Properties

Label 966.2.i.n.415.3
Level $966$
Weight $2$
Character 966.415
Analytic conductor $7.714$
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] = [966,2,Mod(277,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.277");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), 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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.173309020416.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 415.3
Root \(2.93560 + 0.167344i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.n.277.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.239514 - 0.414851i) q^{5} +1.00000 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.239514 - 0.414851i) q^{5} +1.00000 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.239514 - 0.414851i) q^{10} +(2.67511 + 4.63343i) q^{11} +(0.500000 - 0.866025i) q^{12} -4.70448 q^{13} +2.64575 q^{14} +0.479029 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.08336 + 1.87644i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.87321 - 3.24449i) q^{19} -0.479029 q^{20} +(-1.32288 + 2.29129i) q^{21} +5.35023 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.38527 + 4.13140i) q^{25} +(-2.35224 + 4.07420i) q^{26} -1.00000 q^{27} +(1.32288 - 2.29129i) q^{28} -4.74642 q^{29} +(0.239514 - 0.414851i) q^{30} +(4.88527 + 8.46153i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.67511 + 4.63343i) q^{33} +2.16672 q^{34} +1.26739 q^{35} +1.00000 q^{36} +(1.35224 - 2.34215i) q^{37} +(-1.87321 - 3.24449i) q^{38} +(-2.35224 - 4.07420i) q^{39} +(-0.239514 + 0.414851i) q^{40} +0.253580 q^{41} +(1.32288 + 2.29129i) q^{42} +2.00000 q^{43} +(2.67511 - 4.63343i) q^{44} +(0.239514 + 0.414851i) q^{45} +(0.500000 + 0.866025i) q^{46} +(4.96496 - 8.59957i) q^{47} -1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} +4.77053 q^{50} +(-1.08336 + 1.87644i) q^{51} +(2.35224 + 4.07420i) q^{52} +(-1.23951 - 2.14690i) q^{53} +(-0.500000 + 0.866025i) q^{54} +2.56291 q^{55} +(-1.32288 - 2.29129i) q^{56} +3.74642 q^{57} +(-2.37321 + 4.11052i) q^{58} +(-6.27945 - 10.8763i) q^{59} +(-0.239514 - 0.414851i) q^{60} +(4.47903 - 7.75791i) q^{61} +9.77053 q^{62} -2.64575 q^{63} +1.00000 q^{64} +(-1.12679 + 1.95166i) q^{65} +(2.67511 + 4.63343i) q^{66} +(3.35023 + 5.80277i) q^{67} +(1.08336 - 1.87644i) q^{68} -1.00000 q^{69} +(0.633696 - 1.09759i) q^{70} +0.774551 q^{71} +(0.500000 - 0.866025i) q^{72} +(5.61071 + 9.71804i) q^{73} +(-1.35224 - 2.34215i) q^{74} +(-2.38527 + 4.13140i) q^{75} -3.74642 q^{76} +(-7.07769 + 12.2589i) q^{77} -4.70448 q^{78} +(-0.423544 + 0.733600i) q^{79} +(0.239514 + 0.414851i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.126790 - 0.219607i) q^{82} +10.9299 q^{83} +2.64575 q^{84} +1.03792 q^{85} +(1.00000 - 1.73205i) q^{86} +(-2.37321 - 4.11052i) q^{87} +(-2.67511 - 4.63343i) q^{88} +(1.60582 - 2.78136i) q^{89} +0.479029 q^{90} +(-6.22344 - 10.7793i) q^{91} +1.00000 q^{92} +(-4.88527 + 8.46153i) q^{93} +(-4.96496 - 8.59957i) q^{94} +(-0.897321 - 1.55421i) q^{95} +(-0.500000 + 0.866025i) q^{96} +13.0098 q^{97} +(3.50000 + 6.06218i) q^{98} -5.35023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.239514 0.414851i 0.107114 0.185527i −0.807486 0.589887i \(-0.799172\pi\)
0.914600 + 0.404360i \(0.132506\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.32288 + 2.29129i 0.500000 + 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.239514 0.414851i −0.0757411 0.131187i
\(11\) 2.67511 + 4.63343i 0.806577 + 1.39703i 0.915221 + 0.402952i \(0.132016\pi\)
−0.108644 + 0.994081i \(0.534651\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −4.70448 −1.30479 −0.652394 0.757880i \(-0.726235\pi\)
−0.652394 + 0.757880i \(0.726235\pi\)
\(14\) 2.64575 0.707107
\(15\) 0.479029 0.123685
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.08336 + 1.87644i 0.262754 + 0.455103i 0.966973 0.254880i \(-0.0820360\pi\)
−0.704219 + 0.709983i \(0.748703\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 1.87321 3.24449i 0.429744 0.744338i −0.567106 0.823644i \(-0.691937\pi\)
0.996850 + 0.0793064i \(0.0252705\pi\)
\(20\) −0.479029 −0.107114
\(21\) −1.32288 + 2.29129i −0.288675 + 0.500000i
\(22\) 5.35023 1.14067
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.38527 + 4.13140i 0.477053 + 0.826280i
\(26\) −2.35224 + 4.07420i −0.461312 + 0.799016i
\(27\) −1.00000 −0.192450
\(28\) 1.32288 2.29129i 0.250000 0.433013i
\(29\) −4.74642 −0.881388 −0.440694 0.897657i \(-0.645268\pi\)
−0.440694 + 0.897657i \(0.645268\pi\)
\(30\) 0.239514 0.414851i 0.0437291 0.0757411i
\(31\) 4.88527 + 8.46153i 0.877420 + 1.51974i 0.854163 + 0.520006i \(0.174070\pi\)
0.0232569 + 0.999730i \(0.492596\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −2.67511 + 4.63343i −0.465678 + 0.806577i
\(34\) 2.16672 0.371590
\(35\) 1.26739 0.214228
\(36\) 1.00000 0.166667
\(37\) 1.35224 2.34215i 0.222307 0.385046i −0.733201 0.680012i \(-0.761975\pi\)
0.955508 + 0.294965i \(0.0953080\pi\)
\(38\) −1.87321 3.24449i −0.303875 0.526327i
\(39\) −2.35224 4.07420i −0.376660 0.652394i
\(40\) −0.239514 + 0.414851i −0.0378706 + 0.0655937i
\(41\) 0.253580 0.0396026 0.0198013 0.999804i \(-0.493697\pi\)
0.0198013 + 0.999804i \(0.493697\pi\)
\(42\) 1.32288 + 2.29129i 0.204124 + 0.353553i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 2.67511 4.63343i 0.403289 0.698516i
\(45\) 0.239514 + 0.414851i 0.0357047 + 0.0618424i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 4.96496 8.59957i 0.724214 1.25438i −0.235082 0.971975i \(-0.575536\pi\)
0.959297 0.282400i \(-0.0911307\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) 4.77053 0.674655
\(51\) −1.08336 + 1.87644i −0.151701 + 0.262754i
\(52\) 2.35224 + 4.07420i 0.326197 + 0.564989i
\(53\) −1.23951 2.14690i −0.170260 0.294900i 0.768250 0.640149i \(-0.221128\pi\)
−0.938511 + 0.345250i \(0.887794\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 2.56291 0.345583
\(56\) −1.32288 2.29129i −0.176777 0.306186i
\(57\) 3.74642 0.496225
\(58\) −2.37321 + 4.11052i −0.311618 + 0.539738i
\(59\) −6.27945 10.8763i −0.817514 1.41598i −0.907508 0.420034i \(-0.862018\pi\)
0.0899940 0.995942i \(-0.471315\pi\)
\(60\) −0.239514 0.414851i −0.0309212 0.0535570i
\(61\) 4.47903 7.75791i 0.573481 0.993298i −0.422724 0.906258i \(-0.638926\pi\)
0.996205 0.0870395i \(-0.0277406\pi\)
\(62\) 9.77053 1.24086
\(63\) −2.64575 −0.333333
\(64\) 1.00000 0.125000
\(65\) −1.12679 + 1.95166i −0.139761 + 0.242073i
\(66\) 2.67511 + 4.63343i 0.329284 + 0.570336i
\(67\) 3.35023 + 5.80277i 0.409296 + 0.708921i 0.994811 0.101741i \(-0.0324412\pi\)
−0.585515 + 0.810661i \(0.699108\pi\)
\(68\) 1.08336 1.87644i 0.131377 0.227551i
\(69\) −1.00000 −0.120386
\(70\) 0.633696 1.09759i 0.0757411 0.131187i
\(71\) 0.774551 0.0919223 0.0459612 0.998943i \(-0.485365\pi\)
0.0459612 + 0.998943i \(0.485365\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 5.61071 + 9.71804i 0.656684 + 1.13741i 0.981469 + 0.191623i \(0.0613750\pi\)
−0.324784 + 0.945788i \(0.605292\pi\)
\(74\) −1.35224 2.34215i −0.157195 0.272269i
\(75\) −2.38527 + 4.13140i −0.275427 + 0.477053i
\(76\) −3.74642 −0.429744
\(77\) −7.07769 + 12.2589i −0.806577 + 1.39703i
\(78\) −4.70448 −0.532677
\(79\) −0.423544 + 0.733600i −0.0476524 + 0.0825365i −0.888868 0.458164i \(-0.848507\pi\)
0.841215 + 0.540700i \(0.181841\pi\)
\(80\) 0.239514 + 0.414851i 0.0267785 + 0.0463818i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.126790 0.219607i 0.0140016 0.0242515i
\(83\) 10.9299 1.19972 0.599858 0.800107i \(-0.295224\pi\)
0.599858 + 0.800107i \(0.295224\pi\)
\(84\) 2.64575 0.288675
\(85\) 1.03792 0.112578
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −2.37321 4.11052i −0.254435 0.440694i
\(88\) −2.67511 4.63343i −0.285168 0.493926i
\(89\) 1.60582 2.78136i 0.170216 0.294824i −0.768279 0.640115i \(-0.778887\pi\)
0.938495 + 0.345292i \(0.112220\pi\)
\(90\) 0.479029 0.0504941
\(91\) −6.22344 10.7793i −0.652394 1.12998i
\(92\) 1.00000 0.104257
\(93\) −4.88527 + 8.46153i −0.506578 + 0.877420i
\(94\) −4.96496 8.59957i −0.512097 0.886978i
\(95\) −0.897321 1.55421i −0.0920632 0.159458i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 13.0098 1.32094 0.660472 0.750851i \(-0.270356\pi\)
0.660472 + 0.750851i \(0.270356\pi\)
\(98\) 3.50000 + 6.06218i 0.353553 + 0.612372i
\(99\) −5.35023 −0.537718
\(100\) 2.38527 4.13140i 0.238527 0.413140i
\(101\) −2.38527 4.13140i −0.237343 0.411090i 0.722608 0.691258i \(-0.242943\pi\)
−0.959951 + 0.280168i \(0.909610\pi\)
\(102\) 1.08336 + 1.87644i 0.107269 + 0.185795i
\(103\) 3.68918 6.38985i 0.363506 0.629610i −0.625029 0.780601i \(-0.714913\pi\)
0.988535 + 0.150991i \(0.0482464\pi\)
\(104\) 4.70448 0.461312
\(105\) 0.633696 + 1.09759i 0.0618424 + 0.107114i
\(106\) −2.47903 −0.240785
\(107\) −7.46496 + 12.9297i −0.721665 + 1.24996i 0.238667 + 0.971102i \(0.423290\pi\)
−0.960332 + 0.278859i \(0.910044\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −2.26888 3.92981i −0.217319 0.376408i 0.736668 0.676254i \(-0.236398\pi\)
−0.953987 + 0.299846i \(0.903065\pi\)
\(110\) 1.28146 2.21955i 0.122182 0.211626i
\(111\) 2.70448 0.256698
\(112\) −2.64575 −0.250000
\(113\) −14.2455 −1.34011 −0.670054 0.742312i \(-0.733729\pi\)
−0.670054 + 0.742312i \(0.733729\pi\)
\(114\) 1.87321 3.24449i 0.175442 0.303875i
\(115\) 0.239514 + 0.414851i 0.0223348 + 0.0386851i
\(116\) 2.37321 + 4.11052i 0.220347 + 0.381652i
\(117\) 2.35224 4.07420i 0.217465 0.376660i
\(118\) −12.5589 −1.15614
\(119\) −2.86630 + 4.96458i −0.262754 + 0.455103i
\(120\) −0.479029 −0.0437291
\(121\) −8.81247 + 15.2637i −0.801134 + 1.38760i
\(122\) −4.47903 7.75791i −0.405512 0.702368i
\(123\) 0.126790 + 0.219607i 0.0114323 + 0.0198013i
\(124\) 4.88527 8.46153i 0.438710 0.759868i
\(125\) 4.68037 0.418625
\(126\) −1.32288 + 2.29129i −0.117851 + 0.204124i
\(127\) −12.3053 −1.09192 −0.545960 0.837811i \(-0.683835\pi\)
−0.545960 + 0.837811i \(0.683835\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) 1.12679 + 1.95166i 0.0988260 + 0.171172i
\(131\) 4.65781 8.06756i 0.406954 0.704866i −0.587592 0.809157i \(-0.699924\pi\)
0.994547 + 0.104291i \(0.0332574\pi\)
\(132\) 5.35023 0.465678
\(133\) 9.91210 0.859488
\(134\) 6.70046 0.578831
\(135\) −0.239514 + 0.414851i −0.0206141 + 0.0357047i
\(136\) −1.08336 1.87644i −0.0928975 0.160903i
\(137\) −6.60232 11.4356i −0.564074 0.977006i −0.997135 0.0756409i \(-0.975900\pi\)
0.433061 0.901365i \(-0.357434\pi\)
\(138\) −0.500000 + 0.866025i −0.0425628 + 0.0737210i
\(139\) −5.92993 −0.502970 −0.251485 0.967861i \(-0.580919\pi\)
−0.251485 + 0.967861i \(0.580919\pi\)
\(140\) −0.633696 1.09759i −0.0535570 0.0927635i
\(141\) 9.92993 0.836251
\(142\) 0.387276 0.670781i 0.0324995 0.0562907i
\(143\) −12.5850 21.7979i −1.05241 1.82283i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −1.13684 + 1.96906i −0.0944091 + 0.163521i
\(146\) 11.2214 0.928692
\(147\) −7.00000 −0.577350
\(148\) −2.70448 −0.222307
\(149\) 0.587025 1.01676i 0.0480910 0.0832960i −0.840978 0.541069i \(-0.818020\pi\)
0.889069 + 0.457773i \(0.151353\pi\)
\(150\) 2.38527 + 4.13140i 0.194756 + 0.337328i
\(151\) −3.15266 5.46056i −0.256560 0.444374i 0.708758 0.705451i \(-0.249256\pi\)
−0.965318 + 0.261077i \(0.915922\pi\)
\(152\) −1.87321 + 3.24449i −0.151937 + 0.263163i
\(153\) −2.16672 −0.175169
\(154\) 7.07769 + 12.2589i 0.570336 + 0.987851i
\(155\) 4.68037 0.375936
\(156\) −2.35224 + 4.07420i −0.188330 + 0.326197i
\(157\) −1.14209 1.97815i −0.0911485 0.157874i 0.816846 0.576856i \(-0.195720\pi\)
−0.907995 + 0.418982i \(0.862387\pi\)
\(158\) 0.423544 + 0.733600i 0.0336954 + 0.0583621i
\(159\) 1.23951 2.14690i 0.0982999 0.170260i
\(160\) 0.479029 0.0378706
\(161\) −2.64575 −0.208514
\(162\) −1.00000 −0.0785674
\(163\) −2.38728 + 4.13488i −0.186986 + 0.323869i −0.944244 0.329247i \(-0.893205\pi\)
0.757258 + 0.653116i \(0.226539\pi\)
\(164\) −0.126790 0.219607i −0.00990064 0.0171484i
\(165\) 1.28146 + 2.21955i 0.0997613 + 0.172792i
\(166\) 5.46496 9.46559i 0.424163 0.734673i
\(167\) −20.9500 −1.62116 −0.810581 0.585627i \(-0.800848\pi\)
−0.810581 + 0.585627i \(0.800848\pi\)
\(168\) 1.32288 2.29129i 0.102062 0.176777i
\(169\) 9.13211 0.702470
\(170\) 0.518961 0.898867i 0.0398025 0.0689400i
\(171\) 1.87321 + 3.24449i 0.143248 + 0.248113i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 8.61071 14.9142i 0.654660 1.13391i −0.327318 0.944914i \(-0.606145\pi\)
0.981979 0.188991i \(-0.0605217\pi\)
\(174\) −4.74642 −0.359825
\(175\) −6.31082 + 10.9307i −0.477053 + 0.826280i
\(176\) −5.35023 −0.403289
\(177\) 6.27945 10.8763i 0.471992 0.817514i
\(178\) −1.60582 2.78136i −0.120361 0.208472i
\(179\) −12.2634 21.2408i −0.916607 1.58761i −0.804531 0.593911i \(-0.797583\pi\)
−0.112077 0.993700i \(-0.535750\pi\)
\(180\) 0.239514 0.414851i 0.0178523 0.0309212i
\(181\) −20.4123 −1.51723 −0.758616 0.651538i \(-0.774124\pi\)
−0.758616 + 0.651538i \(0.774124\pi\)
\(182\) −12.4469 −0.922624
\(183\) 8.95806 0.662199
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −0.647761 1.12196i −0.0476244 0.0824878i
\(186\) 4.88527 + 8.46153i 0.358205 + 0.620429i
\(187\) −5.79623 + 10.0394i −0.423862 + 0.734151i
\(188\) −9.92993 −0.724214
\(189\) −1.32288 2.29129i −0.0962250 0.166667i
\(190\) −1.79464 −0.130197
\(191\) 0.619630 1.07323i 0.0448348 0.0776562i −0.842737 0.538325i \(-0.819057\pi\)
0.887572 + 0.460669i \(0.152391\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 5.58974 + 9.68172i 0.402359 + 0.696905i 0.994010 0.109288i \(-0.0348572\pi\)
−0.591652 + 0.806194i \(0.701524\pi\)
\(194\) 6.50490 11.2668i 0.467024 0.808910i
\(195\) −2.25358 −0.161382
\(196\) 7.00000 0.500000
\(197\) 22.0956 1.57425 0.787123 0.616796i \(-0.211570\pi\)
0.787123 + 0.616796i \(0.211570\pi\)
\(198\) −2.67511 + 4.63343i −0.190112 + 0.329284i
\(199\) −4.24807 7.35788i −0.301138 0.521586i 0.675256 0.737583i \(-0.264033\pi\)
−0.976394 + 0.215997i \(0.930700\pi\)
\(200\) −2.38527 4.13140i −0.168664 0.292134i
\(201\) −3.35023 + 5.80277i −0.236307 + 0.409296i
\(202\) −4.77053 −0.335653
\(203\) −6.27892 10.8754i −0.440694 0.763304i
\(204\) 2.16672 0.151701
\(205\) 0.0607361 0.105198i 0.00424199 0.00734735i
\(206\) −3.68918 6.38985i −0.257037 0.445202i
\(207\) −0.500000 0.866025i −0.0347524 0.0601929i
\(208\) 2.35224 4.07420i 0.163098 0.282495i
\(209\) 20.0442 1.38649
\(210\) 1.26739 0.0874583
\(211\) 20.3808 1.40307 0.701537 0.712633i \(-0.252498\pi\)
0.701537 + 0.712633i \(0.252498\pi\)
\(212\) −1.23951 + 2.14690i −0.0851302 + 0.147450i
\(213\) 0.387276 + 0.670781i 0.0265357 + 0.0459612i
\(214\) 7.46496 + 12.9297i 0.510294 + 0.883856i
\(215\) 0.479029 0.829702i 0.0326695 0.0565852i
\(216\) 1.00000 0.0680414
\(217\) −12.9252 + 22.3871i −0.877420 + 1.51974i
\(218\) −4.53775 −0.307336
\(219\) −5.61071 + 9.71804i −0.379137 + 0.656684i
\(220\) −1.28146 2.21955i −0.0863958 0.149642i
\(221\) −5.09665 8.82765i −0.342838 0.593812i
\(222\) 1.35224 2.34215i 0.0907563 0.157195i
\(223\) −3.18753 −0.213453 −0.106726 0.994288i \(-0.534037\pi\)
−0.106726 + 0.994288i \(0.534037\pi\)
\(224\) −1.32288 + 2.29129i −0.0883883 + 0.153093i
\(225\) −4.77053 −0.318035
\(226\) −7.12277 + 12.3370i −0.473800 + 0.820645i
\(227\) −2.67913 4.64040i −0.177820 0.307994i 0.763313 0.646028i \(-0.223571\pi\)
−0.941134 + 0.338035i \(0.890238\pi\)
\(228\) −1.87321 3.24449i −0.124056 0.214872i
\(229\) 11.7291 20.3154i 0.775082 1.34248i −0.159667 0.987171i \(-0.551042\pi\)
0.934749 0.355310i \(-0.115625\pi\)
\(230\) 0.479029 0.0315862
\(231\) −14.1554 −0.931355
\(232\) 4.74642 0.311618
\(233\) 12.3902 21.4604i 0.811706 1.40592i −0.0999624 0.994991i \(-0.531872\pi\)
0.911669 0.410926i \(-0.134794\pi\)
\(234\) −2.35224 4.07420i −0.153771 0.266339i
\(235\) −2.37836 4.11944i −0.155147 0.268723i
\(236\) −6.27945 + 10.8763i −0.408757 + 0.707988i
\(237\) −0.847088 −0.0550243
\(238\) 2.86630 + 4.96458i 0.185795 + 0.321806i
\(239\) 4.97187 0.321603 0.160802 0.986987i \(-0.448592\pi\)
0.160802 + 0.986987i \(0.448592\pi\)
\(240\) −0.239514 + 0.414851i −0.0154606 + 0.0267785i
\(241\) 3.74169 + 6.48080i 0.241024 + 0.417465i 0.961006 0.276527i \(-0.0891836\pi\)
−0.719983 + 0.693992i \(0.755850\pi\)
\(242\) 8.81247 + 15.2637i 0.566487 + 0.981185i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −8.95806 −0.573481
\(245\) 1.67660 + 2.90396i 0.107114 + 0.185527i
\(246\) 0.253580 0.0161677
\(247\) −8.81247 + 15.2637i −0.560724 + 0.971203i
\(248\) −4.88527 8.46153i −0.310215 0.537308i
\(249\) 5.46496 + 9.46559i 0.346328 + 0.599858i
\(250\) 2.34018 4.05332i 0.148006 0.256354i
\(251\) −14.9752 −0.945225 −0.472612 0.881270i \(-0.656689\pi\)
−0.472612 + 0.881270i \(0.656689\pi\)
\(252\) 1.32288 + 2.29129i 0.0833333 + 0.144338i
\(253\) −5.35023 −0.336366
\(254\) −6.15266 + 10.6567i −0.386052 + 0.668662i
\(255\) 0.518961 + 0.898867i 0.0324986 + 0.0562892i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.251570 + 0.435732i −0.0156925 + 0.0271802i −0.873765 0.486348i \(-0.838329\pi\)
0.858073 + 0.513529i \(0.171662\pi\)
\(258\) 2.00000 0.124515
\(259\) 7.15537 0.444613
\(260\) 2.25358 0.139761
\(261\) 2.37321 4.11052i 0.146898 0.254435i
\(262\) −4.65781 8.06756i −0.287760 0.498415i
\(263\) 2.49581 + 4.32287i 0.153898 + 0.266560i 0.932657 0.360763i \(-0.117484\pi\)
−0.778759 + 0.627323i \(0.784150\pi\)
\(264\) 2.67511 4.63343i 0.164642 0.285168i
\(265\) −1.18753 −0.0729492
\(266\) 4.95605 8.58413i 0.303875 0.526327i
\(267\) 3.21164 0.196549
\(268\) 3.35023 5.80277i 0.204648 0.354460i
\(269\) −2.06388 3.57474i −0.125837 0.217956i 0.796223 0.605003i \(-0.206828\pi\)
−0.922060 + 0.387048i \(0.873495\pi\)
\(270\) 0.239514 + 0.414851i 0.0145764 + 0.0252470i
\(271\) 1.46898 2.54435i 0.0892344 0.154558i −0.817953 0.575285i \(-0.804891\pi\)
0.907188 + 0.420726i \(0.138225\pi\)
\(272\) −2.16672 −0.131377
\(273\) 6.22344 10.7793i 0.376660 0.652394i
\(274\) −13.2046 −0.797722
\(275\) −12.7617 + 22.1039i −0.769561 + 1.33292i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) 14.3462 + 24.8484i 0.861980 + 1.49299i 0.870015 + 0.493026i \(0.164109\pi\)
−0.00803461 + 0.999968i \(0.502558\pi\)
\(278\) −2.96496 + 5.13547i −0.177827 + 0.308005i
\(279\) −9.77053 −0.584946
\(280\) −1.26739 −0.0757411
\(281\) −14.7833 −0.881897 −0.440949 0.897532i \(-0.645358\pi\)
−0.440949 + 0.897532i \(0.645358\pi\)
\(282\) 4.96496 8.59957i 0.295659 0.512097i
\(283\) 6.55889 + 11.3603i 0.389886 + 0.675302i 0.992434 0.122781i \(-0.0391812\pi\)
−0.602548 + 0.798083i \(0.705848\pi\)
\(284\) −0.387276 0.670781i −0.0229806 0.0398035i
\(285\) 0.897321 1.55421i 0.0531527 0.0920632i
\(286\) −25.1700 −1.48834
\(287\) 0.335455 + 0.581025i 0.0198013 + 0.0342968i
\(288\) −1.00000 −0.0589256
\(289\) 6.15266 10.6567i 0.361921 0.626866i
\(290\) 1.13684 + 1.96906i 0.0667573 + 0.115627i
\(291\) 6.50490 + 11.2668i 0.381324 + 0.660472i
\(292\) 5.61071 9.71804i 0.328342 0.568705i
\(293\) −4.38920 −0.256420 −0.128210 0.991747i \(-0.540923\pi\)
−0.128210 + 0.991747i \(0.540923\pi\)
\(294\) −3.50000 + 6.06218i −0.204124 + 0.353553i
\(295\) −6.01607 −0.350269
\(296\) −1.35224 + 2.34215i −0.0785973 + 0.136134i
\(297\) −2.67511 4.63343i −0.155226 0.268859i
\(298\) −0.587025 1.01676i −0.0340055 0.0588992i
\(299\) 2.35224 4.07420i 0.136033 0.235617i
\(300\) 4.77053 0.275427
\(301\) 2.64575 + 4.58258i 0.152499 + 0.264135i
\(302\) −6.30531 −0.362830
\(303\) 2.38527 4.13140i 0.137030 0.237343i
\(304\) 1.87321 + 3.24449i 0.107436 + 0.186085i
\(305\) −2.14558 3.71626i −0.122856 0.212792i
\(306\) −1.08336 + 1.87644i −0.0619316 + 0.107269i
\(307\) 10.1755 0.580745 0.290372 0.956914i \(-0.406221\pi\)
0.290372 + 0.956914i \(0.406221\pi\)
\(308\) 14.1554 0.806577
\(309\) 7.37836 0.419740
\(310\) 2.34018 4.05332i 0.132913 0.230213i
\(311\) 6.27526 + 10.8691i 0.355837 + 0.616328i 0.987261 0.159110i \(-0.0508624\pi\)
−0.631424 + 0.775438i \(0.717529\pi\)
\(312\) 2.35224 + 4.07420i 0.133169 + 0.230656i
\(313\) −7.94198 + 13.7559i −0.448907 + 0.777530i −0.998315 0.0580240i \(-0.981520\pi\)
0.549408 + 0.835554i \(0.314853\pi\)
\(314\) −2.28417 −0.128903
\(315\) −0.633696 + 1.09759i −0.0357047 + 0.0618424i
\(316\) 0.847088 0.0476524
\(317\) −15.2794 + 26.4648i −0.858179 + 1.48641i 0.0154847 + 0.999880i \(0.495071\pi\)
−0.873664 + 0.486530i \(0.838262\pi\)
\(318\) −1.23951 2.14690i −0.0695085 0.120392i
\(319\) −12.6972 21.9922i −0.710908 1.23133i
\(320\) 0.239514 0.414851i 0.0133893 0.0231909i
\(321\) −14.9299 −0.833307
\(322\) −1.32288 + 2.29129i −0.0737210 + 0.127688i
\(323\) 8.11745 0.451667
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −11.2214 19.4361i −0.622453 1.07812i
\(326\) 2.38728 + 4.13488i 0.132219 + 0.229010i
\(327\) 2.26888 3.92981i 0.125469 0.217319i
\(328\) −0.253580 −0.0140016
\(329\) 26.2721 1.44843
\(330\) 2.56291 0.141084
\(331\) 17.1188 29.6505i 0.940932 1.62974i 0.177232 0.984169i \(-0.443286\pi\)
0.763699 0.645572i \(-0.223381\pi\)
\(332\) −5.46496 9.46559i −0.299929 0.519492i
\(333\) 1.35224 + 2.34215i 0.0741022 + 0.128349i
\(334\) −10.4750 + 18.1432i −0.573167 + 0.992754i
\(335\) 3.20971 0.175365
\(336\) −1.32288 2.29129i −0.0721688 0.125000i
\(337\) −12.2590 −0.667791 −0.333896 0.942610i \(-0.608363\pi\)
−0.333896 + 0.942610i \(0.608363\pi\)
\(338\) 4.56605 7.90864i 0.248361 0.430173i
\(339\) −7.12277 12.3370i −0.386856 0.670054i
\(340\) −0.518961 0.898867i −0.0281446 0.0487479i
\(341\) −26.1373 + 45.2711i −1.41541 + 2.45157i
\(342\) 3.74642 0.202583
\(343\) −18.5203 −1.00000
\(344\) −2.00000 −0.107833
\(345\) −0.239514 + 0.414851i −0.0128950 + 0.0223348i
\(346\) −8.61071 14.9142i −0.462915 0.801792i
\(347\) 4.77053 + 8.26280i 0.256096 + 0.443570i 0.965193 0.261540i \(-0.0842305\pi\)
−0.709097 + 0.705111i \(0.750897\pi\)
\(348\) −2.37321 + 4.11052i −0.127217 + 0.220347i
\(349\) −8.44688 −0.452151 −0.226075 0.974110i \(-0.572590\pi\)
−0.226075 + 0.974110i \(0.572590\pi\)
\(350\) 6.31082 + 10.9307i 0.337328 + 0.584268i
\(351\) 4.70448 0.251106
\(352\) −2.67511 + 4.63343i −0.142584 + 0.246963i
\(353\) −12.2402 21.2007i −0.651481 1.12840i −0.982764 0.184867i \(-0.940815\pi\)
0.331282 0.943532i \(-0.392519\pi\)
\(354\) −6.27945 10.8763i −0.333749 0.578070i
\(355\) 0.185516 0.321323i 0.00984618 0.0170541i
\(356\) −3.21164 −0.170216
\(357\) −5.73261 −0.303402
\(358\) −24.5267 −1.29628
\(359\) −10.1208 + 17.5297i −0.534153 + 0.925181i 0.465051 + 0.885284i \(0.346036\pi\)
−0.999204 + 0.0398965i \(0.987297\pi\)
\(360\) −0.239514 0.414851i −0.0126235 0.0218646i
\(361\) 2.48217 + 4.29924i 0.130640 + 0.226276i
\(362\) −10.2061 + 17.6775i −0.536422 + 0.929111i
\(363\) −17.6249 −0.925070
\(364\) −6.22344 + 10.7793i −0.326197 + 0.564989i
\(365\) 5.37539 0.281361
\(366\) 4.47903 7.75791i 0.234123 0.405512i
\(367\) −2.92520 5.06659i −0.152694 0.264474i 0.779523 0.626374i \(-0.215462\pi\)
−0.932217 + 0.361900i \(0.882128\pi\)
\(368\) −0.500000 0.866025i −0.0260643 0.0451447i
\(369\) −0.126790 + 0.219607i −0.00660043 + 0.0114323i
\(370\) −1.29552 −0.0673510
\(371\) 3.27945 5.68017i 0.170260 0.294900i
\(372\) 9.77053 0.506578
\(373\) −16.5772 + 28.7125i −0.858333 + 1.48668i 0.0151851 + 0.999885i \(0.495166\pi\)
−0.873518 + 0.486792i \(0.838167\pi\)
\(374\) 5.79623 + 10.0394i 0.299716 + 0.519123i
\(375\) 2.34018 + 4.05332i 0.120847 + 0.209312i
\(376\) −4.96496 + 8.59957i −0.256048 + 0.443489i
\(377\) 22.3294 1.15002
\(378\) −2.64575 −0.136083
\(379\) 29.1996 1.49988 0.749941 0.661505i \(-0.230082\pi\)
0.749941 + 0.661505i \(0.230082\pi\)
\(380\) −0.897321 + 1.55421i −0.0460316 + 0.0797291i
\(381\) −6.15266 10.6567i −0.315210 0.545960i
\(382\) −0.619630 1.07323i −0.0317030 0.0549112i
\(383\) 17.6116 30.5042i 0.899910 1.55869i 0.0723029 0.997383i \(-0.476965\pi\)
0.827607 0.561307i \(-0.189701\pi\)
\(384\) 1.00000 0.0510310
\(385\) 3.39042 + 5.87237i 0.172792 + 0.299284i
\(386\) 11.1795 0.569021
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) −6.50490 11.2668i −0.330236 0.571986i
\(389\) 15.3083 + 26.5147i 0.776161 + 1.34435i 0.934140 + 0.356908i \(0.116169\pi\)
−0.157979 + 0.987443i \(0.550498\pi\)
\(390\) −1.12679 + 1.95166i −0.0570572 + 0.0988260i
\(391\) −2.16672 −0.109576
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) 9.31561 0.469911
\(394\) 11.0478 19.1354i 0.556580 0.964025i
\(395\) 0.202890 + 0.351416i 0.0102085 + 0.0176816i
\(396\) 2.67511 + 4.63343i 0.134430 + 0.232839i
\(397\) 8.45291 14.6409i 0.424239 0.734804i −0.572110 0.820177i \(-0.693875\pi\)
0.996349 + 0.0853731i \(0.0272082\pi\)
\(398\) −8.49615 −0.425873
\(399\) 4.95605 + 8.58413i 0.248113 + 0.429744i
\(400\) −4.77053 −0.238527
\(401\) 16.2367 28.1228i 0.810823 1.40439i −0.101465 0.994839i \(-0.532353\pi\)
0.912288 0.409548i \(-0.134314\pi\)
\(402\) 3.35023 + 5.80277i 0.167094 + 0.289416i
\(403\) −22.9826 39.8071i −1.14485 1.98293i
\(404\) −2.38527 + 4.13140i −0.118671 + 0.205545i
\(405\) −0.479029 −0.0238031
\(406\) −12.5578 −0.623235
\(407\) 14.4696 0.717230
\(408\) 1.08336 1.87644i 0.0536344 0.0928975i
\(409\) 13.5098 + 23.3996i 0.668016 + 1.15704i 0.978458 + 0.206446i \(0.0661896\pi\)
−0.310442 + 0.950592i \(0.600477\pi\)
\(410\) −0.0607361 0.105198i −0.00299954 0.00519536i
\(411\) 6.60232 11.4356i 0.325669 0.564074i
\(412\) −7.37836 −0.363506
\(413\) 16.6139 28.7760i 0.817514 1.41598i
\(414\) −1.00000 −0.0491473
\(415\) 2.61787 4.53429i 0.128506 0.222580i
\(416\) −2.35224 4.07420i −0.115328 0.199754i
\(417\) −2.96496 5.13547i −0.145195 0.251485i
\(418\) 10.0221 17.3588i 0.490197 0.849046i
\(419\) 2.08686 0.101950 0.0509748 0.998700i \(-0.483767\pi\)
0.0509748 + 0.998700i \(0.483767\pi\)
\(420\) 0.633696 1.09759i 0.0309212 0.0535570i
\(421\) 23.2805 1.13462 0.567311 0.823504i \(-0.307984\pi\)
0.567311 + 0.823504i \(0.307984\pi\)
\(422\) 10.1904 17.6503i 0.496061 0.859204i
\(423\) 4.96496 + 8.59957i 0.241405 + 0.418125i
\(424\) 1.23951 + 2.14690i 0.0601961 + 0.104263i
\(425\) −5.16821 + 8.95160i −0.250695 + 0.434216i
\(426\) 0.774551 0.0375271
\(427\) 23.7008 1.14696
\(428\) 14.9299 0.721665
\(429\) 12.5850 21.7979i 0.607610 1.05241i
\(430\) −0.479029 0.829702i −0.0231008 0.0400118i
\(431\) 13.3053 + 23.0455i 0.640894 + 1.11006i 0.985233 + 0.171216i \(0.0547697\pi\)
−0.344339 + 0.938845i \(0.611897\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 34.9354 1.67889 0.839443 0.543447i \(-0.182881\pi\)
0.839443 + 0.543447i \(0.182881\pi\)
\(434\) 12.9252 + 22.3871i 0.620429 + 1.07462i
\(435\) −2.27367 −0.109014
\(436\) −2.26888 + 3.92981i −0.108660 + 0.188204i
\(437\) 1.87321 + 3.24449i 0.0896078 + 0.155205i
\(438\) 5.61071 + 9.71804i 0.268090 + 0.464346i
\(439\) 3.86848 6.70041i 0.184633 0.319793i −0.758820 0.651300i \(-0.774224\pi\)
0.943453 + 0.331507i \(0.107557\pi\)
\(440\) −2.56291 −0.122182
\(441\) −3.50000 6.06218i −0.166667 0.288675i
\(442\) −10.1933 −0.484846
\(443\) −9.67162 + 16.7517i −0.459512 + 0.795899i −0.998935 0.0461362i \(-0.985309\pi\)
0.539423 + 0.842035i \(0.318643\pi\)
\(444\) −1.35224 2.34215i −0.0641744 0.111153i
\(445\) −0.769233 1.33235i −0.0364652 0.0631595i
\(446\) −1.59376 + 2.76048i −0.0754669 + 0.130712i
\(447\) 1.17405 0.0555307
\(448\) 1.32288 + 2.29129i 0.0625000 + 0.108253i
\(449\) 16.0718 0.758476 0.379238 0.925299i \(-0.376186\pi\)
0.379238 + 0.925299i \(0.376186\pi\)
\(450\) −2.38527 + 4.13140i −0.112443 + 0.194756i
\(451\) 0.678356 + 1.17495i 0.0319425 + 0.0553261i
\(452\) 7.12277 + 12.3370i 0.335027 + 0.580284i
\(453\) 3.15266 5.46056i 0.148125 0.256560i
\(454\) −5.35827 −0.251476
\(455\) −5.96241 −0.279522
\(456\) −3.74642 −0.175442
\(457\) −7.46697 + 12.9332i −0.349290 + 0.604988i −0.986124 0.166013i \(-0.946911\pi\)
0.636833 + 0.771002i \(0.280244\pi\)
\(458\) −11.7291 20.3154i −0.548065 0.949277i
\(459\) −1.08336 1.87644i −0.0505670 0.0875846i
\(460\) 0.239514 0.414851i 0.0111674 0.0193425i
\(461\) 23.1660 1.07895 0.539474 0.842002i \(-0.318623\pi\)
0.539474 + 0.842002i \(0.318623\pi\)
\(462\) −7.07769 + 12.2589i −0.329284 + 0.570336i
\(463\) 40.4429 1.87954 0.939769 0.341809i \(-0.111040\pi\)
0.939769 + 0.341809i \(0.111040\pi\)
\(464\) 2.37321 4.11052i 0.110174 0.190826i
\(465\) 2.34018 + 4.05332i 0.108523 + 0.187968i
\(466\) −12.3902 21.4604i −0.573963 0.994133i
\(467\) −3.21015 + 5.56015i −0.148548 + 0.257293i −0.930691 0.365806i \(-0.880793\pi\)
0.782143 + 0.623099i \(0.214127\pi\)
\(468\) −4.70448 −0.217465
\(469\) −8.86387 + 15.3527i −0.409296 + 0.708921i
\(470\) −4.75672 −0.219411
\(471\) 1.14209 1.97815i 0.0526246 0.0911485i
\(472\) 6.27945 + 10.8763i 0.289035 + 0.500623i
\(473\) 5.35023 + 9.26687i 0.246004 + 0.426091i
\(474\) −0.423544 + 0.733600i −0.0194540 + 0.0336954i
\(475\) 17.8724 0.820043
\(476\) 5.73261 0.262754
\(477\) 2.47903 0.113507
\(478\) 2.48593 4.30576i 0.113704 0.196941i
\(479\) −4.12679 7.14781i −0.188558 0.326592i 0.756212 0.654327i \(-0.227048\pi\)
−0.944770 + 0.327735i \(0.893715\pi\)
\(480\) 0.239514 + 0.414851i 0.0109323 + 0.0189353i
\(481\) −6.36158 + 11.0186i −0.290063 + 0.502404i
\(482\) 7.48338 0.340859
\(483\) −1.32288 2.29129i −0.0601929 0.104257i
\(484\) 17.6249 0.801134
\(485\) 3.11603 5.39713i 0.141492 0.245071i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −13.7145 23.7543i −0.621464 1.07641i −0.989213 0.146483i \(-0.953205\pi\)
0.367749 0.929925i \(-0.380129\pi\)
\(488\) −4.47903 + 7.75791i −0.202756 + 0.351184i
\(489\) −4.77455 −0.215913
\(490\) 3.35320 0.151482
\(491\) 15.9067 0.717857 0.358929 0.933365i \(-0.383142\pi\)
0.358929 + 0.933365i \(0.383142\pi\)
\(492\) 0.126790 0.219607i 0.00571614 0.00990064i
\(493\) −5.14209 8.90636i −0.231588 0.401122i
\(494\) 8.81247 + 15.2637i 0.396492 + 0.686744i
\(495\) −1.28146 + 2.21955i −0.0575972 + 0.0997613i
\(496\) −9.77053 −0.438710
\(497\) 1.02464 + 1.77472i 0.0459612 + 0.0796071i
\(498\) 10.9299 0.489782
\(499\) 1.63587 2.83342i 0.0732317 0.126841i −0.827084 0.562078i \(-0.810002\pi\)
0.900316 + 0.435237i \(0.143335\pi\)
\(500\) −2.34018 4.05332i −0.104656 0.181270i
\(501\) −10.4750 18.1432i −0.467989 0.810581i
\(502\) −7.48759 + 12.9689i −0.334187 + 0.578830i
\(503\) 1.58267 0.0705678 0.0352839 0.999377i \(-0.488766\pi\)
0.0352839 + 0.999377i \(0.488766\pi\)
\(504\) 2.64575 0.117851
\(505\) −2.28522 −0.101691
\(506\) −2.67511 + 4.63343i −0.118923 + 0.205981i
\(507\) 4.56605 + 7.90864i 0.202786 + 0.351235i
\(508\) 6.15266 + 10.6567i 0.272980 + 0.472815i
\(509\) 8.47719 14.6829i 0.375745 0.650809i −0.614694 0.788766i \(-0.710720\pi\)
0.990438 + 0.137957i \(0.0440536\pi\)
\(510\) 1.03792 0.0459600
\(511\) −14.8446 + 25.7115i −0.656684 + 1.13741i
\(512\) −1.00000 −0.0441942
\(513\) −1.87321 + 3.24449i −0.0827042 + 0.143248i
\(514\) 0.251570 + 0.435732i 0.0110963 + 0.0192193i
\(515\) −1.76722 3.06092i −0.0778732 0.134880i
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) 53.1274 2.33654
\(518\) 3.57769 6.19674i 0.157195 0.272269i
\(519\) 17.2214 0.755937
\(520\) 1.12679 1.95166i 0.0494130 0.0855859i
\(521\) 3.77053 + 6.53075i 0.165190 + 0.286117i 0.936723 0.350072i \(-0.113843\pi\)
−0.771533 + 0.636190i \(0.780510\pi\)
\(522\) −2.37321 4.11052i −0.103873 0.179913i
\(523\) −9.59648 + 16.6216i −0.419625 + 0.726812i −0.995902 0.0904431i \(-0.971172\pi\)
0.576277 + 0.817255i \(0.304505\pi\)
\(524\) −9.31561 −0.406954
\(525\) −12.6216 −0.550854
\(526\) 4.99163 0.217645
\(527\) −10.5850 + 18.3338i −0.461091 + 0.798632i
\(528\) −2.67511 4.63343i −0.116419 0.201644i
\(529\) −0.500000 0.866025i −0.0217391 0.0376533i
\(530\) −0.593763 + 1.02843i −0.0257914 + 0.0446721i
\(531\) 12.5589 0.545010
\(532\) −4.95605 8.58413i −0.214872 0.372169i
\(533\) −1.19296 −0.0516729
\(534\) 1.60582 2.78136i 0.0694906 0.120361i
\(535\) 3.57593 + 6.19370i 0.154601 + 0.267777i
\(536\) −3.35023 5.80277i −0.144708 0.250641i
\(537\) 12.2634 21.2408i 0.529204 0.916607i
\(538\) −4.12775 −0.177960
\(539\) −37.4516 −1.61315
\(540\) 0.479029 0.0206141
\(541\) 14.8973 25.8029i 0.640486 1.10935i −0.344839 0.938662i \(-0.612066\pi\)
0.985324 0.170692i \(-0.0546003\pi\)
\(542\) −1.46898 2.54435i −0.0630982 0.109289i
\(543\) −10.2061 17.6775i −0.437987 0.758616i
\(544\) −1.08336 + 1.87644i −0.0464487 + 0.0804516i
\(545\) −2.17372 −0.0931117
\(546\) −6.22344 10.7793i −0.266339 0.461312i
\(547\) −16.6264 −0.710892 −0.355446 0.934697i \(-0.615671\pi\)
−0.355446 + 0.934697i \(0.615671\pi\)
\(548\) −6.60232 + 11.4356i −0.282037 + 0.488503i
\(549\) 4.47903 + 7.75791i 0.191160 + 0.331099i
\(550\) 12.7617 + 22.1039i 0.544161 + 0.942515i
\(551\) −8.89104 + 15.3997i −0.378771 + 0.656051i
\(552\) 1.00000 0.0425628
\(553\) −2.24119 −0.0953049
\(554\) 28.6924 1.21902
\(555\) 0.647761 1.12196i 0.0274959 0.0476244i
\(556\) 2.96496 + 5.13547i 0.125742 + 0.217792i
\(557\) −8.61490 14.9214i −0.365025 0.632242i 0.623755 0.781620i \(-0.285606\pi\)
−0.988780 + 0.149378i \(0.952273\pi\)
\(558\) −4.88527 + 8.46153i −0.206810 + 0.358205i
\(559\) −9.40895 −0.397956
\(560\) −0.633696 + 1.09759i −0.0267785 + 0.0463818i
\(561\) −11.5925 −0.489434
\(562\) −7.39165 + 12.8027i −0.311798 + 0.540050i
\(563\) −14.9006 25.8085i −0.627984 1.08770i −0.987956 0.154737i \(-0.950547\pi\)
0.359972 0.932963i \(-0.382786\pi\)
\(564\) −4.96496 8.59957i −0.209063 0.362107i
\(565\) −3.41201 + 5.90978i −0.143544 + 0.248626i
\(566\) 13.1178 0.551382
\(567\) 1.32288 2.29129i 0.0555556 0.0962250i
\(568\) −0.774551 −0.0324995
\(569\) −8.32943 + 14.4270i −0.349188 + 0.604811i −0.986105 0.166121i \(-0.946876\pi\)
0.636918 + 0.770932i \(0.280209\pi\)
\(570\) −0.897321 1.55421i −0.0375847 0.0650985i
\(571\) −20.7685 35.9721i −0.869136 1.50539i −0.862881 0.505407i \(-0.831343\pi\)
−0.00625421 0.999980i \(-0.501991\pi\)
\(572\) −12.5850 + 21.7979i −0.526206 + 0.911415i
\(573\) 1.23926 0.0517708
\(574\) 0.670910 0.0280032
\(575\) −4.77053 −0.198945
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 23.0129 + 39.8596i 0.958041 + 1.65938i 0.727251 + 0.686372i \(0.240798\pi\)
0.230790 + 0.973004i \(0.425869\pi\)
\(578\) −6.15266 10.6567i −0.255917 0.443261i
\(579\) −5.58974 + 9.68172i −0.232302 + 0.402359i
\(580\) 2.27367 0.0944091
\(581\) 14.4589 + 25.0436i 0.599858 + 1.03898i
\(582\) 13.0098 0.539273
\(583\) 6.63169 11.4864i 0.274656 0.475719i
\(584\) −5.61071 9.71804i −0.232173 0.402135i
\(585\) −1.12679 1.95166i −0.0465870 0.0806911i
\(586\) −2.19460 + 3.80116i −0.0906581 + 0.157024i
\(587\) −10.5865 −0.436952 −0.218476 0.975842i \(-0.570109\pi\)
−0.218476 + 0.975842i \(0.570109\pi\)
\(588\) 3.50000 + 6.06218i 0.144338 + 0.250000i
\(589\) 36.6045 1.50826
\(590\) −3.00804 + 5.21007i −0.123839 + 0.214495i
\(591\) 11.0478 + 19.1354i 0.454446 + 0.787123i
\(592\) 1.35224 + 2.34215i 0.0555767 + 0.0962616i
\(593\) −20.8632 + 36.1361i −0.856747 + 1.48393i 0.0182672 + 0.999833i \(0.494185\pi\)
−0.875015 + 0.484097i \(0.839148\pi\)
\(594\) −5.35023 −0.219523
\(595\) 1.37304 + 2.37818i 0.0562892 + 0.0974958i
\(596\) −1.17405 −0.0480910
\(597\) 4.24807 7.35788i 0.173862 0.301138i
\(598\) −2.35224 4.07420i −0.0961902 0.166606i
\(599\) −6.48690 11.2356i −0.265047 0.459076i 0.702529 0.711655i \(-0.252054\pi\)
−0.967576 + 0.252580i \(0.918721\pi\)
\(600\) 2.38527 4.13140i 0.0973781 0.168664i
\(601\) 15.1795 0.619184 0.309592 0.950869i \(-0.399808\pi\)
0.309592 + 0.950869i \(0.399808\pi\)
\(602\) 5.29150 0.215666
\(603\) −6.70046 −0.272864
\(604\) −3.15266 + 5.46056i −0.128280 + 0.222187i
\(605\) 4.22143 + 7.31173i 0.171625 + 0.297264i
\(606\) −2.38527 4.13140i −0.0968948 0.167827i
\(607\) 21.8393 37.8268i 0.886430 1.53534i 0.0423641 0.999102i \(-0.486511\pi\)
0.844066 0.536240i \(-0.180156\pi\)
\(608\) 3.74642 0.151937
\(609\) 6.27892 10.8754i 0.254435 0.440694i
\(610\) −4.29117 −0.173744
\(611\) −23.3576 + 40.4565i −0.944946 + 1.63669i
\(612\) 1.08336 + 1.87644i 0.0437923 + 0.0758505i
\(613\) −6.54657 11.3390i −0.264413 0.457978i 0.702996 0.711193i \(-0.251845\pi\)
−0.967410 + 0.253216i \(0.918512\pi\)
\(614\) 5.08773 8.81221i 0.205324 0.355632i
\(615\) 0.121472 0.00489823
\(616\) 7.07769 12.2589i 0.285168 0.493926i
\(617\) −6.04525 −0.243373 −0.121686 0.992569i \(-0.538830\pi\)
−0.121686 + 0.992569i \(0.538830\pi\)
\(618\) 3.68918 6.38985i 0.148401 0.257037i
\(619\) −4.86919 8.43368i −0.195709 0.338978i 0.751424 0.659820i \(-0.229368\pi\)
−0.947133 + 0.320842i \(0.896034\pi\)
\(620\) −2.34018 4.05332i −0.0939840 0.162785i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) 12.5505 0.503230
\(623\) 8.49719 0.340433
\(624\) 4.70448 0.188330
\(625\) −10.8053 + 18.7154i −0.432213 + 0.748614i
\(626\) 7.94198 + 13.7559i 0.317425 + 0.549797i
\(627\) 10.0221 + 17.3588i 0.400244 + 0.693243i
\(628\) −1.14209 + 1.97815i −0.0455742 + 0.0789369i
\(629\) 5.85985 0.233648
\(630\) 0.633696 + 1.09759i 0.0252470 + 0.0437291i
\(631\) −42.7282 −1.70098 −0.850492 0.525989i \(-0.823695\pi\)
−0.850492 + 0.525989i \(0.823695\pi\)
\(632\) 0.423544 0.733600i 0.0168477 0.0291810i
\(633\) 10.1904 + 17.6503i 0.405033 + 0.701537i
\(634\) 15.2794 + 26.4648i 0.606824 + 1.05105i
\(635\) −2.94730 + 5.10487i −0.116960 + 0.202581i
\(636\) −2.47903 −0.0982999
\(637\) 16.4657 28.5194i 0.652394 1.12998i
\(638\) −25.3944 −1.00538
\(639\) −0.387276 + 0.670781i −0.0153204 + 0.0265357i
\(640\) −0.239514 0.414851i −0.00946764 0.0163984i
\(641\) 7.10747 + 12.3105i 0.280728 + 0.486236i 0.971564 0.236776i \(-0.0760907\pi\)
−0.690836 + 0.723011i \(0.742757\pi\)
\(642\) −7.46496 + 12.9297i −0.294619 + 0.510294i
\(643\) 29.3990 1.15938 0.579691 0.814836i \(-0.303173\pi\)
0.579691 + 0.814836i \(0.303173\pi\)
\(644\) 1.32288 + 2.29129i 0.0521286 + 0.0902894i
\(645\) 0.958058 0.0377235
\(646\) 4.05873 7.02992i 0.159688 0.276588i
\(647\) −17.5520 30.4009i −0.690040 1.19518i −0.971824 0.235706i \(-0.924260\pi\)
0.281784 0.959478i \(-0.409074\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 33.5965 58.1908i 1.31878 2.28419i
\(650\) −22.4429 −0.880281
\(651\) −25.8504 −1.01316
\(652\) 4.77455 0.186986
\(653\) −7.66471 + 13.2757i −0.299943 + 0.519517i −0.976123 0.217220i \(-0.930301\pi\)
0.676179 + 0.736737i \(0.263634\pi\)
\(654\) −2.26888 3.92981i −0.0887201 0.153668i
\(655\) −2.23122 3.86459i −0.0871811 0.151002i
\(656\) −0.126790 + 0.219607i −0.00495032 + 0.00857421i
\(657\) −11.2214 −0.437790
\(658\) 13.1361 22.7523i 0.512097 0.886978i
\(659\) −6.98865 −0.272239 −0.136120 0.990692i \(-0.543463\pi\)
−0.136120 + 0.990692i \(0.543463\pi\)
\(660\) 1.28146 2.21955i 0.0498806 0.0863958i
\(661\) 7.10948 + 12.3140i 0.276527 + 0.478959i 0.970519 0.241024i \(-0.0774832\pi\)
−0.693992 + 0.719982i \(0.744150\pi\)
\(662\) −17.1188 29.6505i −0.665339 1.15240i
\(663\) 5.09665 8.82765i 0.197937 0.342838i
\(664\) −10.9299 −0.424163
\(665\) 2.37409 4.11204i 0.0920632 0.159458i
\(666\) 2.70448 0.104796
\(667\) 2.37321 4.11052i 0.0918911 0.159160i
\(668\) 10.4750 + 18.1432i 0.405290 + 0.701983i
\(669\) −1.59376 2.76048i −0.0616184 0.106726i
\(670\) 1.60486 2.77969i 0.0620010 0.107389i
\(671\) 47.9277 1.85023
\(672\) −2.64575 −0.102062
\(673\) −14.0339 −0.540967 −0.270484 0.962725i \(-0.587184\pi\)
−0.270484 + 0.962725i \(0.587184\pi\)
\(674\) −6.12951 + 10.6166i −0.236100 + 0.408937i
\(675\) −2.38527 4.13140i −0.0918089 0.159018i
\(676\) −4.56605 7.90864i −0.175617 0.304178i
\(677\) 11.7353 20.3262i 0.451025 0.781199i −0.547425 0.836855i \(-0.684392\pi\)
0.998450 + 0.0556563i \(0.0177251\pi\)
\(678\) −14.2455 −0.547097
\(679\) 17.2103 + 29.8092i 0.660472 + 1.14397i
\(680\) −1.03792 −0.0398025
\(681\) 2.67913 4.64040i 0.102665 0.177820i
\(682\) 26.1373 + 45.2711i 1.00085 + 1.73352i
\(683\) 11.9588 + 20.7132i 0.457589 + 0.792568i 0.998833 0.0482977i \(-0.0153796\pi\)
−0.541244 + 0.840866i \(0.682046\pi\)
\(684\) 1.87321 3.24449i 0.0716240 0.124056i
\(685\) −6.32541 −0.241681
\(686\) −9.26013 + 16.0390i −0.353553 + 0.612372i
\(687\) 23.4582 0.894987
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 5.83127 + 10.1001i 0.222154 + 0.384781i
\(690\) 0.239514 + 0.414851i 0.00911816 + 0.0157931i
\(691\) −7.34131 + 12.7155i −0.279277 + 0.483721i −0.971205 0.238245i \(-0.923428\pi\)
0.691928 + 0.721966i \(0.256761\pi\)
\(692\) −17.2214 −0.654660
\(693\) −7.07769 12.2589i −0.268859 0.465678i
\(694\) 9.54106 0.362174
\(695\) −1.42030 + 2.46004i −0.0538752 + 0.0933145i
\(696\) 2.37321 + 4.11052i 0.0899563 + 0.155809i
\(697\) 0.274719 + 0.475827i 0.0104057 + 0.0180232i
\(698\) −4.22344 + 7.31521i −0.159860 + 0.276885i
\(699\) 24.7803 0.937278
\(700\) 12.6216 0.477053
\(701\) −13.9383 −0.526442 −0.263221 0.964736i \(-0.584785\pi\)
−0.263221 + 0.964736i \(0.584785\pi\)
\(702\) 2.35224 4.07420i 0.0887795 0.153771i
\(703\) −5.06605 8.77466i −0.191070 0.330943i
\(704\) 2.67511 + 4.63343i 0.100822 + 0.174629i
\(705\) 2.37836 4.11944i 0.0895742 0.155147i
\(706\) −24.4804 −0.921334
\(707\) 6.31082 10.9307i 0.237343 0.411090i
\(708\) −12.5589 −0.471992
\(709\) −6.46172 + 11.1920i −0.242675 + 0.420326i −0.961475 0.274891i \(-0.911358\pi\)
0.718800 + 0.695217i \(0.244692\pi\)
\(710\) −0.185516 0.321323i −0.00696230 0.0120591i
\(711\) −0.423544 0.733600i −0.0158841 0.0275122i
\(712\) −1.60582 + 2.78136i −0.0601806 + 0.104236i
\(713\) −9.77053 −0.365909
\(714\) −2.86630 + 4.96458i −0.107269 + 0.185795i
\(715\) −12.0572 −0.450913
\(716\) −12.2634 + 21.2408i −0.458304 + 0.793805i
\(717\) 2.48593 + 4.30576i 0.0928389 + 0.160802i
\(718\) 10.1208 + 17.5297i 0.377703 + 0.654202i
\(719\) −6.69100 + 11.5892i −0.249532 + 0.432203i −0.963396 0.268082i \(-0.913610\pi\)
0.713864 + 0.700285i \(0.246944\pi\)
\(720\) −0.479029 −0.0178523
\(721\) 19.5213 0.727011
\(722\) 4.96434 0.184754
\(723\) −3.74169 + 6.48080i −0.139155 + 0.241024i
\(724\) 10.2061 + 17.6775i 0.379308 + 0.656981i
\(725\) −11.3215 19.6094i −0.420469 0.728274i
\(726\) −8.81247 + 15.2637i −0.327062 + 0.566487i
\(727\) −47.9963 −1.78009 −0.890043 0.455877i \(-0.849326\pi\)
−0.890043 + 0.455877i \(0.849326\pi\)
\(728\) 6.22344 + 10.7793i 0.230656 + 0.399508i
\(729\) 1.00000 0.0370370
\(730\) 2.68769 4.65522i 0.0994760 0.172297i
\(731\) 2.16672 + 3.75287i 0.0801391 + 0.138805i
\(732\) −4.47903 7.75791i −0.165550 0.286740i
\(733\) −12.7459 + 22.0765i −0.470780 + 0.815416i −0.999441 0.0334174i \(-0.989361\pi\)
0.528661 + 0.848833i \(0.322694\pi\)
\(734\) −5.85040 −0.215942
\(735\) −1.67660 + 2.90396i −0.0618424 + 0.107114i
\(736\) −1.00000 −0.0368605
\(737\) −17.9245 + 31.0461i −0.660257 + 1.14360i
\(738\) 0.126790 + 0.219607i 0.00466721 + 0.00808384i
\(739\) −12.3087 21.3193i −0.452783 0.784243i 0.545775 0.837932i \(-0.316235\pi\)
−0.998558 + 0.0536886i \(0.982902\pi\)
\(740\) −0.647761 + 1.12196i −0.0238122 + 0.0412439i
\(741\) −17.6249 −0.647469
\(742\) −3.27945 5.68017i −0.120392 0.208526i
\(743\) −2.89777 −0.106309 −0.0531545 0.998586i \(-0.516928\pi\)
−0.0531545 + 0.998586i \(0.516928\pi\)
\(744\) 4.88527 8.46153i 0.179103 0.310215i
\(745\) −0.281202 0.487056i −0.0103024 0.0178444i
\(746\) 16.5772 + 28.7125i 0.606933 + 1.05124i
\(747\) −5.46496 + 9.46559i −0.199953 + 0.346328i
\(748\) 11.5925 0.423862
\(749\) −39.5009 −1.44333
\(750\) 4.68037 0.170903
\(751\) 18.4421 31.9427i 0.672964 1.16561i −0.304096 0.952641i \(-0.598354\pi\)
0.977060 0.212966i \(-0.0683123\pi\)
\(752\) 4.96496 + 8.59957i 0.181054 + 0.313594i
\(753\) −7.48759 12.9689i −0.272863 0.472612i
\(754\) 11.1647 19.3378i 0.406595 0.704243i
\(755\) −3.02043 −0.109925
\(756\) −1.32288 + 2.29129i −0.0481125 + 0.0833333i
\(757\) −46.4053 −1.68663 −0.843314 0.537421i \(-0.819399\pi\)
−0.843314 + 0.537421i \(0.819399\pi\)
\(758\) 14.5998 25.2876i 0.530288 0.918486i
\(759\) −2.67511 4.63343i −0.0971005 0.168183i
\(760\) 0.897321 + 1.55421i 0.0325493 + 0.0563770i
\(761\) 21.0738 36.5010i 0.763926 1.32316i −0.176887 0.984231i \(-0.556603\pi\)
0.940813 0.338927i \(-0.110064\pi\)
\(762\) −12.3053 −0.445774
\(763\) 6.00289 10.3973i 0.217319 0.376408i
\(764\) −1.23926 −0.0448348
\(765\) −0.518961 + 0.898867i −0.0187631 + 0.0324986i
\(766\) −17.6116 30.5042i −0.636333 1.10216i
\(767\) 29.5415 + 51.1674i 1.06668 + 1.84755i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −38.8004 −1.39918 −0.699589 0.714545i \(-0.746634\pi\)
−0.699589 + 0.714545i \(0.746634\pi\)
\(770\) 6.78083 0.244364
\(771\) −0.503140 −0.0181202
\(772\) 5.58974 9.68172i 0.201179 0.348453i
\(773\) −3.49284 6.04978i −0.125629 0.217595i 0.796350 0.604836i \(-0.206761\pi\)
−0.921979 + 0.387241i \(0.873428\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) −23.3053 + 40.3660i −0.837152 + 1.44999i
\(776\) −13.0098 −0.467024
\(777\) 3.57769 + 6.19674i 0.128349 + 0.222307i
\(778\) 30.6166 1.09766
\(779\) 0.475009 0.822739i 0.0170190 0.0294777i
\(780\) 1.12679 + 1.95166i 0.0403456 + 0.0698806i
\(781\) 2.07201 + 3.58883i 0.0741425 + 0.128419i
\(782\) −1.08336 + 1.87644i −0.0387409 + 0.0671012i
\(783\) 4.74642 0.169623
\(784\) −3.50000 6.06218i −0.125000 0.216506i
\(785\) −1.09419 −0.0390532
\(786\) 4.65781 8.06756i 0.166138 0.287760i
\(787\) −15.7351 27.2539i −0.560895 0.971498i −0.997419 0.0718055i \(-0.977124\pi\)
0.436524 0.899693i \(-0.356209\pi\)
\(788\) −11.0478 19.1354i −0.393562 0.681669i
\(789\) −2.49581 + 4.32287i −0.0888533 + 0.153898i
\(790\) 0.405780 0.0144370
\(791\) −18.8451 32.6406i −0.670054 1.16057i
\(792\) 5.35023 0.190112
\(793\) −21.0715 + 36.4969i −0.748271 + 1.29604i
\(794\) −8.45291 14.6409i −0.299982 0.519585i
\(795\) −0.593763 1.02843i −0.0210586 0.0364746i
\(796\) −4.24807 + 7.35788i −0.150569 + 0.260793i
\(797\) 8.98024 0.318097 0.159048 0.987271i \(-0.449157\pi\)
0.159048 + 0.987271i \(0.449157\pi\)
\(798\) 9.91210 0.350884
\(799\) 21.5154 0.761160
\(800\) −2.38527 + 4.13140i −0.0843319 + 0.146067i
\(801\) 1.60582 + 2.78136i 0.0567388 + 0.0982745i
\(802\) −16.2367 28.1228i −0.573339 0.993052i
\(803\) −30.0186 + 51.9937i −1.05933 + 1.83482i
\(804\) 6.70046 0.236307
\(805\) −0.633696 + 1.09759i −0.0223348 + 0.0386851i
\(806\) −45.9652 −1.61906
\(807\) 2.06388 3.57474i 0.0726519 0.125837i
\(808\) 2.38527 + 4.13140i 0.0839134 + 0.145342i
\(809\) 16.7098 + 28.9422i 0.587485 + 1.01755i 0.994561 + 0.104160i \(0.0332153\pi\)
−0.407075 + 0.913395i \(0.633451\pi\)
\(810\) −0.239514 + 0.414851i −0.00841568 + 0.0145764i
\(811\) −54.4130 −1.91070 −0.955349 0.295480i \(-0.904520\pi\)
−0.955349 + 0.295480i \(0.904520\pi\)
\(812\) −6.27892 + 10.8754i −0.220347 + 0.381652i
\(813\) 2.93797 0.103039
\(814\) 7.23479 12.5310i 0.253579 0.439212i
\(815\) 1.14357 + 1.98073i 0.0400576 + 0.0693819i
\(816\) −1.08336 1.87644i −0.0379252 0.0656884i
\(817\) 3.74642 6.48899i 0.131071 0.227021i
\(818\) 27.0196 0.944718
\(819\) 12.4469 0.434929
\(820\) −0.121472 −0.00424199
\(821\) 2.54291 4.40444i 0.0887480 0.153716i −0.818234 0.574885i \(-0.805047\pi\)
0.906982 + 0.421169i \(0.138380\pi\)
\(822\) −6.60232 11.4356i −0.230282 0.398861i
\(823\) 5.45421 + 9.44696i 0.190122 + 0.329300i 0.945290 0.326230i \(-0.105778\pi\)
−0.755169 + 0.655530i \(0.772445\pi\)
\(824\) −3.68918 + 6.38985i −0.128519 + 0.222601i
\(825\) −25.5234 −0.888612
\(826\) −16.6139 28.7760i −0.578070 1.00125i
\(827\) 50.5292 1.75707 0.878536 0.477676i \(-0.158521\pi\)
0.878536 + 0.477676i \(0.158521\pi\)
\(828\) −0.500000 + 0.866025i −0.0173762 + 0.0300965i
\(829\) −9.09996 15.7616i −0.316055 0.547423i 0.663607 0.748082i \(-0.269025\pi\)
−0.979661 + 0.200659i \(0.935692\pi\)
\(830\) −2.61787 4.53429i −0.0908678 0.157388i
\(831\) −14.3462 + 24.8484i −0.497664 + 0.861980i
\(832\) −4.70448 −0.163098
\(833\) −15.1671 −0.525507
\(834\) −5.92993 −0.205337
\(835\) −5.01783 + 8.69114i −0.173649 + 0.300769i
\(836\) −10.0221 17.3588i −0.346622 0.600366i
\(837\) −4.88527 8.46153i −0.168859 0.292473i
\(838\) 1.04343 1.80727i 0.0360447 0.0624312i
\(839\) 7.67057 0.264818 0.132409 0.991195i \(-0.457729\pi\)
0.132409 + 0.991195i \(0.457729\pi\)
\(840\) −0.633696 1.09759i −0.0218646 0.0378706i
\(841\) −6.47150 −0.223155
\(842\) 11.6402 20.1615i 0.401149 0.694811i
\(843\) −7.39165 12.8027i −0.254582 0.440949i
\(844\) −10.1904 17.6503i −0.350768 0.607549i
\(845\) 2.18727 3.78847i 0.0752444 0.130327i
\(846\) 9.92993 0.341398
\(847\) −46.6312 −1.60227
\(848\) 2.47903 0.0851302
\(849\) −6.55889 + 11.3603i −0.225101 + 0.389886i
\(850\) 5.16821 + 8.95160i 0.177268 + 0.307037i
\(851\) 1.35224 + 2.34215i 0.0463541 + 0.0802877i
\(852\) 0.387276 0.670781i 0.0132678 0.0229806i
\(853\) 30.6924 1.05089 0.525444 0.850828i \(-0.323899\pi\)
0.525444 + 0.850828i \(0.323899\pi\)
\(854\) 11.8504 20.5255i 0.405512 0.702368i
\(855\) 1.79464 0.0613755
\(856\) 7.46496 12.9297i 0.255147 0.441928i
\(857\) 15.4908 + 26.8309i 0.529157 + 0.916526i 0.999422 + 0.0340010i \(0.0108250\pi\)
−0.470265 + 0.882525i \(0.655842\pi\)
\(858\) −12.5850 21.7979i −0.429645 0.744168i
\(859\) 21.6426 37.4861i 0.738436 1.27901i −0.214763 0.976666i \(-0.568898\pi\)
0.953199 0.302343i \(-0.0977688\pi\)
\(860\) −0.958058 −0.0326695
\(861\) −0.335455 + 0.581025i −0.0114323 + 0.0198013i
\(862\) 26.6106 0.906362
\(863\) −6.25517 + 10.8343i −0.212928 + 0.368803i −0.952630 0.304133i \(-0.901633\pi\)
0.739701 + 0.672935i \(0.234967\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) −4.12478 7.14433i −0.140247 0.242914i
\(866\) 17.4677 30.2549i 0.593576 1.02810i
\(867\) 12.3053 0.417910
\(868\) 25.8504 0.877420
\(869\) −4.53212 −0.153742
\(870\) −1.13684 + 1.96906i −0.0385423 + 0.0667573i
\(871\) −15.7611 27.2990i −0.534044 0.924991i
\(872\) 2.26888 + 3.92981i 0.0768339 + 0.133080i
\(873\) −6.50490 + 11.2668i −0.220157 + 0.381324i
\(874\) 3.74642 0.126725
\(875\) 6.19154 + 10.7241i 0.209312 + 0.362540i
\(876\) 11.2214 0.379137
\(877\) −3.24022 + 5.61223i −0.109415 + 0.189512i −0.915533 0.402242i \(-0.868231\pi\)
0.806119 + 0.591754i \(0.201564\pi\)
\(878\) −3.86848 6.70041i −0.130555 0.226128i
\(879\) −2.19460 3.80116i −0.0740220 0.128210i
\(880\) −1.28146 + 2.21955i −0.0431979 + 0.0748210i
\(881\) 7.96941 0.268496 0.134248 0.990948i \(-0.457138\pi\)
0.134248 + 0.990948i \(0.457138\pi\)
\(882\) −7.00000 −0.235702
\(883\) 6.75270 0.227246 0.113623 0.993524i \(-0.463754\pi\)
0.113623 + 0.993524i \(0.463754\pi\)
\(884\) −5.09665 + 8.82765i −0.171419 + 0.296906i
\(885\) −3.00804 5.21007i −0.101114 0.175135i
\(886\) 9.67162 + 16.7517i 0.324924 + 0.562786i
\(887\) −27.7694 + 48.0980i −0.932405 + 1.61497i −0.153208 + 0.988194i \(0.548960\pi\)
−0.779197 + 0.626779i \(0.784373\pi\)
\(888\) −2.70448 −0.0907563
\(889\) −16.2784 28.1950i −0.545960 0.945630i
\(890\) −1.53847 −0.0515695
\(891\) 2.67511 4.63343i 0.0896197 0.155226i
\(892\) 1.59376 + 2.76048i 0.0533631 + 0.0924277i
\(893\) −18.6008 32.2176i −0.622453 1.07812i
\(894\) 0.587025 1.01676i 0.0196331 0.0340055i
\(895\) −11.7490 −0.392726
\(896\) 2.64575 0.0883883
\(897\) 4.70448 0.157078
\(898\) 8.03591 13.9186i 0.268162 0.464470i
\(899\) −23.1875 40.1620i −0.773347 1.33948i
\(900\) 2.38527 + 4.13140i 0.0795089 + 0.137713i
\(901\) 2.68568 4.65174i 0.0894731 0.154972i
\(902\) 1.35671 0.0451736
\(903\) −2.64575 + 4.58258i −0.0880451 + 0.152499i
\(904\) 14.2455 0.473800
\(905\) −4.88903 + 8.46805i −0.162517 + 0.281487i
\(906\) −3.15266 5.46056i −0.104740 0.181415i
\(907\) 24.8370 + 43.0190i 0.824700 + 1.42842i 0.902148 + 0.431426i \(0.141990\pi\)
−0.0774478 + 0.996996i \(0.524677\pi\)
\(908\) −2.67913 + 4.64040i −0.0889102 + 0.153997i
\(909\) 4.77053 0.158229
\(910\) −2.98121 + 5.16360i −0.0988260 + 0.171172i
\(911\) −4.22403 −0.139948 −0.0699742 0.997549i \(-0.522292\pi\)
−0.0699742 + 0.997549i \(0.522292\pi\)
\(912\) −1.87321 + 3.24449i −0.0620282 + 0.107436i
\(913\) 29.2388 + 50.6431i 0.967663 + 1.67604i
\(914\) 7.46697 + 12.9332i 0.246986 + 0.427791i
\(915\) 2.14558 3.71626i 0.0709308 0.122856i
\(916\) −23.4582 −0.775082
\(917\) 24.6468 0.813909
\(918\) −2.16672 −0.0715125
\(919\) 16.8376 29.1635i 0.555420 0.962016i −0.442451 0.896793i \(-0.645891\pi\)
0.997871 0.0652228i \(-0.0207758\pi\)
\(920\) −0.239514 0.414851i −0.00789656 0.0136772i
\(921\) 5.08773 + 8.81221i 0.167647 + 0.290372i
\(922\) 11.5830 20.0624i 0.381466 0.660718i
\(923\) −3.64386 −0.119939
\(924\) 7.07769 + 12.2589i 0.232839 + 0.403289i
\(925\) 12.9018 0.424208
\(926\) 20.2214 35.0245i 0.664517 1.15098i
\(927\) 3.68918 + 6.38985i 0.121169 + 0.209870i
\(928\) −2.37321 4.11052i −0.0779044 0.134934i
\(929\) −14.1913 + 24.5800i −0.465601 + 0.806445i −0.999228 0.0392750i \(-0.987495\pi\)
0.533627 + 0.845720i \(0.320828\pi\)
\(930\) 4.68037 0.153475
\(931\) 13.1125 + 22.7115i 0.429744 + 0.744338i
\(932\) −24.7803 −0.811706
\(933\) −6.27526 + 10.8691i −0.205443 + 0.355837i
\(934\) 3.21015 + 5.56015i 0.105039 + 0.181934i
\(935\) 2.77656 + 4.80915i 0.0908033 + 0.157276i
\(936\) −2.35224 + 4.07420i −0.0768853 + 0.133169i
\(937\) −26.2115 −0.856291 −0.428146 0.903710i \(-0.640833\pi\)
−0.428146 + 0.903710i \(0.640833\pi\)
\(938\) 8.86387 + 15.3527i 0.289416 + 0.501283i
\(939\) −15.8840 −0.518354
\(940\) −2.37836 + 4.11944i −0.0775736 + 0.134361i
\(941\) −19.2523 33.3459i −0.627606 1.08705i −0.988031 0.154258i \(-0.950701\pi\)
0.360424 0.932788i \(-0.382632\pi\)
\(942\) −1.14209 1.97815i −0.0372112 0.0644517i
\(943\) −0.126790 + 0.219607i −0.00412885 + 0.00715138i
\(944\) 12.5589 0.408757
\(945\) −1.26739 −0.0412282
\(946\) 10.7005 0.347902
\(947\) −7.23680 + 12.5345i −0.235164 + 0.407316i −0.959320 0.282320i \(-0.908896\pi\)
0.724156 + 0.689636i \(0.242229\pi\)
\(948\) 0.423544 + 0.733600i 0.0137561 + 0.0238262i
\(949\) −26.3955 45.7183i −0.856834 1.48408i
\(950\) 8.93621 15.4780i 0.289929 0.502171i
\(951\) −30.5589 −0.990940
\(952\) 2.86630 4.96458i 0.0928975 0.160903i
\(953\) −53.2578 −1.72519 −0.862595 0.505896i \(-0.831162\pi\)
−0.862595 + 0.505896i \(0.831162\pi\)
\(954\) 1.23951 2.14690i 0.0401308 0.0695085i
\(955\) −0.296821 0.514108i −0.00960489 0.0166362i
\(956\) −2.48593 4.30576i −0.0804009 0.139258i
\(957\) 12.6972 21.9922i 0.410443 0.710908i
\(958\) −8.25358 −0.266661
\(959\) 17.4681 30.2556i 0.564074 0.977006i
\(960\) 0.479029 0.0154606
\(961\) −32.2316 + 55.8268i −1.03973 + 1.80087i
\(962\) 6.36158 + 11.0186i 0.205105 + 0.355253i
\(963\) −7.46496 12.9297i −0.240555 0.416654i
\(964\) 3.74169 6.48080i 0.120512 0.208733i
\(965\) 5.35530 0.172393
\(966\) −2.64575 −0.0851257
\(967\) 52.5804 1.69087 0.845436 0.534077i \(-0.179341\pi\)
0.845436 + 0.534077i \(0.179341\pi\)
\(968\) 8.81247 15.2637i 0.283244 0.490592i
\(969\) 4.05873 + 7.02992i 0.130385 + 0.225834i
\(970\) −3.11603 5.39713i −0.100050 0.173291i
\(971\) 18.5601 32.1471i 0.595623 1.03165i −0.397836 0.917457i \(-0.630239\pi\)
0.993459 0.114192i \(-0.0364280\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −7.84455 13.5872i −0.251485 0.435585i
\(974\) −27.4290 −0.878883
\(975\) 11.2214 19.4361i 0.359373 0.622453i
\(976\) 4.47903 + 7.75791i 0.143370 + 0.248325i
\(977\) 1.10364 + 1.91156i 0.0353086 + 0.0611563i 0.883140 0.469110i \(-0.155425\pi\)
−0.847831 + 0.530266i \(0.822092\pi\)
\(978\) −2.38728 + 4.13488i −0.0763367 + 0.132219i
\(979\) 17.1830 0.549171
\(980\) 1.67660 2.90396i 0.0535570 0.0927635i
\(981\) 4.53775 0.144879
\(982\) 7.95333 13.7756i 0.253801 0.439596i
\(983\) −0.0710368 0.123039i −0.00226572 0.00392434i 0.864890 0.501961i \(-0.167388\pi\)
−0.867156 + 0.498037i \(0.834055\pi\)
\(984\) −0.126790 0.219607i −0.00404192 0.00700081i
\(985\) 5.29221 9.16638i 0.168624 0.292065i
\(986\) −10.2842 −0.327515
\(987\) 13.1361 + 22.7523i 0.418125 + 0.724214i
\(988\) 17.6249 0.560724
\(989\) −1.00000 + 1.73205i −0.0317982 + 0.0550760i
\(990\) 1.28146 + 2.21955i 0.0407274 + 0.0705419i
\(991\) −24.1381 41.8085i −0.766773 1.32809i −0.939304 0.343086i \(-0.888528\pi\)
0.172531 0.985004i \(-0.444806\pi\)
\(992\) −4.88527 + 8.46153i −0.155107 + 0.268654i
\(993\) 34.2375 1.08649
\(994\) 2.04927 0.0649989
\(995\) −4.06990 −0.129024
\(996\) 5.46496 9.46559i 0.173164 0.299929i
\(997\) 17.2960 + 29.9575i 0.547769 + 0.948764i 0.998427 + 0.0560671i \(0.0178561\pi\)
−0.450658 + 0.892697i \(0.648811\pi\)
\(998\) −1.63587 2.83342i −0.0517827 0.0896902i
\(999\) −1.35224 + 2.34215i −0.0427829 + 0.0741022i
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 966.2.i.n.415.3 yes 8
7.2 even 3 6762.2.a.cg.1.2 4
7.4 even 3 inner 966.2.i.n.277.3 8
7.5 odd 6 6762.2.a.ch.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.i.n.277.3 8 7.4 even 3 inner
966.2.i.n.415.3 yes 8 1.1 even 1 trivial
6762.2.a.cg.1.2 4 7.2 even 3
6762.2.a.ch.1.3 4 7.5 odd 6