.70978 + 3.29654i −0.725143 + 0.418661i
\(63\) 1.40247 + 2.42916i 0.176695 + 0.306045i
\(64\) 1.00000 0.125000
\(65\) −5.44256 + 5.94798i −0.675067 + 0.737757i
\(66\) 0.594869 0.0732233
\(67\) 3.93121 + 6.80906i 0.480274 + 0.831859i 0.999744 0.0226299i \(-0.00720394\pi\)
−0.519470 + 0.854489i \(0.673871\pi\)
\(68\) 4.98222 2.87649i 0.604183 0.348825i
\(69\) 2.32278 4.02317i 0.279629 0.484332i
\(70\) 5.70582 + 2.60429i 0.681976 + 0.311272i
\(71\) −1.11257 0.642342i −0.132038 0.0762320i 0.432526 0.901621i \(-0.357622\pi\)
−0.564564 + 0.825389i \(0.690956\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −14.5400 −1.70178 −0.850892 0.525341i \(-0.823938\pi\)
−0.850892 + 0.525341i \(0.823938\pi\)
\(74\) −5.18679 + 8.98379i −0.602952 + 1.04434i
\(75\) −4.72570 1.63333i −0.545677 0.188601i
\(76\) 6.59574 3.80805i 0.756584 0.436814i
\(77\) 1.66858i 0.190152i
\(78\) −2.67633 + 2.41604i −0.303035 + 0.273563i
\(79\) −1.83150 −0.206060 −0.103030 0.994678i \(-0.532854\pi\)
−0.103030 + 0.994678i \(0.532854\pi\)
\(80\) 0.213026 + 2.22590i 0.0238170 + 0.248863i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.98222 2.87649i −0.550194 0.317655i
\(83\) −4.19184 −0.460114 −0.230057 0.973177i \(-0.573891\pi\)
−0.230057 + 0.973177i \(0.573891\pi\)
\(84\) 2.42916 + 1.40247i 0.265043 + 0.153022i
\(85\) 7.46410 + 10.4771i 0.809595 + 1.13641i
\(86\) 4.24460i 0.457707i
\(87\) 2.18645 + 1.26235i 0.234412 + 0.135338i
\(88\) 0.515171 0.297434i 0.0549175 0.0317066i
\(89\) −5.24333 + 3.02724i −0.555792 + 0.320886i −0.751455 0.659785i \(-0.770647\pi\)
0.195663 + 0.980671i \(0.437314\pi\)
\(90\) −2.03420 0.928463i −0.214423 0.0978686i
\(91\) 6.77687 + 7.50697i 0.710409 + 0.786945i
\(92\) 4.64555i 0.484332i
\(93\) −3.29654 5.70978i −0.341836 0.592077i
\(94\) −1.44899 2.50973i −0.149452 0.258859i
\(95\) 9.88140 + 13.8702i 1.01381 + 1.42306i
\(96\) 1.00000i 0.102062i
\(97\) 8.45318 14.6413i 0.858291 1.48660i −0.0152677 0.999883i \(-0.504860\pi\)
0.873558 0.486719i \(-0.161807\pi\)
\(98\) 0.433868 0.751482i 0.0438273 0.0759111i
\(99\) 0.594869i 0.0597866i
\(100\) −4.90924 + 0.948346i −0.490924 + 0.0948346i
\(101\) 2.72360 + 4.71741i 0.271008 + 0.469400i 0.969120 0.246589i \(-0.0793096\pi\)
−0.698112 + 0.715988i \(0.745976\pi\)
\(102\) 2.87649 + 4.98222i 0.284814 + 0.493313i
\(103\) 13.7529i 1.35511i −0.735471 0.677556i \(-0.763039\pi\)
0.735471 0.677556i \(-0.236961\pi\)
\(104\) −1.10975 + 3.43052i −0.108820 + 0.336390i
\(105\) −2.60429 + 5.70582i −0.254153 + 0.556831i
\(106\) 12.0343 6.94798i 1.16887 0.674848i
\(107\) −3.66407 + 2.11545i −0.354219 + 0.204509i −0.666542 0.745468i \(-0.732226\pi\)
0.312323 + 0.949976i \(0.398893\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 0.447358i 0.0428491i 0.999770 + 0.0214246i \(0.00682017\pi\)
−0.999770 + 0.0214246i \(0.993180\pi\)
\(110\) 0.771803 + 1.08336i 0.0735885 + 0.103294i
\(111\) −8.98379 5.18679i −0.852703 0.492308i
\(112\) 2.80495 0.265043
\(113\) −8.11206 4.68350i −0.763119 0.440587i 0.0672956 0.997733i \(-0.478563\pi\)
−0.830414 + 0.557146i \(0.811896\pi\)
\(114\) 3.80805 + 6.59574i 0.356657 + 0.617748i
\(115\) 10.3405 0.989622i 0.964259 0.0922827i
\(116\) 2.52469 0.234412
\(117\) −2.41604 2.67633i −0.223363 0.247427i
\(118\) 9.70293i 0.893227i
\(119\) 13.9749 8.06839i 1.28107 0.739628i
\(120\) −2.22590 + 0.213026i −0.203196 + 0.0194465i
\(121\) −5.32307 + 9.21982i −0.483915 + 0.838165i
\(122\) −6.82619 −0.618014
\(123\) 2.87649 4.98222i 0.259364 0.449232i
\(124\) −5.70978 3.29654i −0.512753 0.296038i
\(125\) −3.15672 10.7254i −0.282345 0.959313i
\(126\) −1.40247 + 2.42916i −0.124942 + 0.216406i
\(127\) 5.79190 3.34395i 0.513948 0.296728i −0.220507 0.975385i \(-0.570771\pi\)
0.734455 + 0.678658i \(0.237438\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −4.24460 −0.373716
\(130\) −7.87239 1.73941i −0.690454 0.152556i
\(131\) −11.6724 −1.01982 −0.509911 0.860227i \(-0.670322\pi\)
−0.509911 + 0.860227i \(0.670322\pi\)
\(132\) 0.297434 + 0.515171i 0.0258883 + 0.0448399i
\(133\) 18.5007 10.6814i 1.60422 0.926194i
\(134\) −3.93121 + 6.80906i −0.339605 + 0.588213i
\(135\) 0.928463 2.03420i 0.0799094 0.175076i
\(136\) 4.98222 + 2.87649i 0.427222 + 0.246657i
\(137\) −3.40142 + 5.89144i −0.290603 + 0.503339i −0.973953 0.226752i \(-0.927189\pi\)
0.683349 + 0.730092i \(0.260523\pi\)
\(138\) 4.64555 0.395456
\(139\) −3.54908 + 6.14719i −0.301029 + 0.521397i −0.976369 0.216109i \(-0.930663\pi\)
0.675340 + 0.737506i \(0.263997\pi\)
\(140\) 0.597526 + 6.24353i 0.0505001 + 0.527674i
\(141\) 2.50973 1.44899i 0.211357 0.122027i
\(142\) 1.28468i 0.107808i
\(143\) 0.448642 + 2.09738i 0.0375173 + 0.175392i
\(144\) −1.00000 −0.0833333
\(145\) 0.537824 + 5.61971i 0.0446639 + 0.466691i
\(146\) −7.27002 12.5920i −0.601671 1.04213i
\(147\) 0.751482 + 0.433868i 0.0619812 + 0.0357848i
\(148\) −10.3736 −0.852703
\(149\) −3.02342 1.74557i −0.247688 0.143003i 0.371017 0.928626i \(-0.379009\pi\)
−0.618705 + 0.785623i \(0.712342\pi\)
\(150\) −0.948346 4.90924i −0.0774321 0.400838i
\(151\) 4.54988i 0.370264i −0.982714 0.185132i \(-0.940729\pi\)
0.982714 0.185132i \(-0.0592713\pi\)
\(152\) 6.59574 + 3.80805i 0.534985 + 0.308874i
\(153\) −4.98222 + 2.87649i −0.402789 + 0.232550i
\(154\) 1.44503 0.834288i 0.116444 0.0672288i
\(155\) 6.12144 13.4116i 0.491686 1.07725i
\(156\) −3.43052 1.10975i −0.274661 0.0888512i
\(157\) 11.4957i 0.917460i −0.888576 0.458730i \(-0.848305\pi\)
0.888576 0.458730i \(-0.151695\pi\)
\(158\) −0.915751 1.58613i −0.0728532 0.126186i
\(159\) 6.94798 + 12.0343i 0.551011 + 0.954379i
\(160\) −1.82117 + 1.29743i −0.143976 + 0.102571i
\(161\) 13.0305i 1.02695i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −6.91443 + 11.9762i −0.541580 + 0.938045i 0.457233 + 0.889347i \(0.348840\pi\)
−0.998814 + 0.0486977i \(0.984493\pi\)
\(164\) 5.75297i 0.449232i
\(165\) −1.08336 + 0.771803i −0.0843393 + 0.0600848i
\(166\) −2.09592 3.63024i −0.162675 0.281761i
\(167\) 10.7700 + 18.6542i 0.833409 + 1.44351i 0.895319 + 0.445425i \(0.146948\pi\)
−0.0619099 + 0.998082i \(0.519719\pi\)
\(168\) 2.80495i 0.216406i
\(169\) −10.5369 7.61404i −0.810531 0.585696i
\(170\) −5.34142 + 11.7027i −0.409668 + 0.897554i
\(171\) −6.59574 + 3.80805i −0.504389 + 0.291209i
\(172\) −3.67593 + 2.12230i −0.280287 + 0.161824i
\(173\) 11.8342 + 6.83251i 0.899741 + 0.519466i 0.877116 0.480278i \(-0.159464\pi\)
0.0226249 + 0.999744i \(0.492798\pi\)
\(174\) 2.52469i 0.191396i
\(175\) −13.7702 + 2.66006i −1.04093 + 0.201082i
\(176\) 0.515171 + 0.297434i 0.0388325 + 0.0224200i
\(177\) −9.70293 −0.729317
\(178\) −5.24333 3.02724i −0.393004 0.226901i
\(179\) 5.37886 + 9.31647i 0.402035 + 0.696345i 0.993971 0.109639i \(-0.0349696\pi\)
−0.591936 + 0.805985i \(0.701636\pi\)
\(180\) −0.213026 2.22590i −0.0158780 0.165909i
\(181\) 5.86469 0.435919 0.217959 0.975958i \(-0.430060\pi\)
0.217959 + 0.975958i \(0.430060\pi\)
\(182\) −3.11280 + 9.62243i −0.230736 + 0.713262i
\(183\) 6.82619i 0.504606i
\(184\) 4.02317 2.32278i 0.296592 0.171237i
\(185\) −2.20984 23.0905i −0.162471 1.69765i
\(186\) 3.29654 5.70978i 0.241714 0.418661i
\(187\) 3.42226 0.250261
\(188\) 1.44899 2.50973i 0.105679 0.183041i
\(189\) −2.42916 1.40247i −0.176695 0.102015i
\(190\) −7.07128 + 15.4927i −0.513004 + 1.12396i
\(191\) 6.91728 11.9811i 0.500517 0.866921i −0.499483 0.866324i \(-0.666477\pi\)
1.00000 0.000597179i \(-0.000190088\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −8.50322 14.7280i −0.612075 1.06014i −0.990890 0.134673i \(-0.957002\pi\)
0.378815 0.925472i \(-0.376332\pi\)
\(194\) 16.9064 1.21381
\(195\) 1.73941 7.87239i 0.124561 0.563753i
\(196\) 0.867736 0.0619812
\(197\) −3.16487 5.48171i −0.225487 0.390556i 0.730978 0.682401i \(-0.239064\pi\)
−0.956466 + 0.291845i \(0.905731\pi\)
\(198\) −0.515171 + 0.297434i −0.0366116 + 0.0211377i
\(199\) 8.31782 14.4069i 0.589634 1.02128i −0.404646 0.914473i \(-0.632605\pi\)
0.994280 0.106803i \(-0.0340615\pi\)
\(200\) −3.27591 3.77735i −0.231642 0.267099i
\(201\) −6.80906 3.93121i −0.480274 0.277286i
\(202\) −2.72360 + 4.71741i −0.191632 + 0.331916i
\(203\) 7.08163 0.497033
\(204\) −2.87649 + 4.98222i −0.201394 + 0.348825i
\(205\) 12.8055 1.22553i 0.894377 0.0855947i
\(206\) 11.9104 6.87645i 0.829834 0.479105i
\(207\) 4.64555i 0.322888i
\(208\) −3.52579 + 0.754186i −0.244470 + 0.0522934i
\(209\) 4.53058 0.313387
\(210\) −6.24353 + 0.597526i −0.430844 + 0.0412332i
\(211\) −8.27443 14.3317i −0.569635 0.986637i −0.996602 0.0823697i \(-0.973751\pi\)
0.426967 0.904267i \(-0.359582\pi\)
\(212\) 12.0343 + 6.94798i 0.826516 + 0.477190i
\(213\) 1.28468 0.0880251
\(214\) −3.66407 2.11545i −0.250471 0.144609i
\(215\) −5.50709 7.73014i −0.375580 0.527191i
\(216\) 1.00000i 0.0680414i
\(217\) −16.0156 9.24663i −1.08721 0.627702i
\(218\) −0.387423 + 0.223679i −0.0262396 + 0.0151495i
\(219\) 12.5920 7.27002i 0.850892 0.491262i
\(220\) −0.552314 + 1.21008i −0.0372370 + 0.0815836i
\(221\) −15.3969 + 13.8994i −1.03570 + 0.934975i
\(222\) 10.3736i 0.696229i
\(223\) 8.32779 + 14.4242i 0.557670 + 0.965913i 0.997690 + 0.0679254i \(0.0216380\pi\)
−0.440020 + 0.897988i \(0.645029\pi\)
\(224\) 1.40247 + 2.42916i 0.0937068 + 0.162305i
\(225\) 4.90924 0.948346i 0.327283 0.0632231i
\(226\) 9.36701i 0.623084i
\(227\) 1.51105 2.61722i 0.100292 0.173711i −0.811513 0.584334i \(-0.801356\pi\)
0.911805 + 0.410624i \(0.134689\pi\)
\(228\) −3.80805 + 6.59574i −0.252195 + 0.436814i
\(229\) 16.4472i 1.08686i −0.839453 0.543432i \(-0.817125\pi\)
0.839453 0.543432i \(-0.182875\pi\)
\(230\) 6.02730 + 8.46035i 0.397428 + 0.557859i
\(231\) 0.834288 + 1.44503i 0.0548921 + 0.0950759i
\(232\) 1.26235 + 2.18645i 0.0828771 + 0.143547i
\(233\) 13.8289i 0.905959i 0.891521 + 0.452980i \(0.149639\pi\)
−0.891521 + 0.452980i \(0.850361\pi\)
\(234\) 1.10975 3.43052i 0.0725467 0.224260i
\(235\) 5.89507 + 2.69067i 0.384552 + 0.175520i
\(236\) −8.40299 + 4.85147i −0.546988 + 0.315804i
\(237\) 1.58613 0.915751i 0.103030 0.0594844i
\(238\) 13.9749 + 8.06839i 0.905856 + 0.522996i
\(239\) 4.60216i 0.297689i −0.988861 0.148845i \(-0.952445\pi\)
0.988861 0.148845i \(-0.0475554\pi\)
\(240\) −1.29743 1.82117i −0.0837490 0.117556i
\(241\) 5.38108 + 3.10677i 0.346626 + 0.200125i 0.663198 0.748444i \(-0.269199\pi\)
−0.316572 + 0.948568i \(0.602532\pi\)
\(242\) −10.6461 −0.684359
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −3.41309 5.91165i −0.218501 0.378455i
\(245\) 0.184850 + 1.93149i 0.0118096 + 0.123399i
\(246\) 5.75297 0.366796
\(247\) −20.3832 + 18.4008i −1.29695 + 1.17082i
\(248\) 6.59309i 0.418661i
\(249\) 3.63024 2.09592i 0.230057 0.132824i
\(250\) 7.71015 8.09652i 0.487633 0.512069i
\(251\) 8.19386 14.1922i 0.517192 0.895802i −0.482609 0.875836i \(-0.660311\pi\)
0.999801 0.0199663i \(-0.00635591\pi\)
\(252\) −2.80495 −0.176695
\(253\) 1.38175 2.39326i 0.0868697 0.150463i
\(254\) 5.79190 + 3.34395i 0.363416 + 0.209818i
\(255\) −11.7027 5.34142i −0.732850 0.334493i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.28269 + 4.20466i −0.454282 + 0.262280i −0.709637 0.704568i \(-0.751141\pi\)
0.255355 + 0.966847i \(0.417808\pi\)
\(258\) −2.12230 3.67593i −0.132129 0.228853i
\(259\) −29.0974 −1.80802
\(260\) −2.42982 7.68739i −0.150691 0.476752i
\(261\) −2.52469 −0.156275
\(262\) −5.83620 10.1086i −0.360562 0.624511i
\(263\) 5.10152 2.94536i 0.314573 0.181619i −0.334398 0.942432i \(-0.608533\pi\)
0.648971 + 0.760813i \(0.275200\pi\)
\(264\) −0.297434 + 0.515171i −0.0183058 + 0.0317066i
\(265\) −12.9019 + 28.2671i −0.792557 + 1.73644i
\(266\) 18.5007 + 10.6814i 1.13435 + 0.654918i
\(267\) 3.02724 5.24333i 0.185264 0.320886i
\(268\) −7.86242 −0.480274
\(269\) 11.4228 19.7848i 0.696459 1.20630i −0.273228 0.961949i \(-0.588091\pi\)
0.969686 0.244352i \(-0.0785754\pi\)
\(270\) 2.22590 0.213026i 0.135464 0.0129643i
\(271\) −23.2565 + 13.4271i −1.41273 + 0.815639i −0.995645 0.0932285i \(-0.970281\pi\)
−0.417084 + 0.908868i \(0.636948\pi\)
\(272\) 5.75297i 0.348825i
\(273\) −9.62243 3.11280i −0.582376 0.188395i
\(274\) −6.80285 −0.410975
\(275\) −2.81117 0.971616i −0.169520 0.0585906i
\(276\) 2.32278 + 4.02317i 0.139815 + 0.242166i
\(277\) 9.20150 + 5.31249i 0.552865 + 0.319197i 0.750277 0.661124i \(-0.229920\pi\)
−0.197412 + 0.980321i \(0.563254\pi\)
\(278\) −7.09816 −0.425719
\(279\) 5.70978 + 3.29654i 0.341836 + 0.197359i
\(280\) −5.10829 + 3.63924i −0.305279 + 0.217486i
\(281\) 28.3732i 1.69260i 0.532705 + 0.846301i \(0.321176\pi\)
−0.532705 + 0.846301i \(0.678824\pi\)
\(282\) 2.50973 + 1.44899i 0.149452 + 0.0862862i
\(283\) −4.91005 + 2.83482i −0.291872 + 0.168512i −0.638786 0.769385i \(-0.720563\pi\)
0.346914 + 0.937897i \(0.387230\pi\)
\(284\) 1.11257 0.642342i 0.0660188 0.0381160i
\(285\) −15.4927 7.07128i −0.917706 0.418866i
\(286\) −1.59207 + 1.43723i −0.0941408 + 0.0849850i
\(287\) 16.1368i 0.952524i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 8.04834 + 13.9401i 0.473431 + 0.820007i
\(290\) −4.59790 + 3.27562i −0.269998 + 0.192351i
\(291\) 16.9064i 0.991069i
\(292\) 7.27002 12.5920i 0.425446 0.736894i
\(293\) −0.829176 + 1.43617i −0.0484410 + 0.0839022i −0.889229 0.457462i \(-0.848759\pi\)
0.840788 + 0.541364i \(0.182092\pi\)
\(294\) 0.867736i 0.0506074i
\(295\) −12.5889 17.6707i −0.732955 1.02883i
\(296\) −5.18679 8.98379i −0.301476 0.522172i
\(297\) −0.297434 0.515171i −0.0172589 0.0298933i
\(298\) 3.49115i 0.202237i
\(299\) 3.50361 + 16.3793i 0.202619 + 0.947237i
\(300\) 3.77735 3.27591i 0.218086 0.189135i
\(301\) −10.3108 + 5.95294i −0.594304 + 0.343122i
\(302\) 3.94031 2.27494i 0.226740 0.130908i
\(303\) −4.71741 2.72360i −0.271008 0.156467i
\(304\) 7.61611i 0.436814i
\(305\) 12.4317 8.85653i 0.711835 0.507123i
\(306\) −4.98222 2.87649i −0.284814 0.164438i
\(307\) 0.384087 0.0219210 0.0109605 0.999940i \(-0.496511\pi\)
0.0109605 + 0.999940i \(0.496511\pi\)
\(308\) 1.44503 + 0.834288i 0.0823382 + 0.0475380i
\(309\) 6.87645 + 11.9104i 0.391187 + 0.677556i
\(310\) 14.6755 1.40450i 0.833514 0.0797700i
\(311\) −11.6920 −0.662993 −0.331497 0.943456i \(-0.607554\pi\)
−0.331497 + 0.943456i \(0.607554\pi\)
\(312\) −0.754186 3.52579i −0.0426974 0.199609i
\(313\) 10.5788i 0.597948i −0.954261 0.298974i \(-0.903356\pi\)
0.954261 0.298974i \(-0.0966444\pi\)
\(314\) 9.95560 5.74787i 0.561827 0.324371i
\(315\) −0.597526 6.24353i −0.0336668 0.351783i
\(316\) 0.915751 1.58613i 0.0515150 0.0892266i
\(317\) 22.1023 1.24139 0.620695 0.784052i \(-0.286850\pi\)
0.620695 + 0.784052i \(0.286850\pi\)
\(318\) −6.94798 + 12.0343i −0.389624 + 0.674848i
\(319\) 1.30065 + 0.750930i 0.0728224 + 0.0420440i
\(320\) −2.03420 0.928463i −0.113715 0.0519027i
\(321\) 2.11545 3.66407i 0.118073 0.204509i
\(322\) 11.2848 6.51527i 0.628876 0.363082i
\(323\) 21.9076 + 37.9451i 1.21897 + 2.11132i
\(324\) 1.00000 0.0555556
\(325\) 16.5937 7.04615i 0.920454 0.390850i
\(326\) −13.8289 −0.765910
\(327\) −0.223679 0.387423i −0.0123695 0.0214246i
\(328\) 4.98222 2.87649i 0.275097 0.158827i
\(329\) 4.06435 7.03966i 0.224075 0.388109i
\(330\) −1.21008 0.552314i −0.0666127 0.0304039i
\(331\) −5.28809 3.05308i −0.290660 0.167812i 0.347580 0.937650i \(-0.387004\pi\)
−0.638239 + 0.769838i \(0.720337\pi\)
\(332\) 2.09592 3.63024i 0.115029 0.199235i
\(333\) 10.3736 0.568469
\(334\) −10.7700 + 18.6542i −0.589309 + 1.02071i
\(335\) −1.67490 17.5009i −0.0915094 0.956179i
\(336\) −2.42916 + 1.40247i −0.132521 + 0.0765112i
\(337\) 4.29852i 0.234155i 0.993123 + 0.117078i \(0.0373526\pi\)
−0.993123 + 0.117078i \(0.962647\pi\)
\(338\) 1.32550 12.9322i 0.0720979 0.703422i
\(339\) 9.36701 0.508746
\(340\) −12.8055 + 1.22553i −0.694477 + 0.0664637i
\(341\) −1.96101 3.39657i −0.106195 0.183935i
\(342\) −6.59574 3.80805i −0.356657 0.205916i
\(343\) −17.2007 −0.928750
\(344\) −3.67593 2.12230i −0.198193 0.114427i
\(345\) −8.46035 + 6.02730i −0.455490 + 0.324499i
\(346\) 13.6650i 0.734636i
\(347\) −29.7444 17.1730i −1.59677 0.921893i −0.992105 0.125409i \(-0.959976\pi\)
−0.604660 0.796484i \(-0.706691\pi\)
\(348\) −2.18645 + 1.26235i −0.117206 + 0.0676689i
\(349\) 13.8581 8.00099i 0.741808 0.428283i −0.0809181 0.996721i \(-0.525785\pi\)
0.822726 + 0.568438i \(0.192452\pi\)
\(350\) −9.18876 10.5953i −0.491160 0.566342i
\(351\) 3.43052 + 1.10975i 0.183107 + 0.0592341i
\(352\) 0.594869i 0.0317066i
\(353\) 9.69607 + 16.7941i 0.516070 + 0.893859i 0.999826 + 0.0186563i \(0.00593884\pi\)
−0.483756 + 0.875203i \(0.660728\pi\)
\(354\) −4.85147 8.40299i −0.257853 0.446614i
\(355\) 1.66679 + 2.33963i 0.0884642 + 0.124175i
\(356\) 6.05447i 0.320886i
\(357\) −8.06839 + 13.9749i −0.427025 + 0.739628i
\(358\) −5.37886 + 9.31647i −0.284282 + 0.492391i
\(359\) 15.8342i 0.835699i 0.908516 + 0.417850i \(0.137216\pi\)
−0.908516 + 0.417850i \(0.862784\pi\)
\(360\) 1.82117 1.29743i 0.0959841 0.0683808i
\(361\) 19.5026 + 33.7794i 1.02645 + 1.77786i
\(362\) 2.93234 + 5.07897i 0.154121 + 0.266945i
\(363\) 10.6461i 0.558777i
\(364\) −9.88966 + 2.11545i −0.518359 + 0.110880i
\(365\) 29.5773 + 13.4999i 1.54815 + 0.706617i
\(366\) 5.91165 3.41309i 0.309007 0.178405i
\(367\) 13.2440 7.64645i 0.691333 0.399141i −0.112778 0.993620i \(-0.535975\pi\)
0.804111 + 0.594479i \(0.202642\pi\)
\(368\) 4.02317 + 2.32278i 0.209722 + 0.121083i
\(369\) 5.75297i 0.299488i
\(370\) 18.8921 13.4590i 0.982152 0.699702i
\(371\) 33.7555 + 19.4887i 1.75250 + 1.01180i
\(372\) 6.59309 0.341836
\(373\) 18.7508 + 10.8258i 0.970881 + 0.560538i 0.899505 0.436911i \(-0.143928\pi\)
0.0713760 + 0.997449i \(0.477261\pi\)
\(374\) 1.71113 + 2.96377i 0.0884805 + 0.153253i
\(375\) 8.09652 + 7.71015i 0.418102 + 0.398150i
\(376\) 2.89798 0.149452
\(377\) −8.90154 + 1.90409i −0.458453 + 0.0980655i
\(378\) 2.80495i 0.144271i
\(379\) 7.81479 4.51187i 0.401419 0.231759i −0.285677 0.958326i \(-0.592218\pi\)
0.687096 + 0.726567i \(0.258885\pi\)
\(380\) −16.9527 + 1.62243i −0.869654 + 0.0832287i
\(381\) −3.34395 + 5.79190i −0.171316 + 0.296728i
\(382\) 13.8346 0.707838
\(383\) −5.03703 + 8.72439i −0.257380 + 0.445795i −0.965539 0.260257i \(-0.916193\pi\)
0.708159 + 0.706053i \(0.249526\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) −1.54921 + 3.39421i −0.0789551 + 0.172985i
\(386\) 8.50322 14.7280i 0.432802 0.749636i
\(387\) 3.67593 2.12230i 0.186858 0.107883i
\(388\) 8.45318 + 14.6413i 0.429145 + 0.743301i
\(389\) −24.3591 −1.23505 −0.617527 0.786550i \(-0.711865\pi\)
−0.617527 + 0.786550i \(0.711865\pi\)
\(390\) 7.68739 2.42982i 0.389266 0.123039i
\(391\) 26.7257 1.35158
\(392\) 0.433868 + 0.751482i 0.0219137 + 0.0379556i
\(393\) 10.1086 5.83620i 0.509911 0.294397i
\(394\) 3.16487 5.48171i 0.159444 0.276165i
\(395\) 3.72564 + 1.70048i 0.187457 + 0.0855606i
\(396\) −0.515171 0.297434i −0.0258883 0.0149466i
\(397\) −15.0190 + 26.0137i −0.753784 + 1.30559i 0.192193 + 0.981357i \(0.438440\pi\)
−0.945977 + 0.324234i \(0.894893\pi\)
\(398\) 16.6356 0.833869
\(399\) −10.6814 + 18.5007i −0.534739 + 0.926194i
\(400\) 1.63333 4.72570i 0.0816664 0.236285i
\(401\) 2.35786 1.36131i 0.117746 0.0679807i −0.439970 0.898012i \(-0.645011\pi\)
0.557716 + 0.830032i \(0.311678\pi\)
\(402\) 7.86242i 0.392142i
\(403\) 22.6177 + 7.31669i 1.12667 + 0.364470i
\(404\) −5.44720 −0.271008
\(405\) 0.213026 + 2.22590i 0.0105853 + 0.110606i
\(406\) 3.54082 + 6.13287i 0.175728 + 0.304369i
\(407\) −5.34417 3.08546i −0.264901 0.152941i
\(408\) −5.75297 −0.284814
\(409\) −33.1032 19.1121i −1.63685 0.945034i −0.981909 0.189352i \(-0.939361\pi\)
−0.654938 0.755683i \(-0.727305\pi\)
\(410\) 7.46410 + 10.4771i 0.368626 + 0.517429i
\(411\) 6.80285i 0.335560i
\(412\) 11.9104 + 6.87645i 0.586781 + 0.338778i
\(413\) −23.5699 + 13.6081i −1.15980 + 0.669612i
\(414\) −4.02317 + 2.32278i −0.197728 + 0.114158i
\(415\) 8.52703 + 3.89197i 0.418575 + 0.191049i
\(416\) −2.41604 2.67633i −0.118456 0.131218i
\(417\) 7.09816i 0.347598i
\(418\) 2.26529 + 3.92360i 0.110799 + 0.191910i
\(419\) 14.9365 + 25.8708i 0.729695 + 1.26387i 0.957012 + 0.290048i \(0.0936714\pi\)
−0.227317 + 0.973821i \(0.572995\pi\)
\(420\) −3.63924 5.10829i −0.177577 0.249259i
\(421\) 14.2033i 0.692226i −0.938193 0.346113i \(-0.887501\pi\)
0.938193 0.346113i \(-0.112499\pi\)
\(422\) 8.27443 14.3317i 0.402793 0.697658i
\(423\) −1.44899 + 2.50973i −0.0704524 + 0.122027i
\(424\) 13.8960i 0.674848i
\(425\) −5.45581 28.2427i −0.264646 1.36997i
\(426\) 0.642342 + 1.11257i 0.0311216 + 0.0539042i
\(427\) −9.57355 16.5819i −0.463297 0.802453i
\(428\) 4.23091i 0.204509i
\(429\) −1.43723 1.59207i −0.0693899 0.0768657i
\(430\) 3.94095 8.63435i 0.190050 0.416385i
\(431\) −8.09901 + 4.67596i −0.390115 + 0.225233i −0.682210 0.731156i \(-0.738981\pi\)
0.292095 + 0.956389i \(0.405648\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 3.42954 + 1.98005i 0.164813 + 0.0951549i 0.580138 0.814518i \(-0.302999\pi\)
−0.415325 + 0.909673i \(0.636332\pi\)
\(434\) 18.4933i 0.887705i
\(435\) −3.27562 4.59790i −0.157054 0.220452i
\(436\) −0.387423 0.223679i −0.0185542 0.0107123i
\(437\) 35.3810 1.69250
\(438\) 12.5920 + 7.27002i 0.601671 + 0.347375i
\(439\) −11.2992 19.5708i −0.539281 0.934062i −0.998943 0.0459680i \(-0.985363\pi\)
0.459662 0.888094i \(-0.347971\pi\)
\(440\) −1.32412 + 0.126722i −0.0631248 + 0.00604125i
\(441\) −0.867736 −0.0413208
\(442\) −19.7357 6.38437i −0.938730 0.303673i
\(443\) 29.0428i 1.37987i 0.723873 + 0.689933i \(0.242360\pi\)
−0.723873 + 0.689933i \(0.757640\pi\)
\(444\) 8.98379 5.18679i 0.426352 0.246154i
\(445\) 13.4766 1.28976i 0.638854 0.0611404i
\(446\) −8.32779 + 14.4242i −0.394332 + 0.683004i
\(447\) 3.49115 0.165125
\(448\) −1.40247 + 2.42916i −0.0662607 + 0.114767i
\(449\) 23.7886 + 13.7343i 1.12265 + 0.648164i 0.942077 0.335397i \(-0.108870\pi\)
0.180576 + 0.983561i \(0.442204\pi\)
\(450\) 3.27591 + 3.77735i 0.154428 + 0.178066i
\(451\) 1.71113 2.96377i 0.0805740 0.139558i
\(452\) 8.11206 4.68350i 0.381559 0.220293i
\(453\) 2.27494 + 3.94031i 0.106886 + 0.185132i
\(454\) 3.02210 0.141834
\(455\) −6.81553 21.5627i −0.319517 1.01088i
\(456\) −7.61611 −0.356657
\(457\) −2.19087 3.79470i −0.102485 0.177508i 0.810223 0.586122i \(-0.199346\pi\)
−0.912708 + 0.408613i \(0.866013\pi\)
\(458\) 14.2437 8.22361i 0.665565 0.384264i
\(459\) 2.87649 4.98222i 0.134263 0.232550i
\(460\) −4.31323 + 9.44997i −0.201105 + 0.440607i
\(461\) −21.0593 12.1586i −0.980829 0.566282i −0.0783090 0.996929i \(-0.524952\pi\)
−0.902520 + 0.430647i \(0.858285\pi\)
\(462\) −0.834288 + 1.44503i −0.0388146 + 0.0672288i
\(463\) −19.0660 −0.886071 −0.443035 0.896504i \(-0.646098\pi\)
−0.443035 + 0.896504i \(0.646098\pi\)
\(464\) −1.26235 + 2.18645i −0.0586030 + 0.101503i
\(465\) 1.40450 + 14.6755i 0.0651319 + 0.680562i
\(466\) −11.9762 + 6.91443i −0.554784 + 0.320305i
\(467\) 10.1176i 0.468188i −0.972214 0.234094i \(-0.924788\pi\)
0.972214 0.234094i \(-0.0752123\pi\)
\(468\) 3.52579 0.754186i 0.162980 0.0348623i
\(469\) −22.0537 −1.01834
\(470\) 0.617345 + 6.45062i 0.0284760 + 0.297545i
\(471\) 5.74787 + 9.95560i 0.264848 + 0.458730i
\(472\) −8.40299 4.85147i −0.386779 0.223307i
\(473\) −2.52498 −0.116099
\(474\) 1.58613 + 0.915751i 0.0728532 + 0.0420618i
\(475\) −7.22271 37.3893i −0.331401 1.71554i
\(476\) 16.1368i 0.739628i
\(477\) −12.0343 6.94798i −0.551011 0.318126i
\(478\) 3.98559 2.30108i 0.182297 0.105249i
\(479\) −24.8215 + 14.3307i −1.13412 + 0.654786i −0.944969 0.327161i \(-0.893908\pi\)
−0.189155 + 0.981947i \(0.560575\pi\)
\(480\) 0.928463 2.03420i 0.0423784 0.0928479i
\(481\) 36.5751 7.82361i 1.66768 0.356726i
\(482\) 6.21354i 0.283019i
\(483\) 6.51527 + 11.2848i 0.296455 + 0.513475i
\(484\) −5.32307 9.21982i −0.241958 0.419083i
\(485\) −30.7894 + 21.9349i −1.39807 + 0.996012i
\(486\) 1.00000i 0.0453609i
\(487\) −8.71990 + 15.1033i −0.395136 + 0.684396i −0.993119 0.117113i \(-0.962636\pi\)
0.597982 + 0.801509i \(0.295969\pi\)
\(488\) 3.41309 5.91165i 0.154504 0.267608i
\(489\) 13.8289i 0.625363i
\(490\) −1.58030 + 1.12583i −0.0713905 + 0.0508599i
\(491\) −11.2233 19.4394i −0.506503 0.877288i −0.999972 0.00752493i \(-0.997605\pi\)
0.493469 0.869763i \(-0.335729\pi\)
\(492\) 2.87649 + 4.98222i 0.129682 + 0.224616i
\(493\) 14.5245i 0.654150i
\(494\) −26.1272 8.45199i −1.17552 0.380273i
\(495\) 0.552314 1.21008i 0.0248247 0.0543890i
\(496\) 5.70978 3.29654i 0.256377 0.148019i
\(497\) 3.12070 1.80174i 0.139983 0.0808189i
\(498\) 3.63024 + 2.09592i 0.162675 + 0.0939204i
\(499\) 10.4136i 0.466177i 0.972456 + 0.233088i \(0.0748832\pi\)
−0.972456 + 0.233088i \(0.925117\pi\)
\(500\) 10.8669 + 2.62893i 0.485981 + 0.117569i
\(501\) −18.6542 10.7700i −0.833409 0.481169i
\(502\) 16.3877 0.731420
\(503\) −5.00387 2.88899i −0.223112 0.128814i 0.384279 0.923217i \(-0.374450\pi\)
−0.607390 + 0.794404i \(0.707784\pi\)
\(504\) −1.40247 2.42916i −0.0624712 0.108203i
\(505\) −1.16039 12.1249i −0.0516368 0.539551i
\(506\) 2.76349 0.122852
\(507\) 12.9322 + 1.32550i 0.574341 + 0.0588677i
\(508\) 6.68791i 0.296728i
\(509\) −6.18024 + 3.56816i −0.273934 + 0.158156i −0.630674 0.776048i \(-0.717222\pi\)
0.356740 + 0.934204i \(0.383888\pi\)
\(510\) −1.22553 12.8055i −0.0542674 0.567038i
\(511\) 20.3920 35.3200i 0.902090 1.56247i
\(512\) −1.00000 −0.0441942
\(513\) 3.80805 6.59574i 0.168130 0.291209i
\(514\) −7.28269 4.20466i −0.321226 0.185460i
\(515\) −12.7691 + 27.9761i −0.562672 + 1.23277i
\(516\) 2.12230 3.67593i 0.0934290 0.161824i
\(517\) 1.49296 0.861960i 0.0656603 0.0379090i
\(518\) −14.5487 25.1991i −0.639232 1.10718i
\(519\) −13.6650 −0.599827
\(520\) 5.44256 5.94798i 0.238672 0.260836i
\(521\) 1.09782 0.0480965 0.0240483 0.999711i \(-0.492344\pi\)
0.0240483 + 0.999711i \(0.492344\pi\)
\(522\) −1.26235 2.18645i −0.0552514 0.0956982i
\(523\) −12.9411 + 7.47153i −0.565873 + 0.326707i −0.755499 0.655149i \(-0.772606\pi\)
0.189626 + 0.981856i \(0.439272\pi\)
\(524\) 5.83620 10.1086i 0.254956 0.441596i
\(525\) 10.5953 9.18876i 0.462416 0.401031i
\(526\) 5.10152 + 2.94536i 0.222437 + 0.128424i
\(527\) 18.9649 32.8482i 0.826125 1.43089i
\(528\) −0.594869 −0.0258883
\(529\) −0.709414 + 1.22874i −0.0308441 + 0.0534235i
\(530\) −30.9310 + 2.96020i −1.34356 + 0.128583i
\(531\) 8.40299 4.85147i 0.364659 0.210536i
\(532\) 21.3628i 0.926194i
\(533\) 4.33881 + 20.2838i 0.187935 + 0.878588i
\(534\) 6.05447 0.262003
\(535\) 9.41756 0.901291i 0.407157 0.0389662i
\(536\) −3.93121 6.80906i −0.169802 0.294106i
\(537\) −9.31647 5.37886i −0.402035 0.232115i
\(538\) 22.8455 0.984941
\(539\) 0.447033 + 0.258095i 0.0192551 + 0.0111169i
\(540\) 1.29743 + 1.82117i 0.0558327 + 0.0783707i
\(541\) 19.3888i 0.833589i −0.909001 0.416794i \(-0.863154\pi\)
0.909001 0.416794i \(-0.136846\pi\)
\(542\) −23.2565 13.4271i −0.998950 0.576744i
\(543\) −5.07897 + 2.93234i −0.217959 + 0.125839i
\(544\) −4.98222 + 2.87649i −0.213611 + 0.123328i
\(545\) 0.415355 0.910014i 0.0177919 0.0389807i
\(546\) −2.11545 9.88966i −0.0905330 0.423239i
\(547\) 26.1335i 1.11739i −0.829374 0.558693i \(-0.811303\pi\)
0.829374 0.558693i \(-0.188697\pi\)
\(548\) −3.40142 5.89144i −0.145302 0.251670i
\(549\) 3.41309 + 5.91165i 0.145667 + 0.252303i
\(550\) −0.564141 2.92035i −0.0240551 0.124524i
\(551\) 19.2283i 0.819155i
\(552\) −2.32278 + 4.02317i −0.0988640 + 0.171237i
\(553\) 2.56863 4.44901i 0.109229 0.189191i
\(554\) 10.6250i 0.451412i
\(555\) 13.4590 + 18.8921i 0.571305 + 0.801924i
\(556\) −3.54908 6.14719i −0.150514 0.260699i
\(557\) 17.6927 + 30.6446i 0.749663 + 1.29846i 0.947984 + 0.318318i \(0.103118\pi\)
−0.198321 + 0.980137i \(0.563549\pi\)
\(558\) 6.59309i 0.279108i
\(559\) 11.3600 10.2551i 0.480475 0.433745i
\(560\) −5.70582 2.60429i −0.241115 0.110051i
\(561\) −2.96377 + 1.71113i −0.125130 + 0.0722440i
\(562\) −24.5719 + 14.1866i −1.03650 + 0.598425i
\(563\) −25.8011 14.8963i −1.08739 0.627804i −0.154509 0.987991i \(-0.549379\pi\)
−0.932880 + 0.360187i \(0.882713\pi\)
\(564\) 2.89798i 0.122027i
\(565\) 12.1531 + 17.0589i 0.511284 + 0.717674i
\(566\) −4.91005 2.83482i −0.206385 0.119156i
\(567\) 2.80495 0.117797
\(568\) 1.11257 + 0.642342i 0.0466824 + 0.0269521i
\(569\) −7.14388 12.3736i −0.299487 0.518727i 0.676532 0.736414i \(-0.263482\pi\)
−0.976019 + 0.217687i \(0.930149\pi\)
\(570\) −1.62243 16.9527i −0.0679559 0.710070i
\(571\) −37.4439 −1.56698 −0.783490 0.621404i \(-0.786562\pi\)
−0.783490 + 0.621404i \(0.786562\pi\)
\(572\) −2.04071 0.660156i −0.0853263 0.0276025i
\(573\) 13.8346i 0.577947i
\(574\) 13.9749 8.06839i 0.583300 0.336768i
\(575\) −21.9535 7.58771i −0.915524 0.316430i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −47.6052 −1.98183 −0.990916 0.134485i \(-0.957062\pi\)
−0.990916 + 0.134485i \(0.957062\pi\)
\(578\) −8.04834 + 13.9401i −0.334767 + 0.579833i
\(579\) 14.7280 + 8.50322i 0.612075 + 0.353382i
\(580\) −5.13572 2.34408i −0.213249 0.0973328i
\(581\) 5.87895 10.1826i 0.243900 0.422447i
\(582\) −14.6413 + 8.45318i −0.606903 + 0.350396i
\(583\) 4.13314 + 7.15881i 0.171177 + 0.296487i
\(584\) 14.5400 0.601671
\(585\) 2.42982 + 7.68739i 0.100461 + 0.317834i
\(586\) −1.65835 −0.0685059
\(587\) −18.8016 32.5654i −0.776027 1.34412i −0.934216 0.356709i \(-0.883899\pi\)
0.158189 0.987409i \(-0.449435\pi\)
\(588\) −0.751482 + 0.433868i −0.0309906 + 0.0178924i
\(589\) 25.1068 43.4863i 1.03451 1.79182i
\(590\) 9.00882 19.7377i 0.370887 0.812587i
\(591\) 5.48171 + 3.16487i 0.225487 + 0.130185i
\(592\) 5.18679 8.98379i 0.213176 0.369231i
\(593\) −24.0046 −0.985752 −0.492876 0.870100i \(-0.664054\pi\)
−0.492876 + 0.870100i \(0.664054\pi\)
\(594\) 0.297434 0.515171i 0.0122039 0.0211377i
\(595\) −35.9188 + 3.43755i −1.47253 + 0.140926i
\(596\) 3.02342 1.74557i 0.123844 0.0715014i
\(597\) 16.6356i 0.680851i
\(598\) −12.4330 + 11.2238i −0.508425 + 0.458977i
\(599\) −23.7092 −0.968731 −0.484365 0.874866i \(-0.660949\pi\)
−0.484365 + 0.874866i \(0.660949\pi\)
\(600\) 4.72570 + 1.63333i 0.192926 + 0.0666803i
\(601\) 0.918249 + 1.59045i 0.0374562 + 0.0648760i 0.884146 0.467211i \(-0.154741\pi\)
−0.846690 + 0.532087i \(0.821408\pi\)
\(602\) −10.3108 5.95294i −0.420237 0.242624i
\(603\) 7.86242 0.320183
\(604\) 3.94031 + 2.27494i 0.160329 + 0.0925661i
\(605\) 19.3884 13.8127i 0.788252 0.561564i
\(606\) 5.44720i 0.221277i
\(607\) 30.2214 + 17.4483i 1.22665 + 0.708206i 0.966327 0.257316i \(-0.0828382\pi\)
0.260321 + 0.965522i \(0.416172\pi\)
\(608\) −6.59574 + 3.80805i −0.267493 + 0.154437i
\(609\) −6.13287 + 3.54082i −0.248517 + 0.143481i
\(610\) 13.8858 + 6.33786i 0.562220 + 0.256613i
\(611\) −3.21604 + 9.94159i −0.130107 + 0.402194i
\(612\) 5.75297i 0.232550i
\(613\) 4.70575 + 8.15061i 0.190064 + 0.329200i 0.945271 0.326286i \(-0.105797\pi\)
−0.755207 + 0.655486i \(0.772464\pi\)
\(614\) 0.192044 + 0.332629i 0.00775025 + 0.0134238i
\(615\) −10.4771 + 7.46410i −0.422479 + 0.300982i
\(616\) 1.66858i 0.0672288i
\(617\) −5.47577 + 9.48432i −0.220446 + 0.381824i −0.954944 0.296787i \(-0.904085\pi\)
0.734497 + 0.678612i \(0.237418\pi\)
\(618\) −6.87645 + 11.9104i −0.276611 + 0.479105i
\(619\) 1.00216i 0.0402803i 0.999797 + 0.0201402i \(0.00641125\pi\)
−0.999797 + 0.0201402i \(0.993589\pi\)
\(620\) 8.55410 + 12.0071i 0.343541 + 0.482218i
\(621\) −2.32278 4.02317i −0.0932098 0.161444i
\(622\) −5.84601 10.1256i −0.234404 0.405999i
\(623\) 16.9825i 0.680389i
\(624\) 2.67633 2.41604i 0.107139 0.0967190i
\(625\) −3.53680 + 24.7486i −0.141472 + 0.989942i
\(626\) 9.16150 5.28939i 0.366167 0.211407i
\(627\) −3.92360 + 2.26529i −0.156694 + 0.0904671i
\(628\) 9.95560 + 5.74787i 0.397272 + 0.229365i
\(629\) 59.6789i 2.37955i
\(630\) 5.10829 3.63924i 0.203519 0.144991i
\(631\) −33.5167 19.3509i −1.33428 0.770346i −0.348327 0.937373i \(-0.613250\pi\)
−0.985952 + 0.167027i \(0.946583\pi\)
\(632\) 1.83150 0.0728532
\(633\) 14.3317 + 8.27443i 0.569635 + 0.328879i
\(634\) 11.0512 + 19.1412i 0.438898 + 0.760193i
\(635\) −14.8866 + 1.42469i −0.590756 + 0.0565373i
\(636\) −13.8960 −0.551011
\(637\) −3.05946 + 0.654435i −0.121220 + 0.0259296i
\(638\) 1.50186i 0.0594592i
\(639\) −1.11257 + 0.642342i −0.0440126 + 0.0254107i
\(640\) −0.213026 2.22590i −0.00842057 0.0879863i
\(641\) 4.99961 8.65957i 0.197473 0.342033i −0.750236 0.661170i \(-0.770060\pi\)
0.947708 + 0.319138i \(0.103393\pi\)
\(642\) 4.23091 0.166981
\(643\) 3.38728 5.86694i 0.133581 0.231369i −0.791473 0.611204i \(-0.790686\pi\)
0.925055 + 0.379834i \(0.124019\pi\)
\(644\) 11.2848 + 6.51527i 0.444683 + 0.256738i
\(645\) 8.63435 + 3.94095i 0.339977 + 0.155175i
\(646\) −21.9076 + 37.9451i −0.861944 + 1.49293i
\(647\) 14.8850 8.59384i 0.585188 0.337859i −0.178004 0.984030i \(-0.556964\pi\)
0.763193 + 0.646171i \(0.223631\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −5.77197 −0.226570
\(650\) 14.3990 + 10.8475i 0.564776 + 0.425474i
\(651\) 18.4933 0.724808
\(652\) −6.91443 11.9762i −0.270790 0.469022i
\(653\) −21.5401 + 12.4362i −0.842930 + 0.486666i −0.858259 0.513217i \(-0.828454\pi\)
0.0153292 + 0.999883i \(0.495120\pi\)
\(654\) 0.223679 0.387423i 0.00874654 0.0151495i
\(655\) 23.7440 + 10.8374i 0.927753 + 0.423452i
\(656\) 4.98222 + 2.87649i 0.194523 + 0.112308i
\(657\) −7.27002 + 12.5920i −0.283631 + 0.491262i
\(658\) 8.12870 0.316890
\(659\) −4.12151 + 7.13867i −0.160551 + 0.278083i −0.935067 0.354472i \(-0.884661\pi\)
0.774515 + 0.632555i \(0.217994\pi\)
\(660\) −0.126722 1.32412i −0.00493266 0.0515412i
\(661\) 22.3962 12.9305i 0.871112 0.502937i 0.00339467 0.999994i \(-0.498919\pi\)
0.867718 + 0.497057i \(0.165586\pi\)
\(662\) 6.10616i 0.237323i
\(663\) 6.38437 19.7357i 0.247948 0.766470i
\(664\) 4.19184 0.162675
\(665\) −47.5514 + 4.55082i −1.84396 + 0.176473i
\(666\) 5.18679 + 8.98379i 0.200984 + 0.348115i
\(667\) 10.1573 + 5.86430i 0.393291 + 0.227067i
\(668\) −21.5400 −0.833409
\(669\) −14.4242 8.32779i −0.557670 0.321971i
\(670\) 14.3188 10.2010i 0.553184 0.394098i
\(671\) 4.06069i 0.156761i
\(672\) −2.42916 1.40247i −0.0937068 0.0541016i
\(673\) 5.99820 3.46306i 0.231213 0.133491i −0.379918 0.925020i \(-0.624048\pi\)
0.611132 + 0.791529i \(0.290715\pi\)
\(674\) −3.72263 + 2.14926i −0.143390 + 0.0827864i
\(675\) −3.77735 + 3.27591i −0.145390 + 0.126090i
\(676\) 11.8624 5.31820i 0.456246 0.204546i
\(677\) 4.72639i 0.181650i 0.995867 + 0.0908250i \(0.0289504\pi\)
−0.995867 + 0.0908250i \(0.971050\pi\)
\(678\) 4.68350 + 8.11206i 0.179869 + 0.311542i
\(679\) 23.7107 + 41.0682i 0.909935 + 1.57605i
\(680\) −7.46410 10.4771i −0.286235 0.401780i
\(681\) 3.02210i 0.115807i
\(682\) 1.96101 3.39657i 0.0750910 0.130061i
\(683\) 9.78995 16.9567i 0.374602 0.648830i −0.615665 0.788008i \(-0.711113\pi\)
0.990267 + 0.139178i \(0.0444460\pi\)
\(684\) 7.61611i 0.291209i
\(685\) 12.3891 8.82625i 0.473365 0.337234i
\(686\) −8.60034 14.8962i −0.328363 0.568741i
\(687\) 8.22361 + 14.2437i 0.313750 + 0.543432i
\(688\) 4.24460i 0.161824i
\(689\) −47.6704 15.4211i −1.81610 0.587496i
\(690\) −9.44997 4.31323i −0.359754 0.164202i
\(691\) −10.7079 + 6.18224i −0.407350 + 0.235183i −0.689650 0.724143i \(-0.742236\pi\)
0.282301 + 0.959326i \(0.408902\pi\)
\(692\) −11.8342 + 6.83251i −0.449871 + 0.259733i
\(693\) −1.44503 0.834288i −0.0548921 0.0316920i
\(694\) 34.3459i 1.30375i
\(695\) 12.9270 9.20939i 0.490348 0.349332i
\(696\) −2.18645 1.26235i −0.0828771 0.0478491i
\(697\) 33.0967 1.25363
\(698\) 13.8581 + 8.00099i 0.524538 + 0.302842i
\(699\) −6.91443 11.9762i −0.261528 0.452980i
\(700\) 4.58140 13.2553i 0.173161 0.501005i
\(701\) 43.7550 1.65260 0.826302 0.563227i \(-0.190441\pi\)
0.826302 + 0.563227i \(0.190441\pi\)
\(702\) 0.754186 + 3.52579i 0.0284649 + 0.133072i
\(703\) 79.0063i 2.97978i
\(704\) −0.515171 + 0.297434i −0.0194163 + 0.0112100i
\(705\) −6.45062 + 0.617345i −0.242944 + 0.0232506i
\(706\) −9.69607 + 16.7941i −0.364916 + 0.632054i
\(707\) −15.2791 −0.574630
\(708\) 4.85147 8.40299i 0.182329 0.315804i
\(709\) 16.4104 + 9.47457i 0.616307 + 0.355825i 0.775430 0.631434i \(-0.217533\pi\)
−0.159123 + 0.987259i \(0.550867\pi\)
\(710\) −1.19278 + 2.61330i −0.0447643 + 0.0980754i
\(711\) −0.915751 + 1.58613i −0.0343434 + 0.0594844i
\(712\) 5.24333 3.02724i 0.196502 0.113451i
\(713\) −15.3143 26.5251i −0.573524 0.993372i
\(714\) −16.1368 −0.603904
\(715\) 1.03472 4.68304i 0.0386962 0.175136i
\(716\) −10.7577 −0.402035
\(717\) 2.30108 + 3.98559i 0.0859355 + 0.148845i
\(718\) −13.7129 + 7.91712i −0.511759 + 0.295464i
\(719\) −23.5155 + 40.7301i −0.876981 + 1.51898i −0.0223436 + 0.999750i \(0.507113\pi\)
−0.854637 + 0.519225i \(0.826221\pi\)
\(720\) 2.03420 + 0.928463i 0.0758100 + 0.0346018i
\(721\) 33.4079 + 19.2881i 1.24418 + 0.718326i
\(722\) −19.5026 + 33.7794i −0.725810 + 1.25714i
\(723\) −6.21354 −0.231084
\(724\) −2.93234 + 5.07897i −0.108980 + 0.188758i
\(725\) 4.12365 11.9309i 0.153149 0.443104i
\(726\) 9.21982 5.32307i 0.342180 0.197557i
\(727\) 4.10440i 0.152224i 0.997099 + 0.0761119i \(0.0242506\pi\)
−0.997099 + 0.0761119i \(0.975749\pi\)
\(728\) −6.77687 7.50697i −0.251167 0.278227i
\(729\) −1.00000 −0.0370370
\(730\) 3.09740 + 32.3646i 0.114640 + 1.19787i
\(731\) −12.2095 21.1475i −0.451586 0.782169i
\(732\) 5.91165 + 3.41309i 0.218501 + 0.126152i
\(733\) 24.2968 0.897421 0.448711 0.893677i \(-0.351883\pi\)
0.448711 + 0.893677i \(0.351883\pi\)
\(734\) 13.2440 + 7.64645i 0.488847 + 0.282236i
\(735\) −1.12583 1.58030i −0.0415269 0.0582901i
\(736\) 4.64555i 0.171237i
\(737\) −4.05050 2.33855i −0.149202 0.0861418i
\(738\) −4.98222 + 2.87649i −0.183398 + 0.105885i
\(739\) −35.0414 + 20.2311i −1.28902 + 0.744215i −0.978479 0.206346i \(-0.933843\pi\)
−0.310539 + 0.950561i \(0.600509\pi\)
\(740\) 21.1019 + 9.63149i 0.775722 + 0.354061i
\(741\) 8.45199 26.1272i 0.310492 0.959806i
\(742\) 38.9775i 1.43091i
\(743\) 15.7497 + 27.2794i 0.577802 + 1.00078i 0.995731 + 0.0923027i \(0.0294227\pi\)
−0.417929 + 0.908480i \(0.637244\pi\)
\(744\) 3.29654 + 5.70978i 0.120857 + 0.209331i
\(745\) 4.52953 + 6.35797i 0.165949 + 0.232938i
\(746\) 21.6516i 0.792721i
\(747\) −2.09592 + 3.63024i −0.0766857 + 0.132824i
\(748\) −1.71113 + 2.96377i −0.0625651 + 0.108366i
\(749\) 11.8675i 0.433628i
\(750\) −2.62893 + 10.8669i −0.0959948 + 0.396802i
\(751\) −8.37551 14.5068i −0.305627 0.529361i 0.671774 0.740756i \(-0.265533\pi\)
−0.977401 + 0.211395i \(0.932199\pi\)
\(752\) 1.44899 + 2.50973i 0.0528393 + 0.0915204i
\(753\) 16.3877i 0.597202i
\(754\) −6.09976 6.75692i −0.222140 0.246072i
\(755\) −4.22440 + 9.25536i −0.153742 + 0.336837i
\(756\) 2.42916 1.40247i 0.0883476 0.0510075i
\(757\) 23.1908 13.3892i 0.842885 0.486640i −0.0153589 0.999882i \(-0.504889\pi\)
0.858244 + 0.513242i \(0.171556\pi\)
\(758\) 7.81479 + 4.51187i 0.283846 + 0.163879i
\(759\) 2.76349i 0.100308i
\(760\) −9.88140 13.8702i −0.358436 0.503126i
\(761\) −0.217029 0.125302i −0.00786729 0.00454218i 0.496061 0.868288i \(-0.334779\pi\)
−0.503928 + 0.863745i \(0.668112\pi\)
\(762\) −6.68791 −0.242277
\(763\) −1.08670 0.627408i −0.0393413 0.0227137i
\(764\) 6.91728 + 11.9811i 0.250259 + 0.433461i
\(765\) 12.8055 1.22553i 0.462985 0.0443091i
\(766\) −10.0741 −0.363990
\(767\) 25.9683 23.4427i 0.937660 0.846466i
\(768\) 1.00000i 0.0360844i
\(769\) 17.1777 9.91755i 0.619444 0.357636i −0.157209 0.987565i \(-0.550250\pi\)
0.776652 + 0.629929i \(0.216916\pi\)
\(770\) −3.71408 + 0.355449i −0.133846 + 0.0128095i
\(771\) 4.20466 7.28269i 0.151427 0.262280i
\(772\) 17.0064 0.612075
\(773\) 18.3185 31.7285i 0.658869 1.14120i −0.322039 0.946726i \(-0.604368\pi\)
0.980909 0.194469i \(-0.0622984\pi\)
\(774\) 3.67593 + 2.12230i 0.132129 + 0.0762845i
\(775\) −24.9044 + 21.5984i −0.894593 + 0.775836i
\(776\) −8.45318 + 14.6413i −0.303452 + 0.525594i
\(777\) 25.1991 14.5487i 0.904011 0.521931i
\(778\) −12.1795 21.0956i −0.436658 0.756313i
\(779\) 43.8152 1.56984
\(780\) 5.94798 + 5.44256i 0.212972 + 0.194875i
\(781\) 0.764218 0.0273459
\(782\) 13.3629 + 23.1452i 0.477855 + 0.827669i
\(783\) 2.18645 1.26235i 0.0781373 0.0451126i
\(784\) −0.433868 + 0.751482i −0.0154953 + 0.0268386i
\(785\) −10.6734 + 23.3846i −0.380949 + 0.834632i
\(786\) 10.1086 + 5.83620i 0.360562 + 0.208170i
\(787\) −17.9505 + 31.0911i −0.639865 + 1.10828i 0.345597 + 0.938383i \(0.387677\pi\)
−0.985462 + 0.169896i \(0.945657\pi\)
\(788\) 6.32974 0.225487
\(789\) −2.94536 + 5.10152i −0.104858 + 0.181619i
\(790\) 0.390157 + 4.07674i 0.0138812 + 0.145044i
\(791\) 22.7539 13.1370i 0.809036 0.467097i
\(792\) 0.594869i 0.0211377i
\(793\) 16.4923 + 18.2691i 0.585660 + 0.648756i
\(794\) −30.0381 −1.06601
\(795\) −2.96020 30.9310i −0.104987 1.09701i
\(796\) 8.31782 + 14.4069i 0.294817 + 0.510638i
\(797\) −4.30187 2.48369i −0.152380 0.0879767i 0.421871 0.906656i \(-0.361373\pi\)
−0.574251 + 0.818679i \(0.694707\pi\)
\(798\) −21.3628 −0.756235
\(799\) 14.4384 + 8.33601i 0.510794 + 0.294907i
\(800\) 4.90924 0.948346i 0.173568 0.0335291i
\(801\) 6.05447i 0.213924i
\(802\) 2.35786 + 1.36131i 0.0832590 + 0.0480696i
\(803\) 7.49061 4.32471i 0.264338 0.152616i
\(804\) 6.80906 3.93121i 0.240137 0.138643i
\(805\) −12.0984 + 26.5067i −0.426412 + 0.934238i
\(806\) 4.97241 + 23.2458i 0.175146 + 0.818800i
\(807\) 22.8455i 0.804201i
\(808\) −2.72360 4.71741i −0.0958159 0.165958i
\(809\) 20.1296 + 34.8656i 0.707720 + 1.22581i 0.965701 + 0.259658i \(0.0836097\pi\)
−0.257980 + 0.966150i \(0.583057\pi\)
\(810\) −1.82117 + 1.29743i −0.0639894 + 0.0455872i
\(811\) 7.62969i 0.267914i −0.990987 0.133957i \(-0.957232\pi\)
0.990987 0.133957i \(-0.0427685\pi\)
\(812\) −3.54082 + 6.13287i −0.124258 + 0.215222i
\(813\) 13.4271 23.2565i 0.470910 0.815639i
\(814\) 6.17092i 0.216291i
\(815\) 25.1847 17.9420i 0.882183 0.628483i
\(816\) −2.87649 4.98222i −0.100697 0.174413i
\(817\) −16.1637 27.9963i −0.565495 0.979466i
\(818\) 38.2243i 1.33648i
\(819\) 9.88966 2.11545i 0.345573 0.0739199i
\(820\) −5.34142 + 11.7027i −0.186531 + 0.408675i
\(821\) −20.8682 + 12.0483i −0.728306 + 0.420487i −0.817802 0.575500i \(-0.804808\pi\)
0.0894964 + 0.995987i \(0.471474\pi\)
\(822\) 5.89144 3.40142i 0.205487 0.118638i
\(823\) −18.6227 10.7518i −0.649145 0.374784i 0.138984 0.990295i \(-0.455616\pi\)
−0.788129 + 0.615511i \(0.788950\pi\)
\(824\) 13.7529i 0.479105i
\(825\) 2.92035 0.564141i 0.101674 0.0196409i
\(826\) −23.5699 13.6081i −0.820103 0.473487i
\(827\) 38.8887 1.35229 0.676147 0.736767i \(-0.263648\pi\)
0.676147 + 0.736767i \(0.263648\pi\)
\(828\) −4.02317 2.32278i −0.139815 0.0807221i
\(829\) 12.2944 + 21.2945i 0.427001 + 0.739587i 0.996605 0.0823320i \(-0.0262368\pi\)
−0.569604 + 0.821919i \(0.692903\pi\)
\(830\) 0.892969 + 9.33061i 0.0309954 + 0.323870i
\(831\) −10.6250 −0.368576
\(832\) 1.10975 3.43052i 0.0384737 0.118932i
\(833\) 4.99206i 0.172965i
\(834\) 6.14719 3.54908i 0.212860 0.122895i
\(835\) −4.58858 47.9459i −0.158794 1.65924i
\(836\) −2.26529 + 3.92360i −0.0783468 + 0.135701i
\(837\) −6.59309 −0.227890
\(838\) −14.9365 + 25.8708i −0.515972 + 0.893690i
\(839\) 45.1686 + 26.0781i 1.55939 + 0.900316i 0.997315 + 0.0732324i \(0.0233315\pi\)
0.562079 + 0.827084i \(0.310002\pi\)
\(840\) 2.60429 5.70582i 0.0898566 0.196869i
\(841\) 11.3130 19.5946i 0.390102 0.675677i
\(842\) 12.3004 7.10165i 0.423900 0.244739i
\(843\) −14.1866 24.5719i −0.488612 0.846301i
\(844\) 16.5489 0.569635
\(845\) 14.3648 + 25.2716i 0.494163 + 0.869369i
\(846\) −2.89798 −0.0996348
\(847\) −14.9309 25.8611i −0.513033 0.888599i
\(848\) −12.0343 + 6.94798i −0.413258 + 0.238595i
\(849\) 2.83482 4.91005i 0.0972907 0.168512i
\(850\) 21.7310 18.8462i 0.745367 0.646420i
\(851\) −41.7347 24.0955i −1.43065 0.825984i
\(852\) −0.642342 + 1.11257i −0.0220063 + 0.0381160i
\(853\) −2.06762 −0.0707938 −0.0353969 0.999373i \(-0.511270\pi\)
−0.0353969 + 0.999373i \(0.511270\pi\)
\(854\) 9.57355 16.5819i 0.327600 0.567420i
\(855\) 16.9527 1.62243i 0.579769 0.0554858i
\(856\) 3.66407 2.11545i 0.125235 0.0723047i
\(857\) 20.1793i 0.689310i 0.938729 + 0.344655i \(0.112004\pi\)
−0.938729 + 0.344655i \(0.887996\pi\)
\(858\) 0.660156 2.04071i 0.0225374 0.0696686i
\(859\) −34.4160 −1.17426 −0.587129 0.809493i \(-0.699742\pi\)
−0.587129 + 0.809493i \(0.699742\pi\)
\(860\) 9.44804 0.904208i 0.322176 0.0308332i
\(861\) 8.06839 + 13.9749i 0.274970 + 0.476262i
\(862\) −8.09901 4.67596i −0.275853 0.159264i
\(863\) −1.02382 −0.0348514 −0.0174257 0.999848i \(-0.505547\pi\)
−0.0174257 + 0.999848i \(0.505547\pi\)
\(864\) 0.866025 + 0.500000i 0.0294628 + 0.0170103i
\(865\) −17.7295 24.8863i −0.602820 0.846160i
\(866\) 3.96009i 0.134569i
\(867\) −13.9401 8.04834i −0.473431 0.273336i
\(868\) 16.0156 9.24663i 0.543606 0.313851i
\(869\) 0.943538 0.544752i 0.0320073 0.0184794i
\(870\) 2.34408 5.13572i 0.0794719 0.174117i
\(871\) 27.7213 5.92973i 0.939299 0.200921i
\(872\) 0.447358i 0.0151495i
\(873\) −8.45318 14.6413i −0.286097 0.495534i
\(874\) 17.6905 + 30.6409i 0.598391 + 1.03644i
\(875\) 30.4810 + 7.37400i 1.03045 + 0.249287i
\(876\) 14.5400i 0.491262i
\(877\) 7.46097 12.9228i 0.251939 0.436371i −0.712121 0.702057i \(-0.752265\pi\)
0.964060 + 0.265686i \(0.0855984\pi\)
\(878\) 11.2992 19.5708i 0.381329 0.660481i
\(879\) 1.65835i 0.0559348i
\(880\) −0.771803 1.08336i −0.0260175 0.0365200i
\(881\) 21.5282 + 37.2879i 0.725303 + 1.25626i 0.958849 + 0.283916i \(0.0916336\pi\)
−0.233546 + 0.972346i \(0.575033\pi\)
\(882\) −0.433868 0.751482i −0.0146091 0.0253037i
\(883\) 30.1817i 1.01569i 0.861447 + 0.507847i \(0.169559\pi\)
−0.861447 + 0.507847i \(0.830441\pi\)
\(884\) −4.33881 20.2838i −0.145930 0.682217i
\(885\) 19.7377 + 9.00882i 0.663475 + 0.302828i
\(886\) −25.1518 + 14.5214i −0.844992 + 0.487856i
\(887\) −18.7593 + 10.8307i −0.629877 + 0.363660i −0.780705 0.624900i \(-0.785140\pi\)
0.150827 + 0.988560i \(0.451806\pi\)
\(888\) 8.98379 + 5.18679i 0.301476 + 0.174057i
\(889\) 18.7592i 0.629164i
\(890\) 7.85528 + 11.0262i 0.263310 + 0.369600i
\(891\) 0.515171 + 0.297434i 0.0172589 + 0.00996443i
\(892\) −16.6556 −0.557670
\(893\) 19.1144 + 11.0357i 0.639638 + 0.369295i
\(894\) 1.74557 + 3.02342i 0.0583807 + 0.101118i
\(895\) −2.29167 23.9456i −0.0766021 0.800413i
\(896\) −2.80495 −0.0937068
\(897\) −11.2238 12.4330i −0.374753 0.415127i
\(898\) 27.4687i 0.916642i
\(899\) 14.4154 8.32276i 0.480782 0.277580i
\(900\) −1.63333 + 4.72570i −0.0544443 + 0.157523i
\(901\) −39.9715 + 69.2328i −1.33165 + 2.30648i
\(902\) 3.42226 0.113949
\(903\) 5.95294 10.3108i 0.198101 0.343122i
\(904\) 8.11206 + 4.68350i 0.269803 + 0.155771i
\(905\) −11.9299 5.44515i −0.396564 0.181003i
\(906\) −2.27494 + 3.94031i −0.0755799 + 0.130908i
\(907\) 2.42051 1.39748i 0.0803717 0.0464026i −0.459276 0.888294i \(-0.651891\pi\)
0.539647 + 0.841891i \(0.318558\pi\)
\(908\) 1.51105 + 2.61722i 0.0501460 + 0.0868554i
\(909\) 5.44720 0.180672
\(910\) 15.2661 16.6838i 0.506067 0.553062i
\(911\) 24.2193 0.802422 0.401211 0.915986i \(-0.368589\pi\)
0.401211 + 0.915986i \(0.368589\pi\)
\(912\) −3.80805 6.59574i −0.126097 0.218407i
\(913\) 2.15952 1.24680i 0.0714695 0.0412630i
\(914\) 2.19087 3.79470i 0.0724675 0.125517i
\(915\) −6.33786 + 13.8858i −0.209523 + 0.459051i
\(916\) 14.2437 + 8.22361i 0.470626 + 0.271716i
\(917\) 16.3702 28.3541i 0.540593 0.936334i
\(918\) 5.75297 0.189876
\(919\) −6.54988 + 11.3447i −0.216061 + 0.374228i −0.953600 0.301076i \(-0.902654\pi\)
0.737539 + 0.675304i \(0.235988\pi\)
\(920\) −10.3405 + 0.989622i −0.340917 + 0.0326269i
\(921\) −0.332629 + 0.192044i −0.0109605 + 0.00632805i
\(922\) 24.3172i 0.800844i
\(923\) −3.43824 + 3.10385i −0.113171 + 0.102164i
\(924\) −1.66858 −0.0548921
\(925\) −16.9435 + 49.0224i −0.557098 + 1.61185i
\(926\) −9.53298 16.5116i −0.313273 0.542605i
\(927\) −11.9104 6.87645i −0.391187 0.225852i
\(928\) −2.52469 −0.0828771
\(929\) 24.1564 + 13.9467i 0.792544 + 0.457576i 0.840858 0.541257i \(-0.182051\pi\)
−0.0483131 + 0.998832i \(0.515385\pi\)
\(930\) −12.0071 + 8.55410i −0.393730 + 0.280500i
\(931\) 6.60877i 0.216594i
\(932\) −11.9762 6.91443i −0.392292 0.226490i
\(933\) 10.1256 5.84601i 0.331497 0.191390i
\(934\) 8.76211 5.05881i 0.286705 0.165529i
\(935\) −6.96155 3.17744i −0.227667 0.103914i
\(936\) 2.41604 + 2.67633i 0.0789707 + 0.0874786i
\(937\) 49.9741i 1.63258i 0.577640 + 0.816292i \(0.303974\pi\)
−0.577640 + 0.816292i \(0.696026\pi\)
\(938\) −11.0268 19.0991i −0.360039 0.623606i
\(939\) 5.28939 + 9.16150i 0.172613 + 0.298974i
\(940\) −5.27773 + 3.75995i −0.172140 + 0.122636i
\(941\) 9.56099i 0.311680i 0.987782 + 0.155840i \(0.0498083\pi\)
−0.987782 + 0.155840i \(0.950192\pi\)
\(942\) −5.74787 + 9.95560i −0.187276 + 0.324371i
\(943\) 13.3629 23.1452i 0.435155 0.753710i
\(944\) 9.70293i 0.315804i
\(945\) 3.63924 + 5.10829i 0.118384 + 0.166173i
\(946\) −1.26249 2.18670i −0.0410471 0.0710956i
\(947\) −22.0817 38.2466i −0.717558 1.24285i −0.961964 0.273175i \(-0.911926\pi\)
0.244406 0.969673i \(-0.421407\pi\)
\(948\) 1.83150i 0.0594844i
\(949\) −16.1358 + 49.8799i −0.523791 + 1.61917i
\(950\) 28.7687 24.9497i 0.933381 0.809475i
\(951\) −19.1412 + 11.0512i −0.620695 + 0.358359i
\(952\) −13.9749 + 8.06839i −0.452928 + 0.261498i
\(953\) −12.8310 7.40798i −0.415637 0.239968i 0.277572 0.960705i \(-0.410470\pi\)
−0.693209 + 0.720737i \(0.743804\pi\)
\(954\) 13.8960i 0.449899i
\(955\) −25.1951 + 17.9494i −0.815295 + 0.580830i
\(956\) 3.98559 + 2.30108i 0.128903 + 0.0744223i
\(957\) −1.50186 −0.0485483
\(958\) −24.8215 14.3307i −0.801946 0.463004i
\(959\) −9.54082 16.5252i −0.308089 0.533626i
\(960\) 2.22590 0.213026i 0.0718405 0.00687537i
\(961\) −12.4688 −0.402219
\(962\) 25.0630 + 27.7632i 0.808063 + 0.895120i
\(963\) 4.23091i 0.136339i
\(964\) −5.38108 + 3.10677i −0.173313 + 0.100062i
\(965\) 3.62280 + 37.8546i 0.116622 + 1.21858i
\(966\) −6.51527 + 11.2848i −0.209625 + 0.363082i
\(967\) 1.88667 0.0606711 0.0303356 0.999540i \(-0.490342\pi\)
0.0303356 + 0.999540i \(0.490342\pi\)
\(968\) 5.32307 9.21982i 0.171090 0.296336i
\(969\) −37.9451 21.9076i −1.21897 0.703774i
\(970\) −34.3909 15.6969i −1.10422 0.503998i
\(971\) 23.9611 41.5018i 0.768947 1.33186i −0.169187 0.985584i \(-0.554114\pi\)
0.938134 0.346271i \(-0.112552\pi\)
\(972\) −0.866025 + 0.500000i −0.0277778 + 0.0160375i
\(973\) −9.95499 17.2425i −0.319142 0.552770i
\(974\) −17.4398 −0.558807
\(975\) −10.8475 + 14.3990i −0.347398 + 0.461137i
\(976\) 6.82619 0.218501
\(977\) 16.1581 + 27.9867i 0.516945 + 0.895374i 0.999806 + 0.0196777i \(0.00626400\pi\)
−0.482862 + 0.875697i \(0.660403\pi\)
\(978\) 11.9762 6.91443i 0.382955 0.221099i
\(979\) 1.80081 3.11909i 0.0575541 0.0996866i
\(980\) −1.76515 0.805661i −0.0563855 0.0257359i
\(981\) 0.387423 + 0.223679i 0.0123695 + 0.00714152i
\(982\) 11.2233 19.4394i 0.358151 0.620336i
\(983\) −20.4850 −0.653370 −0.326685 0.945133i \(-0.605932\pi\)
−0.326685 + 0.945133i \(0.605932\pi\)
\(984\) −2.87649 + 4.98222i −0.0916990 + 0.158827i
\(985\) 1.34840 + 14.0893i 0.0429635 + 0.448924i
\(986\) −12.5786 + 7.26224i −0.400583 + 0.231277i
\(987\) 8.12870i 0.258739i
\(988\) −5.74396 26.8528i −0.182740 0.854302i
\(989\) −19.7185 −0.627012
\(990\) 1.32412 0.126722i 0.0420832 0.00402750i
\(991\) 0.834181 + 1.44484i 0.0264986 + 0.0458970i 0.878971 0.476876i \(-0.158231\pi\)
−0.852472 + 0.522773i \(0.824898\pi\)
\(992\) 5.70978 + 3.29654i 0.181286 + 0.104665i
\(993\) 6.10616 0.193773
\(994\) 3.12070 + 1.80174i 0.0989826 + 0.0571476i
\(995\) −30.2963 + 21.5836i −0.960458 + 0.684247i
\(996\) 4.19184i 0.132824i
\(997\) 2.71512 + 1.56758i 0.0859887 + 0.0496456i 0.542378 0.840135i \(-0.317524\pi\)
−0.456389 + 0.889780i \(0.650857\pi\)
\(998\) −9.01844 + 5.20680i −0.285474 + 0.164818i
\(999\) −8.98379 + 5.18679i −0.284234 + 0.164103i
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 390.2.x.b.49.1 yes 12
3.2 odd 2 1170.2.bj.c.829.6 12
5.2 odd 4 1950.2.bc.j.751.1 12
5.3 odd 4 1950.2.bc.i.751.6 12
5.4 even 2 390.2.x.a.49.6 12
13.4 even 6 390.2.x.a.199.6 yes 12
15.14 odd 2 1170.2.bj.d.829.1 12
39.17 odd 6 1170.2.bj.d.199.1 12
65.4 even 6 inner 390.2.x.b.199.1 yes 12
65.17 odd 12 1950.2.bc.j.901.1 12
65.43 odd 12 1950.2.bc.i.901.6 12
195.134 odd 6 1170.2.bj.c.199.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.x.a.49.6 12 5.4 even 2
390.2.x.a.199.6 yes 12 13.4 even 6
390.2.x.b.49.1 yes 12 1.1 even 1 trivial
390.2.x.b.199.1 yes 12 65.4 even 6 inner
1170.2.bj.c.199.6 12 195.134 odd 6
1170.2.bj.c.829.6 12 3.2 odd 2
1170.2.bj.d.199.1 12 39.17 odd 6
1170.2.bj.d.829.1 12 15.14 odd 2
1950.2.bc.i.751.6 12 5.3 odd 4
1950.2.bc.i.901.6 12 65.43 odd 12
1950.2.bc.j.751.1 12 5.2 odd 4
1950.2.bc.j.901.1 12 65.17 odd 12