Properties

Label 390.2.bb.c.121.2
Level $390$
Weight $2$
Character 390.121
Analytic conductor $3.114$
Analytic rank $0$
Dimension $8$
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(121,390)]
 
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, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.bb (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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) 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 121.2
Root \(-1.80668 - 1.80668i\) of defining polynomial
Character \(\chi\) \(=\) 390.121
Dual form 390.2.bb.c.361.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.14539 - 0.661290i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(0.866025 - 0.500000i) q^{6} +(1.14539 - 0.661290i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-3.99528 - 2.30668i) q^{11} -1.00000 q^{12} +(3.20002 - 1.66129i) q^{13} -1.32258 q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(1.98387 - 1.14539i) q^{19} +(0.866025 - 0.500000i) q^{20} +1.32258i q^{21} +(2.30668 + 3.99528i) q^{22} +(4.33399 - 7.50670i) q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-3.60194 - 0.161290i) q^{26} +1.00000 q^{27} +(1.14539 + 0.661290i) q^{28} +(1.01141 - 1.75182i) q^{29} +(-0.500000 - 0.866025i) q^{30} -10.1321i q^{31} +(0.866025 - 0.500000i) q^{32} +(3.99528 - 2.30668i) q^{33} -4.00000i q^{34} +(-0.661290 - 1.14539i) q^{35} +(0.500000 - 0.866025i) q^{36} +(5.89721 + 3.40475i) q^{37} -2.29078 q^{38} +(-0.161290 + 3.60194i) q^{39} -1.00000 q^{40} +(-4.02283 - 2.32258i) q^{41} +(0.661290 - 1.14539i) q^{42} +(4.30281 + 7.45269i) q^{43} -4.61335i q^{44} +(-0.866025 + 0.500000i) q^{45} +(-7.50670 + 4.33399i) q^{46} -9.10926i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.62539 + 4.54731i) q^{49} +(0.866025 + 0.500000i) q^{50} -4.00000 q^{51} +(3.03873 + 1.94065i) q^{52} +0.826674 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.30668 + 3.99528i) q^{55} +(-0.661290 - 1.14539i) q^{56} +2.29078i q^{57} +(-1.75182 + 1.01141i) q^{58} +(2.72064 - 1.57076i) q^{59} +1.00000i q^{60} +(-0.267949 - 0.464102i) q^{61} +(-5.06604 + 8.77464i) q^{62} +(-1.14539 - 0.661290i) q^{63} -1.00000 q^{64} +(-1.66129 - 3.20002i) q^{65} -4.61335 q^{66} +(-2.75488 - 1.59053i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(4.33399 + 7.50670i) q^{69} +1.32258i q^{70} +(-9.81724 + 5.66799i) q^{71} +(-0.866025 + 0.500000i) q^{72} -6.28304i q^{73} +(-3.40475 - 5.89721i) q^{74} +(0.500000 - 0.866025i) q^{75} +(1.98387 + 1.14539i) q^{76} -6.10153 q^{77} +(1.94065 - 3.03873i) q^{78} +2.96774 q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.32258 + 4.02283i) q^{82} +15.8719i q^{83} +(-1.14539 + 0.661290i) q^{84} +(3.46410 - 2.00000i) q^{85} -8.60562i q^{86} +(1.01141 + 1.75182i) q^{87} +(-2.30668 + 3.99528i) q^{88} +(10.2746 + 5.93207i) q^{89} +1.00000 q^{90} +(2.56667 - 4.01896i) q^{91} +8.66799 q^{92} +(8.77464 + 5.06604i) q^{93} +(-4.55463 + 7.88885i) q^{94} +(-1.14539 - 1.98387i) q^{95} +1.00000i q^{96} +(-7.63743 + 4.40947i) q^{97} +(4.54731 - 2.62539i) q^{98} +4.61335i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 4 q^{14} - 4 q^{16} + 16 q^{17} - 6 q^{19} + 2 q^{22} + 4 q^{23} - 8 q^{25} - 12 q^{26} + 8 q^{27} - 8 q^{29} - 4 q^{30} - 6 q^{33} + 2 q^{35} + 4 q^{36} + 30 q^{37} + 6 q^{39} - 8 q^{40} - 2 q^{42} + 14 q^{43} - 6 q^{46} - 4 q^{48} + 14 q^{49} - 32 q^{51} - 6 q^{52} + 16 q^{53} - 2 q^{55} + 2 q^{56} - 6 q^{58} + 24 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 6 q^{65} - 4 q^{66} + 24 q^{67} - 16 q^{68} + 4 q^{69} - 12 q^{71} + 10 q^{74} + 4 q^{75} - 6 q^{76} + 16 q^{77} + 6 q^{78} - 20 q^{79} - 4 q^{81} + 4 q^{82} - 8 q^{87} - 2 q^{88} + 42 q^{89} + 8 q^{90} - 10 q^{91} + 8 q^{92} + 30 q^{93} - 8 q^{94} - 24 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 1.14539 0.661290i 0.432916 0.249944i −0.267672 0.963510i \(-0.586254\pi\)
0.700588 + 0.713566i \(0.252921\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −3.99528 2.30668i −1.20462 0.695489i −0.243043 0.970015i \(-0.578146\pi\)
−0.961580 + 0.274526i \(0.911479\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.20002 1.66129i 0.887525 0.460759i
\(14\) −1.32258 −0.353474
\(15\) 0.866025 + 0.500000i 0.223607 + 0.129099i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.98387 1.14539i 0.455131 0.262770i −0.254864 0.966977i \(-0.582031\pi\)
0.709995 + 0.704207i \(0.248697\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 1.32258i 0.288611i
\(22\) 2.30668 + 3.99528i 0.491785 + 0.851797i
\(23\) 4.33399 7.50670i 0.903700 1.56525i 0.0810471 0.996710i \(-0.474174\pi\)
0.822653 0.568544i \(-0.192493\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −1.00000 −0.200000
\(26\) −3.60194 0.161290i −0.706399 0.0316315i
\(27\) 1.00000 0.192450
\(28\) 1.14539 + 0.661290i 0.216458 + 0.124972i
\(29\) 1.01141 1.75182i 0.187815 0.325305i −0.756707 0.653755i \(-0.773193\pi\)
0.944521 + 0.328450i \(0.106526\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 10.1321i 1.81978i −0.414853 0.909888i \(-0.636167\pi\)
0.414853 0.909888i \(-0.363833\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 3.99528 2.30668i 0.695489 0.401541i
\(34\) 4.00000i 0.685994i
\(35\) −0.661290 1.14539i −0.111778 0.193606i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 5.89721 + 3.40475i 0.969495 + 0.559738i 0.899082 0.437780i \(-0.144235\pi\)
0.0704126 + 0.997518i \(0.477568\pi\)
\(38\) −2.29078 −0.371613
\(39\) −0.161290 + 3.60194i −0.0258270 + 0.576772i
\(40\) −1.00000 −0.158114
\(41\) −4.02283 2.32258i −0.628260 0.362726i 0.151818 0.988408i \(-0.451487\pi\)
−0.780078 + 0.625682i \(0.784821\pi\)
\(42\) 0.661290 1.14539i 0.102039 0.176737i
\(43\) 4.30281 + 7.45269i 0.656173 + 1.13652i 0.981598 + 0.190957i \(0.0611590\pi\)
−0.325426 + 0.945568i \(0.605508\pi\)
\(44\) 4.61335i 0.695489i
\(45\) −0.866025 + 0.500000i −0.129099 + 0.0745356i
\(46\) −7.50670 + 4.33399i −1.10680 + 0.639012i
\(47\) 9.10926i 1.32872i −0.747412 0.664361i \(-0.768704\pi\)
0.747412 0.664361i \(-0.231296\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −2.62539 + 4.54731i −0.375056 + 0.649616i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) −4.00000 −0.560112
\(52\) 3.03873 + 1.94065i 0.421396 + 0.269120i
\(53\) 0.826674 0.113552 0.0567762 0.998387i \(-0.481918\pi\)
0.0567762 + 0.998387i \(0.481918\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −2.30668 + 3.99528i −0.311032 + 0.538724i
\(56\) −0.661290 1.14539i −0.0883686 0.153059i
\(57\) 2.29078i 0.303421i
\(58\) −1.75182 + 1.01141i −0.230025 + 0.132805i
\(59\) 2.72064 1.57076i 0.354197 0.204496i −0.312335 0.949972i \(-0.601111\pi\)
0.666532 + 0.745476i \(0.267778\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −0.267949 0.464102i −0.0343074 0.0594221i 0.848362 0.529417i \(-0.177589\pi\)
−0.882669 + 0.469995i \(0.844256\pi\)
\(62\) −5.06604 + 8.77464i −0.643388 + 1.11438i
\(63\) −1.14539 0.661290i −0.144305 0.0833147i
\(64\) −1.00000 −0.125000
\(65\) −1.66129 3.20002i −0.206058 0.396913i
\(66\) −4.61335 −0.567865
\(67\) −2.75488 1.59053i −0.336562 0.194314i 0.322189 0.946675i \(-0.395581\pi\)
−0.658751 + 0.752361i \(0.728915\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 4.33399 + 7.50670i 0.521751 + 0.903700i
\(70\) 1.32258i 0.158079i
\(71\) −9.81724 + 5.66799i −1.16509 + 0.672666i −0.952519 0.304479i \(-0.901518\pi\)
−0.212573 + 0.977145i \(0.568184\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 6.28304i 0.735375i −0.929949 0.367687i \(-0.880150\pi\)
0.929949 0.367687i \(-0.119850\pi\)
\(74\) −3.40475 5.89721i −0.395795 0.685536i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 1.98387 + 1.14539i 0.227565 + 0.131385i
\(77\) −6.10153 −0.695334
\(78\) 1.94065 3.03873i 0.219736 0.344068i
\(79\) 2.96774 0.333897 0.166948 0.985966i \(-0.446609\pi\)
0.166948 + 0.985966i \(0.446609\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.32258 + 4.02283i 0.256486 + 0.444247i
\(83\) 15.8719i 1.74216i 0.491138 + 0.871082i \(0.336581\pi\)
−0.491138 + 0.871082i \(0.663419\pi\)
\(84\) −1.14539 + 0.661290i −0.124972 + 0.0721526i
\(85\) 3.46410 2.00000i 0.375735 0.216930i
\(86\) 8.60562i 0.927968i
\(87\) 1.01141 + 1.75182i 0.108435 + 0.187815i
\(88\) −2.30668 + 3.99528i −0.245893 + 0.425899i
\(89\) 10.2746 + 5.93207i 1.08911 + 0.628798i 0.933339 0.358995i \(-0.116881\pi\)
0.155771 + 0.987793i \(0.450214\pi\)
\(90\) 1.00000 0.105409
\(91\) 2.56667 4.01896i 0.269060 0.421302i
\(92\) 8.66799 0.903700
\(93\) 8.77464 + 5.06604i 0.909888 + 0.525324i
\(94\) −4.55463 + 7.88885i −0.469774 + 0.813673i
\(95\) −1.14539 1.98387i −0.117514 0.203541i
\(96\) 1.00000i 0.102062i
\(97\) −7.63743 + 4.40947i −0.775463 + 0.447714i −0.834820 0.550523i \(-0.814428\pi\)
0.0593568 + 0.998237i \(0.481095\pi\)
\(98\) 4.54731 2.62539i 0.459348 0.265205i
\(99\) 4.61335i 0.463660i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −3.61335 + 6.25851i −0.359542 + 0.622745i −0.987884 0.155192i \(-0.950400\pi\)
0.628342 + 0.777937i \(0.283734\pi\)
\(102\) 3.46410 + 2.00000i 0.342997 + 0.198030i
\(103\) −18.4000 −1.81301 −0.906505 0.422196i \(-0.861260\pi\)
−0.906505 + 0.422196i \(0.861260\pi\)
\(104\) −1.66129 3.20002i −0.162903 0.313788i
\(105\) 1.32258 0.129071
\(106\) −0.715920 0.413337i −0.0695363 0.0401468i
\(107\) −1.53590 + 2.66025i −0.148481 + 0.257176i −0.930666 0.365869i \(-0.880772\pi\)
0.782185 + 0.623046i \(0.214105\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 13.2267i 1.26689i 0.773788 + 0.633445i \(0.218360\pi\)
−0.773788 + 0.633445i \(0.781640\pi\)
\(110\) 3.99528 2.30668i 0.380935 0.219933i
\(111\) −5.89721 + 3.40475i −0.559738 + 0.323165i
\(112\) 1.32258i 0.124972i
\(113\) 4.04322 + 7.00306i 0.380354 + 0.658792i 0.991113 0.133024i \(-0.0424689\pi\)
−0.610759 + 0.791817i \(0.709136\pi\)
\(114\) 1.14539 1.98387i 0.107275 0.185806i
\(115\) −7.50670 4.33399i −0.700003 0.404147i
\(116\) 2.02283 0.187815
\(117\) −3.03873 1.94065i −0.280931 0.179413i
\(118\) −3.14152 −0.289201
\(119\) 4.58155 + 2.64516i 0.419990 + 0.242481i
\(120\) 0.500000 0.866025i 0.0456435 0.0790569i
\(121\) 5.14152 + 8.90538i 0.467411 + 0.809580i
\(122\) 0.535898i 0.0485180i
\(123\) 4.02283 2.32258i 0.362726 0.209420i
\(124\) 8.77464 5.06604i 0.787986 0.454944i
\(125\) 1.00000i 0.0894427i
\(126\) 0.661290 + 1.14539i 0.0589124 + 0.102039i
\(127\) 5.73592 9.93490i 0.508980 0.881580i −0.490966 0.871179i \(-0.663356\pi\)
0.999946 0.0104008i \(-0.00331073\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −8.60562 −0.757683
\(130\) −0.161290 + 3.60194i −0.0141461 + 0.315911i
\(131\) −15.9906 −1.39710 −0.698551 0.715560i \(-0.746172\pi\)
−0.698551 + 0.715560i \(0.746172\pi\)
\(132\) 3.99528 + 2.30668i 0.347745 + 0.200771i
\(133\) 1.51487 2.62383i 0.131356 0.227515i
\(134\) 1.59053 + 2.75488i 0.137401 + 0.237985i
\(135\) 1.00000i 0.0860663i
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) 13.9168 8.03486i 1.18899 0.686465i 0.230914 0.972974i \(-0.425828\pi\)
0.958077 + 0.286509i \(0.0924950\pi\)
\(138\) 8.66799i 0.737868i
\(139\) −4.66129 8.07359i −0.395365 0.684793i 0.597782 0.801658i \(-0.296049\pi\)
−0.993148 + 0.116865i \(0.962715\pi\)
\(140\) 0.661290 1.14539i 0.0558892 0.0968029i
\(141\) 7.88885 + 4.55463i 0.664361 + 0.383569i
\(142\) 11.3360 0.951294
\(143\) −16.6170 0.744087i −1.38959 0.0622237i
\(144\) 1.00000 0.0833333
\(145\) −1.75182 1.01141i −0.145481 0.0839933i
\(146\) −3.14152 + 5.44128i −0.259994 + 0.450323i
\(147\) −2.62539 4.54731i −0.216539 0.375056i
\(148\) 6.80951i 0.559738i
\(149\) 3.53788 2.04259i 0.289834 0.167336i −0.348033 0.937482i \(-0.613150\pi\)
0.637867 + 0.770146i \(0.279817\pi\)
\(150\) −0.866025 + 0.500000i −0.0707107 + 0.0408248i
\(151\) 19.9811i 1.62604i −0.582235 0.813021i \(-0.697822\pi\)
0.582235 0.813021i \(-0.302178\pi\)
\(152\) −1.14539 1.98387i −0.0929032 0.160913i
\(153\) 2.00000 3.46410i 0.161690 0.280056i
\(154\) 5.28408 + 3.05076i 0.425803 + 0.245838i
\(155\) −10.1321 −0.813829
\(156\) −3.20002 + 1.66129i −0.256206 + 0.133010i
\(157\) 7.13379 0.569338 0.284669 0.958626i \(-0.408116\pi\)
0.284669 + 0.958626i \(0.408116\pi\)
\(158\) −2.57014 1.48387i −0.204469 0.118050i
\(159\) −0.413337 + 0.715920i −0.0327797 + 0.0567762i
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 11.4641i 0.903498i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −8.56906 + 4.94735i −0.671180 + 0.387506i −0.796524 0.604607i \(-0.793330\pi\)
0.125343 + 0.992113i \(0.459997\pi\)
\(164\) 4.64516i 0.362726i
\(165\) −2.30668 3.99528i −0.179575 0.311032i
\(166\) 7.93593 13.7454i 0.615948 1.06685i
\(167\) 20.8171 + 12.0187i 1.61087 + 0.930037i 0.989168 + 0.146785i \(0.0468925\pi\)
0.621704 + 0.783253i \(0.286441\pi\)
\(168\) 1.32258 0.102039
\(169\) 7.48023 10.6323i 0.575402 0.817870i
\(170\) −4.00000 −0.306786
\(171\) −1.98387 1.14539i −0.151710 0.0875900i
\(172\) −4.30281 + 7.45269i −0.328086 + 0.568262i
\(173\) 1.26408 + 2.18946i 0.0961065 + 0.166461i 0.910070 0.414455i \(-0.136028\pi\)
−0.813963 + 0.580916i \(0.802694\pi\)
\(174\) 2.02283i 0.153350i
\(175\) −1.14539 + 0.661290i −0.0865832 + 0.0499888i
\(176\) 3.99528 2.30668i 0.301156 0.173872i
\(177\) 3.14152i 0.236131i
\(178\) −5.93207 10.2746i −0.444627 0.770117i
\(179\) −3.13784 + 5.43490i −0.234533 + 0.406223i −0.959137 0.282942i \(-0.908689\pi\)
0.724604 + 0.689166i \(0.242023\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) −12.2830 −0.912991 −0.456496 0.889726i \(-0.650896\pi\)
−0.456496 + 0.889726i \(0.650896\pi\)
\(182\) −4.23228 + 2.19719i −0.313717 + 0.162866i
\(183\) 0.535898 0.0396147
\(184\) −7.50670 4.33399i −0.553401 0.319506i
\(185\) 3.40475 5.89721i 0.250322 0.433571i
\(186\) −5.06604 8.77464i −0.371460 0.643388i
\(187\) 18.4534i 1.34945i
\(188\) 7.88885 4.55463i 0.575354 0.332181i
\(189\) 1.14539 0.661290i 0.0833147 0.0481018i
\(190\) 2.29078i 0.166190i
\(191\) 4.87357 + 8.44128i 0.352639 + 0.610789i 0.986711 0.162485i \(-0.0519509\pi\)
−0.634072 + 0.773274i \(0.718618\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −11.9188 6.88130i −0.857932 0.495327i 0.00538741 0.999985i \(-0.498285\pi\)
−0.863319 + 0.504658i \(0.831618\pi\)
\(194\) 8.81894 0.633163
\(195\) 3.60194 + 0.161290i 0.257940 + 0.0115502i
\(196\) −5.25078 −0.375056
\(197\) −8.78282 5.07076i −0.625750 0.361277i 0.153354 0.988171i \(-0.450992\pi\)
−0.779104 + 0.626894i \(0.784326\pi\)
\(198\) 2.30668 3.99528i 0.163928 0.283932i
\(199\) 4.78668 + 8.29078i 0.339319 + 0.587717i 0.984305 0.176477i \(-0.0564701\pi\)
−0.644986 + 0.764194i \(0.723137\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 2.75488 1.59053i 0.194314 0.112187i
\(202\) 6.25851 3.61335i 0.440348 0.254235i
\(203\) 2.67535i 0.187773i
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) −2.32258 + 4.02283i −0.162216 + 0.280966i
\(206\) 15.9349 + 9.20002i 1.11024 + 0.640996i
\(207\) −8.66799 −0.602467
\(208\) −0.161290 + 3.60194i −0.0111834 + 0.249750i
\(209\) −10.5682 −0.731015
\(210\) −1.14539 0.661290i −0.0790393 0.0456333i
\(211\) 0.542594 0.939800i 0.0373537 0.0646985i −0.846744 0.532000i \(-0.821441\pi\)
0.884098 + 0.467302i \(0.154774\pi\)
\(212\) 0.413337 + 0.715920i 0.0283881 + 0.0491696i
\(213\) 11.3360i 0.776728i
\(214\) 2.66025 1.53590i 0.181851 0.104992i
\(215\) 7.45269 4.30281i 0.508269 0.293449i
\(216\) 1.00000i 0.0680414i
\(217\) −6.70025 11.6052i −0.454842 0.787810i
\(218\) 6.61335 11.4547i 0.447913 0.775808i
\(219\) 5.44128 + 3.14152i 0.367687 + 0.212284i
\(220\) −4.61335 −0.311032
\(221\) 12.1549 + 7.76261i 0.817628 + 0.522170i
\(222\) 6.80951 0.457024
\(223\) 21.6001 + 12.4708i 1.44645 + 0.835106i 0.998268 0.0588375i \(-0.0187394\pi\)
0.448179 + 0.893944i \(0.352073\pi\)
\(224\) 0.661290 1.14539i 0.0441843 0.0765294i
\(225\) 0.500000 + 0.866025i 0.0333333 + 0.0577350i
\(226\) 8.08643i 0.537902i
\(227\) −16.7321 + 9.66025i −1.11055 + 0.641174i −0.938971 0.343998i \(-0.888219\pi\)
−0.171575 + 0.985171i \(0.554885\pi\)
\(228\) −1.98387 + 1.14539i −0.131385 + 0.0758551i
\(229\) 4.15491i 0.274564i 0.990532 + 0.137282i \(0.0438367\pi\)
−0.990532 + 0.137282i \(0.956163\pi\)
\(230\) 4.33399 + 7.50670i 0.285775 + 0.494977i
\(231\) 3.05076 5.28408i 0.200726 0.347667i
\(232\) −1.75182 1.01141i −0.115013 0.0664025i
\(233\) 16.9665 1.11151 0.555756 0.831346i \(-0.312429\pi\)
0.555756 + 0.831346i \(0.312429\pi\)
\(234\) 1.66129 + 3.20002i 0.108602 + 0.209192i
\(235\) −9.10926 −0.594223
\(236\) 2.72064 + 1.57076i 0.177098 + 0.102248i
\(237\) −1.48387 + 2.57014i −0.0963877 + 0.166948i
\(238\) −2.64516 4.58155i −0.171460 0.296978i
\(239\) 6.34416i 0.410370i −0.978723 0.205185i \(-0.934220\pi\)
0.978723 0.205185i \(-0.0657795\pi\)
\(240\) −0.866025 + 0.500000i −0.0559017 + 0.0322749i
\(241\) 20.9452 12.0927i 1.34920 0.778962i 0.361065 0.932541i \(-0.382413\pi\)
0.988136 + 0.153579i \(0.0490800\pi\)
\(242\) 10.2830i 0.661019i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0.267949 0.464102i 0.0171537 0.0297111i
\(245\) 4.54731 + 2.62539i 0.290517 + 0.167730i
\(246\) −4.64516 −0.296165
\(247\) 4.44560 6.96104i 0.282867 0.442921i
\(248\) −10.1321 −0.643388
\(249\) −13.7454 7.93593i −0.871082 0.502919i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 4.41249 + 7.64265i 0.278514 + 0.482400i 0.971016 0.239016i \(-0.0768249\pi\)
−0.692502 + 0.721416i \(0.743492\pi\)
\(252\) 1.32258i 0.0833147i
\(253\) −34.6311 + 19.9942i −2.17724 + 1.25703i
\(254\) −9.93490 + 5.73592i −0.623371 + 0.359903i
\(255\) 4.00000i 0.250490i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.19247 7.26157i 0.261519 0.452964i −0.705127 0.709081i \(-0.749110\pi\)
0.966646 + 0.256117i \(0.0824432\pi\)
\(258\) 7.45269 + 4.30281i 0.463984 + 0.267881i
\(259\) 9.00612 0.559613
\(260\) 1.94065 3.03873i 0.120354 0.188454i
\(261\) −2.02283 −0.125210
\(262\) 13.8482 + 7.99528i 0.855547 + 0.493950i
\(263\) −0.960648 + 1.66389i −0.0592361 + 0.102600i −0.894123 0.447822i \(-0.852200\pi\)
0.834887 + 0.550422i \(0.185533\pi\)
\(264\) −2.30668 3.99528i −0.141966 0.245893i
\(265\) 0.826674i 0.0507822i
\(266\) −2.62383 + 1.51487i −0.160877 + 0.0928824i
\(267\) −10.2746 + 5.93207i −0.628798 + 0.363037i
\(268\) 3.18106i 0.194314i
\(269\) 16.1549 + 27.9811i 0.984982 + 1.70604i 0.642014 + 0.766693i \(0.278099\pi\)
0.342968 + 0.939347i \(0.388568\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 20.3105 + 11.7263i 1.23378 + 0.712322i 0.967815 0.251662i \(-0.0809770\pi\)
0.265962 + 0.963983i \(0.414310\pi\)
\(272\) −4.00000 −0.242536
\(273\) 2.19719 + 4.23228i 0.132980 + 0.256149i
\(274\) −16.0697 −0.970808
\(275\) 3.99528 + 2.30668i 0.240925 + 0.139098i
\(276\) −4.33399 + 7.50670i −0.260876 + 0.451850i
\(277\) −4.50283 7.79913i −0.270549 0.468604i 0.698454 0.715655i \(-0.253872\pi\)
−0.969002 + 0.247051i \(0.920538\pi\)
\(278\) 9.32258i 0.559131i
\(279\) −8.77464 + 5.06604i −0.525324 + 0.303296i
\(280\) −1.14539 + 0.661290i −0.0684500 + 0.0395196i
\(281\) 1.71696i 0.102425i 0.998688 + 0.0512125i \(0.0163086\pi\)
−0.998688 + 0.0512125i \(0.983691\pi\)
\(282\) −4.55463 7.88885i −0.271224 0.469774i
\(283\) −0.774645 + 1.34172i −0.0460479 + 0.0797572i −0.888131 0.459591i \(-0.847996\pi\)
0.842083 + 0.539348i \(0.181329\pi\)
\(284\) −9.81724 5.66799i −0.582546 0.336333i
\(285\) 2.29078 0.135694
\(286\) 14.0187 + 8.95292i 0.828945 + 0.529397i
\(287\) −6.14359 −0.362645
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 1.01141 + 1.75182i 0.0593922 + 0.102870i
\(291\) 8.81894i 0.516976i
\(292\) 5.44128 3.14152i 0.318427 0.183844i
\(293\) 26.3321 15.2028i 1.53834 0.888160i 0.539402 0.842049i \(-0.318650\pi\)
0.998936 0.0461113i \(-0.0146829\pi\)
\(294\) 5.25078i 0.306232i
\(295\) −1.57076 2.72064i −0.0914532 0.158402i
\(296\) 3.40475 5.89721i 0.197897 0.342768i
\(297\) −3.99528 2.30668i −0.231830 0.133847i
\(298\) −4.08519 −0.236649
\(299\) 1.39806 31.2216i 0.0808518 1.80559i
\(300\) 1.00000 0.0577350
\(301\) 9.85677 + 5.69081i 0.568135 + 0.328013i
\(302\) −9.99057 + 17.3042i −0.574892 + 0.995743i
\(303\) −3.61335 6.25851i −0.207582 0.359542i
\(304\) 2.29078i 0.131385i
\(305\) −0.464102 + 0.267949i −0.0265744 + 0.0153427i
\(306\) −3.46410 + 2.00000i −0.198030 + 0.114332i
\(307\) 9.82622i 0.560812i 0.959882 + 0.280406i \(0.0904691\pi\)
−0.959882 + 0.280406i \(0.909531\pi\)
\(308\) −3.05076 5.28408i −0.173833 0.301088i
\(309\) 9.20002 15.9349i 0.523371 0.906505i
\(310\) 8.77464 + 5.06604i 0.498366 + 0.287732i
\(311\) −3.40049 −0.192824 −0.0964121 0.995342i \(-0.530737\pi\)
−0.0964121 + 0.995342i \(0.530737\pi\)
\(312\) 3.60194 + 0.161290i 0.203920 + 0.00913124i
\(313\) −16.2340 −0.917599 −0.458800 0.888540i \(-0.651720\pi\)
−0.458800 + 0.888540i \(0.651720\pi\)
\(314\) −6.17804 3.56690i −0.348647 0.201292i
\(315\) −0.661290 + 1.14539i −0.0372595 + 0.0645353i
\(316\) 1.48387 + 2.57014i 0.0834742 + 0.144582i
\(317\) 23.5231i 1.32119i 0.750742 + 0.660596i \(0.229696\pi\)
−0.750742 + 0.660596i \(0.770304\pi\)
\(318\) 0.715920 0.413337i 0.0401468 0.0231788i
\(319\) −8.08176 + 4.66601i −0.452492 + 0.261246i
\(320\) 1.00000i 0.0559017i
\(321\) −1.53590 2.66025i −0.0857255 0.148481i
\(322\) −5.73205 + 9.92820i −0.319435 + 0.553277i
\(323\) 7.93548 + 4.58155i 0.441542 + 0.254924i
\(324\) −1.00000 −0.0555556
\(325\) −3.20002 + 1.66129i −0.177505 + 0.0921518i
\(326\) 9.89470 0.548016
\(327\) −11.4547 6.61335i −0.633445 0.365719i
\(328\) −2.32258 + 4.02283i −0.128243 + 0.222123i
\(329\) −6.02386 10.4336i −0.332106 0.575225i
\(330\) 4.61335i 0.253957i
\(331\) 15.6667 9.04520i 0.861122 0.497169i −0.00326597 0.999995i \(-0.501040\pi\)
0.864388 + 0.502826i \(0.167706\pi\)
\(332\) −13.7454 + 7.93593i −0.754379 + 0.435541i
\(333\) 6.80951i 0.373159i
\(334\) −12.0187 20.8171i −0.657636 1.13906i
\(335\) −1.59053 + 2.75488i −0.0868999 + 0.150515i
\(336\) −1.14539 0.661290i −0.0624860 0.0360763i
\(337\) −5.69900 −0.310444 −0.155222 0.987880i \(-0.549609\pi\)
−0.155222 + 0.987880i \(0.549609\pi\)
\(338\) −11.7942 + 5.46774i −0.641521 + 0.297406i
\(339\) −8.08643 −0.439195
\(340\) 3.46410 + 2.00000i 0.187867 + 0.108465i
\(341\) −23.3715 + 40.4806i −1.26564 + 2.19214i
\(342\) 1.14539 + 1.98387i 0.0619355 + 0.107275i
\(343\) 16.2026i 0.874860i
\(344\) 7.45269 4.30281i 0.401822 0.231992i
\(345\) 7.50670 4.33399i 0.404147 0.233334i
\(346\) 2.52817i 0.135915i
\(347\) 7.87357 + 13.6374i 0.422676 + 0.732095i 0.996200 0.0870928i \(-0.0277577\pi\)
−0.573525 + 0.819188i \(0.694424\pi\)
\(348\) −1.01141 + 1.75182i −0.0542174 + 0.0939073i
\(349\) 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i \(-0.198847\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(350\) 1.32258 0.0706949
\(351\) 3.20002 1.66129i 0.170804 0.0886731i
\(352\) −4.61335 −0.245893
\(353\) 1.03917 + 0.599964i 0.0553093 + 0.0319328i 0.527400 0.849617i \(-0.323167\pi\)
−0.472090 + 0.881550i \(0.656500\pi\)
\(354\) 1.57076 2.72064i 0.0834850 0.144600i
\(355\) 5.66799 + 9.81724i 0.300825 + 0.521045i
\(356\) 11.8641i 0.628798i
\(357\) −4.58155 + 2.64516i −0.242481 + 0.139997i
\(358\) 5.43490 3.13784i 0.287243 0.165840i
\(359\) 16.2830i 0.859386i 0.902975 + 0.429693i \(0.141378\pi\)
−0.902975 + 0.429693i \(0.858622\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) −6.87617 + 11.9099i −0.361904 + 0.626836i
\(362\) 10.6374 + 6.14152i 0.559091 + 0.322791i
\(363\) −10.2830 −0.539720
\(364\) 4.76386 + 0.213319i 0.249694 + 0.0111809i
\(365\) −6.28304 −0.328870
\(366\) −0.464102 0.267949i −0.0242590 0.0140059i
\(367\) 9.81724 17.0040i 0.512456 0.887599i −0.487440 0.873156i \(-0.662069\pi\)
0.999896 0.0144428i \(-0.00459745\pi\)
\(368\) 4.33399 + 7.50670i 0.225925 + 0.391314i
\(369\) 4.64516i 0.241817i
\(370\) −5.89721 + 3.40475i −0.306581 + 0.177005i
\(371\) 0.946862 0.546671i 0.0491586 0.0283817i
\(372\) 10.1321i 0.525324i
\(373\) 1.27874 + 2.21484i 0.0662106 + 0.114680i 0.897230 0.441563i \(-0.145576\pi\)
−0.831020 + 0.556243i \(0.812242\pi\)
\(374\) −9.22671 + 15.9811i −0.477102 + 0.826365i
\(375\) −0.866025 0.500000i −0.0447214 0.0258199i
\(376\) −9.10926 −0.469774
\(377\) 0.326261 7.28610i 0.0168033 0.375253i
\(378\) −1.32258 −0.0680262
\(379\) −13.0846 7.55440i −0.672111 0.388044i 0.124765 0.992186i \(-0.460182\pi\)
−0.796876 + 0.604143i \(0.793516\pi\)
\(380\) 1.14539 1.98387i 0.0587571 0.101770i
\(381\) 5.73592 + 9.93490i 0.293860 + 0.508980i
\(382\) 9.74715i 0.498707i
\(383\) −16.2210 + 9.36517i −0.828852 + 0.478538i −0.853459 0.521159i \(-0.825500\pi\)
0.0246073 + 0.999697i \(0.492166\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 6.10153i 0.310963i
\(386\) 6.88130 + 11.9188i 0.350249 + 0.606649i
\(387\) 4.30281 7.45269i 0.218724 0.378841i
\(388\) −7.63743 4.40947i −0.387732 0.223857i
\(389\) 6.96899 0.353342 0.176671 0.984270i \(-0.443467\pi\)
0.176671 + 0.984270i \(0.443467\pi\)
\(390\) −3.03873 1.94065i −0.153872 0.0982687i
\(391\) 34.6719 1.75344
\(392\) 4.54731 + 2.62539i 0.229674 + 0.132602i
\(393\) 7.99528 13.8482i 0.403309 0.698551i
\(394\) 5.07076 + 8.78282i 0.255461 + 0.442472i
\(395\) 2.96774i 0.149323i
\(396\) −3.99528 + 2.30668i −0.200771 + 0.115915i
\(397\) −16.0839 + 9.28606i −0.807229 + 0.466054i −0.845993 0.533195i \(-0.820991\pi\)
0.0387637 + 0.999248i \(0.487658\pi\)
\(398\) 9.57336i 0.479869i
\(399\) 1.51487 + 2.62383i 0.0758382 + 0.131356i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −25.7126 14.8452i −1.28403 0.741333i −0.306444 0.951889i \(-0.599139\pi\)
−0.977582 + 0.210556i \(0.932473\pi\)
\(402\) −3.18106 −0.158657
\(403\) −16.8323 32.4229i −0.838478 1.61510i
\(404\) −7.22671 −0.359542
\(405\) 0.866025 + 0.500000i 0.0430331 + 0.0248452i
\(406\) −1.33767 + 2.31692i −0.0663877 + 0.114987i
\(407\) −15.7073 27.2059i −0.778584 1.34855i
\(408\) 4.00000i 0.198030i
\(409\) −21.0752 + 12.1678i −1.04210 + 0.601657i −0.920427 0.390913i \(-0.872159\pi\)
−0.121673 + 0.992570i \(0.538826\pi\)
\(410\) 4.02283 2.32258i 0.198673 0.114704i
\(411\) 16.0697i 0.792661i
\(412\) −9.20002 15.9349i −0.453252 0.785056i
\(413\) 2.07746 3.59826i 0.102225 0.177059i
\(414\) 7.50670 + 4.33399i 0.368934 + 0.213004i
\(415\) 15.8719 0.779119
\(416\) 1.94065 3.03873i 0.0951483 0.148986i
\(417\) 9.32258 0.456529
\(418\) 9.15229 + 5.28408i 0.447653 + 0.258453i
\(419\) 1.44128 2.49636i 0.0704109 0.121955i −0.828671 0.559737i \(-0.810902\pi\)
0.899081 + 0.437781i \(0.144236\pi\)
\(420\) 0.661290 + 1.14539i 0.0322676 + 0.0558892i
\(421\) 4.94707i 0.241106i −0.992707 0.120553i \(-0.961533\pi\)
0.992707 0.120553i \(-0.0384667\pi\)
\(422\) −0.939800 + 0.542594i −0.0457488 + 0.0264131i
\(423\) −7.88885 + 4.55463i −0.383569 + 0.221454i
\(424\) 0.826674i 0.0401468i
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) −5.66799 + 9.81724i −0.274615 + 0.475647i
\(427\) −0.613811 0.354384i −0.0297044 0.0171499i
\(428\) −3.07180 −0.148481
\(429\) 8.95292 14.0187i 0.432251 0.676831i
\(430\) −8.60562 −0.415000
\(431\) −15.3829 8.88130i −0.740967 0.427797i 0.0814539 0.996677i \(-0.474044\pi\)
−0.822421 + 0.568880i \(0.807377\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 17.9188 + 31.0362i 0.861121 + 1.49151i 0.870848 + 0.491553i \(0.163570\pi\)
−0.00972676 + 0.999953i \(0.503096\pi\)
\(434\) 13.4005i 0.643244i
\(435\) 1.75182 1.01141i 0.0839933 0.0484935i
\(436\) −11.4547 + 6.61335i −0.548579 + 0.316722i
\(437\) 19.8564i 0.949861i
\(438\) −3.14152 5.44128i −0.150108 0.259994i
\(439\) 5.04520 8.73854i 0.240794 0.417068i −0.720147 0.693822i \(-0.755925\pi\)
0.960941 + 0.276754i \(0.0892588\pi\)
\(440\) 3.99528 + 2.30668i 0.190468 + 0.109967i
\(441\) 5.25078 0.250037
\(442\) −6.64516 12.8001i −0.316078 0.608837i
\(443\) 13.6981 0.650816 0.325408 0.945574i \(-0.394498\pi\)
0.325408 + 0.945574i \(0.394498\pi\)
\(444\) −5.89721 3.40475i −0.279869 0.161582i
\(445\) 5.93207 10.2746i 0.281207 0.487065i
\(446\) −12.4708 21.6001i −0.590509 1.02279i
\(447\) 4.08519i 0.193223i
\(448\) −1.14539 + 0.661290i −0.0541145 + 0.0312430i
\(449\) 13.2613 7.65639i 0.625837 0.361327i −0.153301 0.988180i \(-0.548990\pi\)
0.779138 + 0.626852i \(0.215657\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) 10.7149 + 18.5587i 0.504544 + 0.873896i
\(452\) −4.04322 + 7.00306i −0.190177 + 0.329396i
\(453\) 17.3042 + 9.99057i 0.813021 + 0.469398i
\(454\) 19.3205 0.906756
\(455\) −4.01896 2.56667i −0.188412 0.120327i
\(456\) 2.29078 0.107275
\(457\) −13.4714 7.77770i −0.630164 0.363826i 0.150651 0.988587i \(-0.451863\pi\)
−0.780816 + 0.624761i \(0.785196\pi\)
\(458\) 2.07746 3.59826i 0.0970732 0.168136i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 8.66799i 0.404147i
\(461\) 13.5473 7.82154i 0.630961 0.364286i −0.150163 0.988661i \(-0.547980\pi\)
0.781124 + 0.624376i \(0.214647\pi\)
\(462\) −5.28408 + 3.05076i −0.245838 + 0.141934i
\(463\) 13.7170i 0.637481i 0.947842 + 0.318741i \(0.103260\pi\)
−0.947842 + 0.318741i \(0.896740\pi\)
\(464\) 1.01141 + 1.75182i 0.0469537 + 0.0813261i
\(465\) 5.06604 8.77464i 0.234932 0.406914i
\(466\) −14.6934 8.48325i −0.680659 0.392979i
\(467\) −0.943666 −0.0436677 −0.0218338 0.999762i \(-0.506950\pi\)
−0.0218338 + 0.999762i \(0.506950\pi\)
\(468\) 0.161290 3.60194i 0.00745563 0.166500i
\(469\) −4.20720 −0.194271
\(470\) 7.88885 + 4.55463i 0.363886 + 0.210089i
\(471\) −3.56690 + 6.17804i −0.164354 + 0.284669i
\(472\) −1.57076 2.72064i −0.0723001 0.125228i
\(473\) 39.7008i 1.82544i
\(474\) 2.57014 1.48387i 0.118050 0.0681564i
\(475\) −1.98387 + 1.14539i −0.0910262 + 0.0525540i
\(476\) 5.29032i 0.242481i
\(477\) −0.413337 0.715920i −0.0189254 0.0327797i
\(478\) −3.17208 + 5.49420i −0.145088 + 0.251299i
\(479\) −9.61460 5.55099i −0.439302 0.253631i 0.263999 0.964523i \(-0.414958\pi\)
−0.703302 + 0.710892i \(0.748292\pi\)
\(480\) 1.00000 0.0456435
\(481\) 24.5275 + 1.09830i 1.11836 + 0.0500784i
\(482\) −24.1855 −1.10162
\(483\) 9.92820 + 5.73205i 0.451749 + 0.260817i
\(484\) −5.14152 + 8.90538i −0.233706 + 0.404790i
\(485\) 4.40947 + 7.63743i 0.200224 + 0.346798i
\(486\) 1.00000i 0.0453609i
\(487\) −28.5283 + 16.4708i −1.29274 + 0.746363i −0.979139 0.203192i \(-0.934868\pi\)
−0.313600 + 0.949555i \(0.601535\pi\)
\(488\) −0.464102 + 0.267949i −0.0210089 + 0.0121295i
\(489\) 9.89470i 0.447454i
\(490\) −2.62539 4.54731i −0.118603 0.205427i
\(491\) 14.2257 24.6396i 0.641996 1.11197i −0.342991 0.939339i \(-0.611440\pi\)
0.984987 0.172630i \(-0.0552266\pi\)
\(492\) 4.02283 + 2.32258i 0.181363 + 0.104710i
\(493\) 8.09130 0.364414
\(494\) −7.33052 + 3.80564i −0.329816 + 0.171224i
\(495\) 4.61335 0.207355
\(496\) 8.77464 + 5.06604i 0.393993 + 0.227472i
\(497\) −7.49636 + 12.9841i −0.336258 + 0.582416i
\(498\) 7.93593 + 13.7454i 0.355618 + 0.615948i
\(499\) 4.10926i 0.183956i −0.995761 0.0919779i \(-0.970681\pi\)
0.995761 0.0919779i \(-0.0293189\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) −20.8171 + 12.0187i −0.930037 + 0.536957i
\(502\) 8.82497i 0.393878i
\(503\) −2.86800 4.96753i −0.127878 0.221491i 0.794976 0.606641i \(-0.207483\pi\)
−0.922854 + 0.385149i \(0.874150\pi\)
\(504\) −0.661290 + 1.14539i −0.0294562 + 0.0510196i
\(505\) 6.25851 + 3.61335i 0.278500 + 0.160792i
\(506\) 39.9885 1.77771
\(507\) 5.46774 + 11.7942i 0.242831 + 0.523800i
\(508\) 11.4718 0.508980
\(509\) −13.1129 7.57076i −0.581221 0.335568i 0.180397 0.983594i \(-0.442262\pi\)
−0.761618 + 0.648026i \(0.775595\pi\)
\(510\) 2.00000 3.46410i 0.0885615 0.153393i
\(511\) −4.15491 7.19652i −0.183803 0.318355i
\(512\) 1.00000i 0.0441942i
\(513\) 1.98387 1.14539i 0.0875900 0.0505701i
\(514\) −7.26157 + 4.19247i −0.320294 + 0.184922i
\(515\) 18.4000i 0.810802i
\(516\) −4.30281 7.45269i −0.189421 0.328086i
\(517\) −21.0121 + 36.3941i −0.924112 + 1.60061i
\(518\) −7.79953 4.50306i −0.342691 0.197853i
\(519\) −2.52817 −0.110974
\(520\) −3.20002 + 1.66129i −0.140330 + 0.0728524i
\(521\) 8.93027 0.391242 0.195621 0.980680i \(-0.437328\pi\)
0.195621 + 0.980680i \(0.437328\pi\)
\(522\) 1.75182 + 1.01141i 0.0766750 + 0.0442683i
\(523\) 4.90844 8.50166i 0.214631 0.371752i −0.738527 0.674223i \(-0.764478\pi\)
0.953158 + 0.302472i \(0.0978118\pi\)
\(524\) −7.99528 13.8482i −0.349276 0.604963i
\(525\) 1.32258i 0.0577221i
\(526\) 1.66389 0.960648i 0.0725491 0.0418863i
\(527\) 35.0986 20.2642i 1.52892 0.882721i
\(528\) 4.61335i 0.200771i
\(529\) −26.0670 45.1493i −1.13335 1.96301i
\(530\) −0.413337 + 0.715920i −0.0179542 + 0.0310976i
\(531\) −2.72064 1.57076i −0.118066 0.0681652i
\(532\) 3.02973 0.131356
\(533\) −16.7316 0.749217i −0.724726 0.0324522i
\(534\) 11.8641 0.513411
\(535\) 2.66025 + 1.53590i 0.115013 + 0.0664027i
\(536\) −1.59053 + 2.75488i −0.0687004 + 0.118993i
\(537\) −3.13784 5.43490i −0.135408 0.234533i
\(538\) 32.3098i 1.39298i
\(539\) 20.9784 12.1119i 0.903602 0.521695i
\(540\) 0.866025 0.500000i 0.0372678 0.0215166i
\(541\) 3.80826i 0.163730i 0.996643 + 0.0818650i \(0.0260876\pi\)
−0.996643 + 0.0818650i \(0.973912\pi\)
\(542\) −11.7263 20.3105i −0.503688 0.872413i
\(543\) 6.14152 10.6374i 0.263558 0.456496i
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) 13.2267 0.566570
\(546\) 0.213319 4.76386i 0.00912920 0.203874i
\(547\) 45.5847 1.94906 0.974530 0.224257i \(-0.0719954\pi\)
0.974530 + 0.224257i \(0.0719954\pi\)
\(548\) 13.9168 + 8.03486i 0.594496 + 0.343232i
\(549\) −0.267949 + 0.464102i −0.0114358 + 0.0198074i
\(550\) −2.30668 3.99528i −0.0983571 0.170359i
\(551\) 4.63384i 0.197408i
\(552\) 7.50670 4.33399i 0.319506 0.184467i
\(553\) 3.39921 1.96254i 0.144549 0.0834555i
\(554\) 9.00566i 0.382614i
\(555\) 3.40475 + 5.89721i 0.144524 + 0.250322i
\(556\) 4.66129 8.07359i 0.197683 0.342397i
\(557\) −31.9209 18.4296i −1.35253 0.780885i −0.363929 0.931427i \(-0.618565\pi\)
−0.988604 + 0.150541i \(0.951898\pi\)
\(558\) 10.1321 0.428925
\(559\) 26.1502 + 16.7005i 1.10603 + 0.706357i
\(560\) 1.32258 0.0558892
\(561\) 15.9811 + 9.22671i 0.674724 + 0.389552i
\(562\) 0.858478 1.48693i 0.0362127 0.0627223i
\(563\) 16.8870 + 29.2491i 0.711701 + 1.23270i 0.964218 + 0.265109i \(0.0854081\pi\)
−0.252518 + 0.967592i \(0.581259\pi\)
\(564\) 9.10926i 0.383569i
\(565\) 7.00306 4.04322i 0.294621 0.170099i
\(566\) 1.34172 0.774645i 0.0563969 0.0325607i
\(567\) 1.32258i 0.0555431i
\(568\) 5.66799 + 9.81724i 0.237823 + 0.411922i
\(569\) −12.7159 + 22.0246i −0.533079 + 0.923320i 0.466175 + 0.884693i \(0.345632\pi\)
−0.999254 + 0.0386274i \(0.987701\pi\)
\(570\) −1.98387 1.14539i −0.0830952 0.0479750i
\(571\) 13.3682 0.559443 0.279722 0.960081i \(-0.409758\pi\)
0.279722 + 0.960081i \(0.409758\pi\)
\(572\) −7.66412 14.7628i −0.320453 0.617264i
\(573\) −9.74715 −0.407193
\(574\) 5.32051 + 3.07180i 0.222074 + 0.128214i
\(575\) −4.33399 + 7.50670i −0.180740 + 0.313051i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 9.57428i 0.398582i −0.979940 0.199291i \(-0.936136\pi\)
0.979940 0.199291i \(-0.0638639\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) 11.9188 6.88130i 0.495327 0.285977i
\(580\) 2.02283i 0.0839933i
\(581\) 10.4959 + 18.1794i 0.435444 + 0.754210i
\(582\) −4.40947 + 7.63743i −0.182778 + 0.316582i
\(583\) −3.30279 1.90687i −0.136788 0.0789745i
\(584\) −6.28304 −0.259994
\(585\) −1.94065 + 3.03873i −0.0802361 + 0.125636i
\(586\) −30.4057 −1.25605
\(587\) 1.21286 + 0.700246i 0.0500602 + 0.0289023i 0.524821 0.851212i \(-0.324132\pi\)
−0.474761 + 0.880115i \(0.657466\pi\)
\(588\) 2.62539 4.54731i 0.108269 0.187528i
\(589\) −11.6052 20.1007i −0.478183 0.828237i
\(590\) 3.14152i 0.129334i
\(591\) 8.78282 5.07076i 0.361277 0.208583i
\(592\) −5.89721 + 3.40475i −0.242374 + 0.139935i
\(593\) 10.7303i 0.440643i −0.975427 0.220321i \(-0.929289\pi\)
0.975427 0.220321i \(-0.0707106\pi\)
\(594\) 2.30668 + 3.99528i 0.0946441 + 0.163928i
\(595\) 2.64516 4.58155i 0.108441 0.187825i
\(596\) 3.53788 + 2.04259i 0.144917 + 0.0836679i
\(597\) −9.57336 −0.391812
\(598\) −16.8215 + 26.3397i −0.687884 + 1.07711i
\(599\) −40.7967 −1.66691 −0.833453 0.552590i \(-0.813640\pi\)
−0.833453 + 0.552590i \(0.813640\pi\)
\(600\) −0.866025 0.500000i −0.0353553 0.0204124i
\(601\) −21.4416 + 37.1379i −0.874621 + 1.51489i −0.0174548 + 0.999848i \(0.505556\pi\)
−0.857166 + 0.515040i \(0.827777\pi\)
\(602\) −5.69081 9.85677i −0.231940 0.401732i
\(603\) 3.18106i 0.129543i
\(604\) 17.3042 9.99057i 0.704097 0.406510i
\(605\) 8.90538 5.14152i 0.362055 0.209033i
\(606\) 7.22671i 0.293565i
\(607\) 3.43616 + 5.95161i 0.139470 + 0.241568i 0.927296 0.374329i \(-0.122127\pi\)
−0.787826 + 0.615897i \(0.788794\pi\)
\(608\) 1.14539 1.98387i 0.0464516 0.0804565i
\(609\) 2.31692 + 1.33767i 0.0938863 + 0.0542053i
\(610\) 0.535898 0.0216979
\(611\) −15.1331 29.1498i −0.612221 1.17927i
\(612\) 4.00000 0.161690
\(613\) −0.659358 0.380681i −0.0266312 0.0153755i 0.486625 0.873611i \(-0.338228\pi\)
−0.513257 + 0.858235i \(0.671561\pi\)
\(614\) 4.91311 8.50975i 0.198277 0.343426i
\(615\) −2.32258 4.02283i −0.0936555 0.162216i
\(616\) 6.10153i 0.245838i
\(617\) 21.3061 12.3011i 0.857753 0.495224i −0.00550613 0.999985i \(-0.501753\pi\)
0.863259 + 0.504761i \(0.168419\pi\)
\(618\) −15.9349 + 9.20002i −0.640996 + 0.370079i
\(619\) 17.2035i 0.691468i 0.938333 + 0.345734i \(0.112370\pi\)
−0.938333 + 0.345734i \(0.887630\pi\)
\(620\) −5.06604 8.77464i −0.203457 0.352398i
\(621\) 4.33399 7.50670i 0.173917 0.301233i
\(622\) 2.94491 + 1.70025i 0.118080 + 0.0681737i
\(623\) 15.6913 0.628657
\(624\) −3.03873 1.94065i −0.121646 0.0776883i
\(625\) 1.00000 0.0400000
\(626\) 14.0590 + 8.11699i 0.561912 + 0.324420i
\(627\) 5.28408 9.15229i 0.211026 0.365507i
\(628\) 3.56690 + 6.17804i 0.142335 + 0.246531i
\(629\) 27.2380i 1.08605i
\(630\) 1.14539 0.661290i 0.0456333 0.0263464i
\(631\) 2.08519 1.20388i 0.0830100 0.0479259i −0.457920 0.888993i \(-0.651406\pi\)
0.540930 + 0.841067i \(0.318072\pi\)
\(632\) 2.96774i 0.118050i
\(633\) 0.542594 + 0.939800i 0.0215662 + 0.0373537i
\(634\) 11.7616 20.3716i 0.467112 0.809061i
\(635\) −9.93490 5.73592i −0.394254 0.227623i
\(636\) −0.826674 −0.0327797
\(637\) −0.846898 + 18.9130i −0.0335553 + 0.749361i
\(638\) 9.33201 0.369458
\(639\) 9.81724 + 5.66799i 0.388364 + 0.224222i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −9.73875 16.8680i −0.384657 0.666246i 0.607064 0.794653i \(-0.292347\pi\)
−0.991722 + 0.128407i \(0.959014\pi\)
\(642\) 3.07180i 0.121234i
\(643\) −20.7451 + 11.9772i −0.818106 + 0.472334i −0.849763 0.527165i \(-0.823255\pi\)
0.0316570 + 0.999499i \(0.489922\pi\)
\(644\) 9.92820 5.73205i 0.391226 0.225874i
\(645\) 8.60562i 0.338846i
\(646\) −4.58155 7.93548i −0.180259 0.312217i
\(647\) 9.10540 15.7710i 0.357970 0.620022i −0.629652 0.776878i \(-0.716802\pi\)
0.987622 + 0.156855i \(0.0501357\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −14.4930 −0.568898
\(650\) 3.60194 + 0.161290i 0.141280 + 0.00632631i
\(651\) 13.4005 0.525207
\(652\) −8.56906 4.94735i −0.335590 0.193753i
\(653\) 24.0793 41.7065i 0.942294 1.63210i 0.181213 0.983444i \(-0.441998\pi\)
0.761081 0.648657i \(-0.224669\pi\)
\(654\) 6.61335 + 11.4547i 0.258603 + 0.447913i
\(655\) 15.9906i 0.624803i
\(656\) 4.02283 2.32258i 0.157065 0.0906815i
\(657\) −5.44128 + 3.14152i −0.212284 + 0.122562i
\(658\) 12.0477i 0.469669i
\(659\) 18.4127 + 31.8917i 0.717257 + 1.24233i 0.962083 + 0.272758i \(0.0879359\pi\)
−0.244826 + 0.969567i \(0.578731\pi\)
\(660\) 2.30668 3.99528i 0.0897873 0.155516i
\(661\) −19.5131 11.2659i −0.758971 0.438192i 0.0699555 0.997550i \(-0.477714\pi\)
−0.828926 + 0.559358i \(0.811048\pi\)
\(662\) −18.0904 −0.703103
\(663\) −12.8001 + 6.64516i −0.497114 + 0.258077i
\(664\) 15.8719 0.615948
\(665\) −2.62383 1.51487i −0.101748 0.0587440i
\(666\) −3.40475 + 5.89721i −0.131932 + 0.228512i
\(667\) −8.76691 15.1847i −0.339456 0.587955i
\(668\) 24.0375i 0.930037i
\(669\) −21.6001 + 12.4708i −0.835106 + 0.482149i
\(670\) 2.75488 1.59053i 0.106430 0.0614475i
\(671\) 2.47229i 0.0954417i
\(672\) 0.661290 + 1.14539i 0.0255098 + 0.0441843i
\(673\) 11.8719 20.5627i 0.457627 0.792633i −0.541208 0.840889i \(-0.682033\pi\)
0.998835 + 0.0482556i \(0.0153662\pi\)
\(674\) 4.93548 + 2.84950i 0.190108 + 0.109759i
\(675\) −1.00000 −0.0384900
\(676\) 12.9480 + 1.16191i 0.497999 + 0.0446890i
\(677\) 1.16559 0.0447975 0.0223987 0.999749i \(-0.492870\pi\)
0.0223987 + 0.999749i \(0.492870\pi\)
\(678\) 7.00306 + 4.04322i 0.268951 + 0.155279i
\(679\) −5.83188 + 10.1011i −0.223807 + 0.387645i
\(680\) −2.00000 3.46410i −0.0766965 0.132842i
\(681\) 19.3205i 0.740363i
\(682\) 40.4806 23.3715i 1.55008 0.894939i
\(683\) 12.0134 6.93593i 0.459680 0.265396i −0.252230 0.967667i \(-0.581164\pi\)
0.711910 + 0.702271i \(0.247831\pi\)
\(684\) 2.29078i 0.0875900i
\(685\) −8.03486 13.9168i −0.306996 0.531733i
\(686\) 8.10132 14.0319i 0.309310 0.535740i
\(687\) −3.59826 2.07746i −0.137282 0.0792599i
\(688\) −8.60562 −0.328086
\(689\) 2.64537 1.37334i 0.100781 0.0523203i
\(690\) −8.66799 −0.329985
\(691\) −35.6967 20.6095i −1.35797 0.784022i −0.368616 0.929582i \(-0.620168\pi\)
−0.989349 + 0.145560i \(0.953502\pi\)
\(692\) −1.26408 + 2.18946i −0.0480532 + 0.0832307i
\(693\) 3.05076 + 5.28408i 0.115889 + 0.200726i
\(694\) 15.7471i 0.597753i
\(695\) −8.07359 + 4.66129i −0.306249 + 0.176813i
\(696\) 1.75182 1.01141i 0.0664025 0.0383375i
\(697\) 18.5806i 0.703792i
\(698\) −7.66025 13.2679i −0.289945 0.502199i
\(699\) −8.48325 + 14.6934i −0.320866 + 0.555756i
\(700\) −1.14539 0.661290i −0.0432916 0.0249944i
\(701\) −23.0112 −0.869122 −0.434561 0.900642i \(-0.643096\pi\)
−0.434561 + 0.900642i \(0.643096\pi\)
\(702\) −3.60194 0.161290i −0.135947 0.00608749i
\(703\) 15.5991 0.588329
\(704\) 3.99528 + 2.30668i 0.150578 + 0.0869362i
\(705\) 4.55463 7.88885i 0.171537 0.297111i
\(706\) −0.599964 1.03917i −0.0225799 0.0391096i
\(707\) 9.55790i 0.359462i
\(708\) −2.72064 + 1.57076i −0.102248 + 0.0590328i
\(709\) −14.7944 + 8.54156i −0.555616 + 0.320785i −0.751384 0.659865i \(-0.770613\pi\)
0.195768 + 0.980650i \(0.437280\pi\)
\(710\) 11.3360i 0.425431i
\(711\) −1.48387 2.57014i −0.0556495 0.0963877i
\(712\) 5.93207 10.2746i 0.222314 0.385059i
\(713\) −76.0585 43.9124i −2.84841 1.64453i
\(714\) 5.29032 0.197985
\(715\) −0.744087 + 16.6170i −0.0278273 + 0.621442i
\(716\) −6.27568 −0.234533
\(717\) 5.49420 + 3.17208i 0.205185 + 0.118463i
\(718\) 8.14152 14.1015i 0.303839 0.526264i
\(719\) −21.8564 37.8564i −0.815106 1.41181i −0.909251 0.416247i \(-0.863345\pi\)
0.0941451 0.995558i \(-0.469988\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) −21.0752 + 12.1678i −0.784880 + 0.453151i
\(722\) 11.9099 6.87617i 0.443240 0.255905i
\(723\) 24.1855i 0.899467i
\(724\) −6.14152 10.6374i −0.228248 0.395337i
\(725\) −1.01141 + 1.75182i −0.0375629 + 0.0650609i
\(726\) 8.90538 + 5.14152i 0.330510 + 0.190820i
\(727\) 31.8453 1.18108 0.590538 0.807010i \(-0.298916\pi\)
0.590538 + 0.807010i \(0.298916\pi\)
\(728\) −4.01896 2.56667i −0.148953 0.0951270i
\(729\) 1.00000 0.0370370
\(730\) 5.44128 + 3.14152i 0.201391 + 0.116273i
\(731\) −17.2112 + 29.8108i −0.636581 + 1.10259i
\(732\) 0.267949 + 0.464102i 0.00990369 + 0.0171537i
\(733\) 5.96774i 0.220423i −0.993908 0.110212i \(-0.964847\pi\)
0.993908 0.110212i \(-0.0351529\pi\)
\(734\) −17.0040 + 9.81724i −0.627627 + 0.362361i
\(735\) −4.54731 + 2.62539i −0.167730 + 0.0968390i
\(736\) 8.66799i 0.319506i
\(737\) 7.33767 + 12.7092i 0.270287 + 0.468150i
\(738\) 2.32258 4.02283i 0.0854953 0.148082i
\(739\) 9.37833 + 5.41458i 0.344988 + 0.199179i 0.662475 0.749084i \(-0.269506\pi\)
−0.317488 + 0.948262i \(0.602839\pi\)
\(740\) 6.80951 0.250322
\(741\) 3.80564 + 7.33052i 0.139804 + 0.269293i
\(742\) −1.09334 −0.0401378
\(743\) 17.1909 + 9.92515i 0.630671 + 0.364118i 0.781012 0.624516i \(-0.214704\pi\)
−0.150341 + 0.988634i \(0.548037\pi\)
\(744\) 5.06604 8.77464i 0.185730 0.321694i
\(745\) −2.04259 3.53788i −0.0748349 0.129618i
\(746\) 2.55748i 0.0936359i
\(747\) 13.7454 7.93593i 0.502919 0.290361i
\(748\) 15.9811 9.22671i 0.584328 0.337362i
\(749\) 4.06270i 0.148448i
\(750\) 0.500000 + 0.866025i 0.0182574 + 0.0316228i
\(751\) −7.66538 + 13.2768i −0.279714 + 0.484479i −0.971314 0.237802i \(-0.923573\pi\)
0.691600 + 0.722281i \(0.256906\pi\)
\(752\) 7.88885 + 4.55463i 0.287677 + 0.166090i
\(753\) −8.82497 −0.321600
\(754\) −3.92560 + 6.14682i −0.142962 + 0.223854i
\(755\) −19.9811 −0.727188
\(756\) 1.14539 + 0.661290i 0.0416573 + 0.0240509i
\(757\) −22.5816 + 39.1125i −0.820744 + 1.42157i 0.0843855 + 0.996433i \(0.473107\pi\)
−0.905129 + 0.425137i \(0.860226\pi\)
\(758\) 7.55440 + 13.0846i 0.274388 + 0.475254i
\(759\) 39.9885i 1.45149i
\(760\) −1.98387 + 1.14539i −0.0719625 + 0.0415476i
\(761\) −18.7978 + 10.8529i −0.681419 + 0.393418i −0.800390 0.599480i \(-0.795374\pi\)
0.118970 + 0.992898i \(0.462041\pi\)
\(762\) 11.4718i 0.415581i
\(763\) 8.74669 + 15.1497i 0.316651 + 0.548456i
\(764\) −4.87357 + 8.44128i −0.176320 + 0.305395i
\(765\) −3.46410 2.00000i −0.125245 0.0723102i
\(766\) 18.7303 0.676755
\(767\) 6.09660 9.54623i 0.220136 0.344694i
\(768\) 1.00000 0.0360844
\(769\) 36.4711 + 21.0566i 1.31518 + 0.759321i 0.982949 0.183877i \(-0.0588647\pi\)
0.332233 + 0.943197i \(0.392198\pi\)
\(770\) 3.05076 5.28408i 0.109942 0.190425i
\(771\) 4.19247 + 7.26157i 0.150988 + 0.261519i
\(772\) 13.7626i 0.495327i
\(773\) 25.7734 14.8803i 0.927004 0.535206i 0.0411413 0.999153i \(-0.486901\pi\)
0.885863 + 0.463947i \(0.153567\pi\)
\(774\) −7.45269 + 4.30281i −0.267881 + 0.154661i
\(775\) 10.1321i 0.363955i
\(776\) 4.40947 + 7.63743i 0.158291 + 0.274168i
\(777\) −4.50306 + 7.79953i −0.161546 + 0.279806i
\(778\) −6.03532 3.48449i −0.216377 0.124925i
\(779\) −10.6410 −0.381254
\(780\) 1.66129 + 3.20002i 0.0594837 + 0.114579i
\(781\) 52.2969 1.87133
\(782\) −30.0268 17.3360i −1.07376 0.619933i
\(783\) 1.01141 1.75182i 0.0361450 0.0626049i
\(784\) −2.62539 4.54731i −0.0937640 0.162404i
\(785\) 7.13379i 0.254616i
\(786\) −13.8482 + 7.99528i −0.493950 + 0.285182i
\(787\) −35.5459 + 20.5224i −1.26707 + 0.731545i −0.974433 0.224678i \(-0.927867\pi\)
−0.292640 + 0.956223i \(0.594534\pi\)
\(788\) 10.1415i 0.361277i
\(789\) −0.960648 1.66389i −0.0342000 0.0592361i
\(790\) −1.48387 + 2.57014i −0.0527937 + 0.0914414i
\(791\) 9.26210 + 5.34748i 0.329322 + 0.190134i
\(792\) 4.61335 0.163928
\(793\) −1.62845 1.03999i −0.0578279 0.0369312i
\(794\) 18.5721 0.659100
\(795\) 0.715920 + 0.413337i 0.0253911 + 0.0146595i
\(796\) −4.78668 + 8.29078i −0.169659 + 0.293859i
\(797\) 22.6263 + 39.1899i 0.801464 + 1.38818i 0.918652 + 0.395067i \(0.129279\pi\)
−0.117188 + 0.993110i \(0.537388\pi\)
\(798\) 3.02973i 0.107251i
\(799\) 31.5554 18.2185i 1.11635 0.644525i
\(800\) −0.866025 + 0.500000i −0.0306186 + 0.0176777i
\(801\) 11.8641i 0.419199i
\(802\) 14.8452 + 25.7126i 0.524201 + 0.907944i
\(803\) −14.4930 + 25.1025i −0.511445 + 0.885849i
\(804\) 2.75488 + 1.59053i 0.0971570 + 0.0560936i
\(805\) −11.4641 −0.404056
\(806\) −1.63420 + 36.4952i −0.0575623 + 1.28549i
\(807\) −32.3098 −1.13736
\(808\) 6.25851 + 3.61335i 0.220174 + 0.127117i
\(809\) 14.2267 24.6414i 0.500184 0.866345i −0.499815 0.866132i \(-0.666599\pi\)
1.00000 0.000213036i \(-6.78113e-5\pi\)
\(810\) −0.500000 0.866025i −0.0175682 0.0304290i
\(811\) 44.4114i 1.55949i −0.626095 0.779747i \(-0.715348\pi\)
0.626095 0.779747i \(-0.284652\pi\)
\(812\) 2.31692 1.33767i 0.0813079 0.0469432i
\(813\) −20.3105 + 11.7263i −0.712322 + 0.411259i
\(814\) 31.4147i 1.10108i
\(815\) 4.94735 + 8.56906i 0.173298 + 0.300161i
\(816\) 2.00000 3.46410i 0.0700140 0.121268i
\(817\) 17.0724 + 9.85677i 0.597289 + 0.344845i
\(818\) 24.3355 0.850871
\(819\) −4.76386 0.213319i −0.166463 0.00745396i
\(820\) −4.64516 −0.162216
\(821\) −39.1169 22.5842i −1.36519 0.788192i −0.374880 0.927073i \(-0.622316\pi\)
−0.990309 + 0.138881i \(0.955649\pi\)
\(822\) 8.03486 13.9168i 0.280248 0.485404i
\(823\) 1.20900 + 2.09404i 0.0421430 + 0.0729938i 0.886328 0.463059i \(-0.153248\pi\)
−0.844185 + 0.536053i \(0.819915\pi\)
\(824\) 18.4000i 0.640996i
\(825\) −3.99528 + 2.30668i −0.139098 + 0.0803082i
\(826\) −3.59826 + 2.07746i −0.125199 + 0.0722840i
\(827\) 4.26832i 0.148424i 0.997242 + 0.0742120i \(0.0236441\pi\)
−0.997242 + 0.0742120i \(0.976356\pi\)
\(828\) −4.33399 7.50670i −0.150617 0.260876i
\(829\) −21.4926 + 37.2263i −0.746468 + 1.29292i 0.203037 + 0.979171i \(0.434919\pi\)
−0.949506 + 0.313750i \(0.898415\pi\)
\(830\) −13.7454 7.93593i −0.477111 0.275460i
\(831\) 9.00566 0.312403
\(832\) −3.20002 + 1.66129i −0.110941 + 0.0575949i
\(833\) −21.0031 −0.727715
\(834\) −8.07359 4.66129i −0.279566 0.161407i
\(835\) 12.0187 20.8171i 0.415925 0.720404i
\(836\) −5.28408 9.15229i −0.182754 0.316539i
\(837\) 10.1321i 0.350216i
\(838\) −2.49636 + 1.44128i −0.0862354 + 0.0497880i
\(839\) −20.1798 + 11.6508i −0.696684 + 0.402231i −0.806111 0.591764i \(-0.798432\pi\)
0.109427 + 0.993995i \(0.465098\pi\)
\(840\) 1.32258i 0.0456333i
\(841\) 12.4541 + 21.5711i 0.429451 + 0.743831i
\(842\) −2.47354 + 4.28429i −0.0852437 + 0.147646i
\(843\) −1.48693 0.858478i −0.0512125 0.0295676i
\(844\) 1.08519 0.0373537
\(845\) −10.6323 7.48023i −0.365763 0.257328i
\(846\) 9.10926 0.313183
\(847\) 11.7781 + 6.80007i 0.404699 + 0.233653i
\(848\) −0.413337 + 0.715920i −0.0141940 + 0.0245848i
\(849\) −0.774645 1.34172i −0.0265857 0.0460479i
\(850\) 4.00000i 0.137199i
\(851\) 51.1169 29.5124i 1.75226 1.01167i
\(852\) 9.81724 5.66799i 0.336333 0.194182i
\(853\) 20.8418i 0.713609i 0.934179 + 0.356804i \(0.116134\pi\)
−0.934179 + 0.356804i \(0.883866\pi\)
\(854\) 0.354384 + 0.613811i 0.0121268 + 0.0210042i
\(855\) −1.14539 + 1.98387i −0.0391714 + 0.0678469i
\(856\) 2.66025 + 1.53590i 0.0909256 + 0.0524959i
\(857\) 36.7250 1.25450 0.627250 0.778818i \(-0.284180\pi\)
0.627250 + 0.778818i \(0.284180\pi\)
\(858\) −14.7628 + 7.66412i −0.503994 + 0.261649i
\(859\) 0.914812 0.0312130 0.0156065 0.999878i \(-0.495032\pi\)
0.0156065 + 0.999878i \(0.495032\pi\)
\(860\) 7.45269 + 4.30281i 0.254135 + 0.146725i
\(861\) 3.07180 5.32051i 0.104687 0.181322i
\(862\) 8.88130 + 15.3829i 0.302498 + 0.523943i
\(863\) 33.6104i 1.14411i 0.820215 + 0.572056i \(0.193854\pi\)
−0.820215 + 0.572056i \(0.806146\pi\)
\(864\) 0.866025 0.500000i 0.0294628 0.0170103i
\(865\) 2.18946 1.26408i 0.0744438 0.0429801i
\(866\) 35.8375i 1.21781i
\(867\) 0.500000 + 0.866025i 0.0169809 + 0.0294118i
\(868\) 6.70025 11.6052i 0.227421 0.393905i
\(869\) −11.8570 6.84562i −0.402220 0.232222i
\(870\) −2.02283 −0.0685802
\(871\) −11.4580 0.513072i −0.388239 0.0173848i
\(872\) 13.2267 0.447913
\(873\) 7.63743 + 4.40947i 0.258488 + 0.149238i
\(874\) −9.92820 + 17.1962i −0.335826 + 0.581669i
\(875\) 0.661290 + 1.14539i 0.0223557 + 0.0387212i
\(876\) 6.28304i 0.212284i
\(877\) −21.0629 + 12.1607i −0.711243 + 0.410637i −0.811521 0.584323i \(-0.801360\pi\)
0.100278 + 0.994959i \(0.468027\pi\)
\(878\) −8.73854 + 5.04520i −0.294911 + 0.170267i
\(879\) 30.4057i 1.02556i
\(880\) −2.30668 3.99528i −0.0777581 0.134681i
\(881\) −4.95207 + 8.57723i −0.166839 + 0.288974i −0.937307 0.348505i \(-0.886689\pi\)
0.770468 + 0.637479i \(0.220023\pi\)
\(882\) −4.54731 2.62539i −0.153116 0.0884015i
\(883\) −43.9718 −1.47977 −0.739884 0.672734i \(-0.765120\pi\)
−0.739884 + 0.672734i \(0.765120\pi\)
\(884\) −0.645159 + 14.4078i −0.0216991 + 0.484586i
\(885\) 3.14152 0.105601
\(886\) −11.8629 6.84904i −0.398542 0.230098i
\(887\) −25.2807 + 43.7875i −0.848843 + 1.47024i 0.0333988 + 0.999442i \(0.489367\pi\)
−0.882242 + 0.470797i \(0.843966\pi\)
\(888\) 3.40475 + 5.89721i 0.114256 + 0.197897i
\(889\) 15.1724i 0.508866i
\(890\) −10.2746 + 5.93207i −0.344407 + 0.198843i
\(891\) 3.99528 2.30668i 0.133847 0.0772766i
\(892\) 24.9416i 0.835106i
\(893\) −10.4336 18.0716i −0.349148 0.604743i
\(894\) 2.04259 3.53788i 0.0683146 0.118324i
\(895\) 5.43490 + 3.13784i 0.181669 + 0.104886i
\(896\) 1.32258 0.0441843
\(897\) 26.3397 + 16.8215i 0.879455 + 0.561655i
\(898\) −15.3128 −0.510994
\(899\) −17.7496 10.2477i −0.591982 0.341781i
\(900\) −0.500000 + 0.866025i −0.0166667 + 0.0288675i
\(901\) 1.65335 + 2.86368i 0.0550810 + 0.0954031i
\(902\) 21.4298i 0.713533i
\(903\) −9.85677 + 5.69081i −0.328013 + 0.189378i
\(904\) 7.00306 4.04322i 0.232918 0.134475i
\(905\) 12.2830i 0.408302i
\(906\) −9.99057 17.3042i −0.331914 0.574892i
\(907\) 7.12175 12.3352i 0.236474 0.409585i −0.723226 0.690611i \(-0.757342\pi\)
0.959700 + 0.281026i \(0.0906749\pi\)
\(908\) −16.7321 9.66025i −0.555273 0.320587i
\(909\) 7.22671 0.239695
\(910\) 2.19719 + 4.23228i 0.0728361 + 0.140299i
\(911\) 21.8108 0.722623 0.361311 0.932445i \(-0.382329\pi\)
0.361311 + 0.932445i \(0.382329\pi\)
\(912\) −1.98387 1.14539i −0.0656925 0.0379276i
\(913\) 36.6113 63.4126i 1.21166 2.09865i
\(914\) 7.77770 + 13.4714i 0.257264 + 0.445594i
\(915\) 0.535898i 0.0177163i
\(916\) −3.59826 + 2.07746i −0.118890 + 0.0686411i
\(917\) −18.3154 + 10.5744i −0.604828 + 0.349197i
\(918\) 4.00000i 0.132020i
\(919\) 2.65289 + 4.59494i 0.0875108 + 0.151573i 0.906458 0.422295i \(-0.138775\pi\)
−0.818948 + 0.573868i \(0.805442\pi\)
\(920\) −4.33399 + 7.50670i −0.142888 + 0.247488i
\(921\) −8.50975 4.91311i −0.280406 0.161892i
\(922\) −15.6431 −0.515178
\(923\) −21.9992 + 34.4469i −0.724112 + 1.13383i
\(924\) 6.10153 0.200726
\(925\) −5.89721 3.40475i −0.193899 0.111948i
\(926\) 6.85848 11.8792i 0.225384 0.390376i
\(927\) 9.20002 + 15.9349i 0.302168 + 0.523371i
\(928\) 2.02283i 0.0664025i
\(929\) −38.4002 + 22.1704i −1.25987 + 0.727386i −0.973049 0.230598i \(-0.925932\pi\)
−0.286821 + 0.957984i \(0.592599\pi\)
\(930\) −8.77464 + 5.06604i −0.287732 + 0.166122i
\(931\) 12.0284i 0.394214i
\(932\) 8.48325 + 14.6934i 0.277878 + 0.481299i
\(933\) 1.70025 2.94491i 0.0556636 0.0964121i
\(934\) 0.817239 + 0.471833i 0.0267409 + 0.0154388i
\(935\) −18.4534 −0.603491
\(936\) −1.94065 + 3.03873i −0.0634322 + 0.0993239i
\(937\) 38.5283 1.25867 0.629333 0.777136i \(-0.283328\pi\)
0.629333 + 0.777136i \(0.283328\pi\)
\(938\) 3.64354 + 2.10360i 0.118966 + 0.0686850i
\(939\) 8.11699 14.0590i 0.264888 0.458800i
\(940\) −4.55463 7.88885i −0.148556 0.257306i
\(941\) 28.8637i 0.940929i 0.882419 + 0.470465i \(0.155914\pi\)
−0.882419 + 0.470465i \(0.844086\pi\)
\(942\) 6.17804 3.56690i 0.201292 0.116216i
\(943\) −34.8698 + 20.1321i −1.13552 + 0.655591i
\(944\) 3.14152i 0.102248i
\(945\) −0.661290 1.14539i −0.0215118 0.0372595i
\(946\) −19.8504 + 34.3819i −0.645392 + 1.11785i
\(947\) 42.6384 + 24.6173i 1.38556 + 0.799955i 0.992811 0.119689i \(-0.0381899\pi\)
0.392752 + 0.919645i \(0.371523\pi\)
\(948\) −2.96774 −0.0963877
\(949\) −10.4380 20.1059i −0.338830 0.652664i
\(950\) 2.29078 0.0743226
\(951\) −20.3716 11.7616i −0.660596 0.381395i
\(952\) 2.64516 4.58155i 0.0857301 0.148489i
\(953\) −13.2548 22.9580i −0.429366 0.743684i 0.567451 0.823407i \(-0.307930\pi\)
−0.996817 + 0.0797233i \(0.974596\pi\)
\(954\) 0.826674i 0.0267645i
\(955\) 8.44128 4.87357i 0.273153 0.157705i
\(956\) 5.49420 3.17208i 0.177695 0.102592i
\(957\) 9.33201i 0.301661i
\(958\) 5.55099 + 9.61460i 0.179344 + 0.310634i
\(959\) 10.6267 18.4061i 0.343156 0.594363i
\(960\) −0.866025 0.500000i −0.0279508 0.0161374i
\(961\) −71.6592 −2.31159
\(962\) −20.6922 13.2149i −0.667145 0.426065i
\(963\) 3.07180 0.0989873
\(964\) 20.9452 + 12.0927i 0.674600 + 0.389481i
\(965\) −6.88130 + 11.9188i −0.221517 + 0.383679i
\(966\) −5.73205 9.92820i −0.184426 0.319435i
\(967\) 52.3877i 1.68468i 0.538950 + 0.842338i \(0.318821\pi\)
−0.538950 + 0.842338i \(0.681179\pi\)
\(968\) 8.90538 5.14152i 0.286230 0.165255i
\(969\) −7.93548 + 4.58155i −0.254924 + 0.147181i
\(970\) 8.81894i 0.283159i
\(971\) 14.3215 + 24.8056i 0.459600 + 0.796051i 0.998940 0.0460375i \(-0.0146594\pi\)
−0.539339 + 0.842088i \(0.681326\pi\)
\(972\) 0.500000 0.866025i 0.0160375 0.0277778i
\(973\) −10.6780 6.16493i −0.342320 0.197638i
\(974\) 32.9416 1.05552
\(975\) 0.161290 3.60194i 0.00516541 0.115354i
\(976\) 0.535898 0.0171537
\(977\) 35.1173 + 20.2750i 1.12350 + 0.648654i 0.942292 0.334791i \(-0.108666\pi\)
0.181209 + 0.983445i \(0.441999\pi\)
\(978\) −4.94735 + 8.56906i −0.158199 + 0.274008i
\(979\) −27.3667 47.4006i −0.874645 1.51493i
\(980\) 5.25078i 0.167730i
\(981\) 11.4547 6.61335i 0.365719 0.211148i
\(982\) −24.6396 + 14.2257i −0.786281 + 0.453960i
\(983\) 22.4160i 0.714958i 0.933921 + 0.357479i \(0.116364\pi\)
−0.933921 + 0.357479i \(0.883636\pi\)
\(984\) −2.32258 4.02283i −0.0740411 0.128243i
\(985\) −5.07076 + 8.78282i −0.161568 + 0.279844i
\(986\) −7.00727 4.04565i −0.223157 0.128840i
\(987\) 12.0477 0.383483
\(988\) 8.25124 + 0.369479i 0.262507 + 0.0117547i
\(989\) 74.5934 2.37193
\(990\) −3.99528 2.30668i −0.126978 0.0733110i
\(991\) 14.2844 24.7413i 0.453759 0.785933i −0.544857 0.838529i \(-0.683416\pi\)
0.998616 + 0.0525955i \(0.0167494\pi\)
\(992\) −5.06604 8.77464i −0.160847 0.278595i
\(993\) 18.0904i 0.574081i
\(994\) 12.9841 7.49636i 0.411830 0.237770i
\(995\) 8.29078 4.78668i 0.262835 0.151748i
\(996\) 15.8719i 0.502919i
\(997\) 17.2000 + 29.7913i 0.544730 + 0.943500i 0.998624 + 0.0524443i \(0.0167012\pi\)
−0.453894 + 0.891056i \(0.649965\pi\)
\(998\) −2.05463 + 3.55872i −0.0650382 + 0.112649i
\(999\) 5.89721 + 3.40475i 0.186579 + 0.107722i
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.bb.c.121.2 8
3.2 odd 2 1170.2.bs.f.901.4 8
5.2 odd 4 1950.2.y.k.199.4 8
5.3 odd 4 1950.2.y.j.199.1 8
5.4 even 2 1950.2.bc.g.901.3 8
13.4 even 6 5070.2.b.ba.1351.2 8
13.6 odd 12 5070.2.a.ca.1.2 4
13.7 odd 12 5070.2.a.bz.1.3 4
13.9 even 3 5070.2.b.ba.1351.7 8
13.10 even 6 inner 390.2.bb.c.361.2 yes 8
39.23 odd 6 1170.2.bs.f.361.4 8
65.23 odd 12 1950.2.y.k.49.4 8
65.49 even 6 1950.2.bc.g.751.3 8
65.62 odd 12 1950.2.y.j.49.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.bb.c.121.2 8 1.1 even 1 trivial
390.2.bb.c.361.2 yes 8 13.10 even 6 inner
1170.2.bs.f.361.4 8 39.23 odd 6
1170.2.bs.f.901.4 8 3.2 odd 2
1950.2.y.j.49.1 8 65.62 odd 12
1950.2.y.j.199.1 8 5.3 odd 4
1950.2.y.k.49.4 8 65.23 odd 12
1950.2.y.k.199.4 8 5.2 odd 4
1950.2.bc.g.751.3 8 65.49 even 6
1950.2.bc.g.901.3 8 5.4 even 2
5070.2.a.bz.1.3 4 13.7 odd 12
5070.2.a.ca.1.2 4 13.6 odd 12
5070.2.b.ba.1351.2 8 13.4 even 6
5070.2.b.ba.1351.7 8 13.9 even 3